Progress in Artificial Intelligence: Knowledge Extraction, Multi-agent Systems, Logic Programming, and Constraint Solving: 10th Portuguese Conference ... (Lecture Notes in Computer Science, 2258) 354043030X, 9783540430308

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Lecture Notes in Artificial Intelligence Subseries of Lecture Notes in Computer Science Edited by J. G. Carbonell and J. Siekmann

Lecture Notes in Computer Science Edited by G. Goos, J. Hartmanis and J. van Leeuwen

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Berlin Heidelberg New York Barcelona Hong Kong London Milan Paris Tokyo

Pavel Brazdil Al´ıpio Jorge (Eds.)

Progress in Artificial Intelligence Knowledge Extraction, Multi-agent Systems, Logic Programming, and Constraint Solving 10th Portuguese Conference on Artificial Intelligence, EPIA 2001 Porto, Portugal, December 17-20, 2001 Proceedings

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Series Editors Jaime G. Carbonell,Carnegie Mellon University, Pittsburgh, PA, USA J¨org Siekmann, University of Saarland, Saarbr¨ucken, Germany Volume Editors Pavel Brazdil Al´ıpio Jorge University of Porto, Faculty of Economics LIACC, Laborat´orio de Inteligˆencia Artificial e Ciˆencia de Computadores Rua do Campo Alegre, 823, 4150-180 Porto, Portugal E-mail:{pbrazdil/amjorge}@liacc.up.pt

Cataloging-in-Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Progress in artificial intelligence : knowledge extraction, multi-agent systems, logic programming and constraint solving ; proceedings / 10th Portuguese Conference on Artificial Intelligence, EPIA 2001, Porto, Portugal, December 17 - 20, 2001. Pavel Brazdil ; Alípio Jorge (ed.). Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London ; Milan ; Paris ; Tokyo : Springer, 2001 (Lecture notes in computer science ; Vol. 2258 : Lecture notes in artificial intelligence) ISBN 3-540-43030-X

CR Subject Classification (1998): I.2 ISBN 3-540-43030-X Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag Berlin Heidelberg New York a member of BertelsmannSpringer Science+Business Media GmbH http://www.springer.de © Springer-Verlag Berlin Heidelberg 2001 Printed in Germany Typesetting: Camera-ready by author Printed on acid-free paper SPIN 10846042

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Preface

The tenth Portuguese Conference on Artificial Intelligence, EPIA 2001 was held in Porto and continued the tradition of previous conferences in the series. It returned to the city in which the first conference took place, about 15 years ago. The conference was organized, as usual, under the auspices of the Portuguese Association for Artificial Intelligence (APPIA, http://www.appia.pt). EPIA maintained its international character and continued to provide a forum for presenting and discussing researc h on different aspects of Artificial Intelligence. To promote motivated discussions among participants, this conference strengthened the role of the thematic workshops. These were not just satellite events, but rather formed an integral part of the conference, with joint sessions when justified. This had the advantage that the work was presented to a motivated audience. This was the first time that EPIA embarked on this experience and so provided us with additional challenges. A word of appreciation must be given to those who actively promoted and organized each of the thematic workshops: – Fernando Moura Pires and Gabriela Guimar˜ aes, for organizing the workshop on Extraction of Knowledge from Data Bases (EKDB 2001); – Eug´enio Oliveira, for organizing the workshop on Multi Agent Systems: Theory and Applications (MASTA 2001); – Jos´e Alferes and Salvador Abreu, for organizing the workshop on Logic Programming for Artificial Intelligence and Information Systems (LPAI); – Pedro Barahona, for organizing the workshop on Constraint Satisfaction and Operational Research Techniques for Problem Solving (CSOR); – Lu´ıs Torgo, for organizing the workshop on Artificial Intelligence Techniques for Financial Time Series Analysis (AIFTSA); The organization of this volume reflects the thematic threads described above with some exceptions. We would also like to thank all the authors who submitted the 88 articles to the conference. From these, 21 (24%) were selected as long papers for this volume. A further 18 (about 20%) were accepted as short papers. Regarding the geographical origin, the first authors of submitted papers come from Portugal (32), Spain (17), Brazil (7), France (5), Slovenia (4), Korea (4), USA (3), Germany (3), UK (3), Sweden (3), Austria (2), and also Chile, The Netherlands, Turkey, Australia, and Poland with one submission each. In terms of scientific areas, there were 27 submissions on knowledge extraction (10 accepted for this volume), 16 on multi-agents (9 accepted), 12 on logic programming (6 accepted), 10 on constraint solving (3 accepted), 8 on financial time series (2 accepted), and 15 on other areas (7 accepted). Some articles not included in this volume were selected for oral presentation at the conference and/or at the thematic workshops. More information can be

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found at the conference site (http://www.niaad.liacc.up.pt/Events/EPIA01/). Special thanks to all members of the Program Committee who took upon most of the burden of reviewing. Thanks also to all other reviewers for their commitment and collaboration. We would also like to gratefully acknowledge the support of the Portuguese Government through FCT (Funda¸c˜ao da Ciˆencia e Tecnologia), University of Porto, Faculty of Economics of Porto, LIACC (Laborat´ orio de Inteligˆencia Artificial e Ciˆencia de Computadores), the company Enabler, and other sponsors whose support is acknowledged at the conference site. Finally, we thank Lu´ıs Paulo Reis for organizing the activities related to robosoccer, Rui Camacho, our Publicity Chair, Rodolfo Matos for technical support and local organization in collaboration with Rui Leite, Vera Costa, Filipa Ribeiro and Joel Silva.

October 2001

Pavel Brazdil and Al´ıpio Jorge

EPIA’01

10th Portuguese Conference on Artificial Intelligence Porto, Portugal, December 2001

Programme Co-Chairs Pavel Brazdil Al´ıpio Jorge

Univ. Porto Univ. Porto

Programme Commitee Paulo Azevedo Pedro Barahona Lu´ıs Camarinha Matos H´elder Coelho Ernesto Costa Jo˜ ao Gama Claude Kirchner Carolina Monard Fernando Moura Pires Arlindo Oliveira Eug´enio Oliveira Ramon Otero David Pearce Gabriel Pereira Lopes Ruy de Queiroz Jan Rauch Jo˜ ao Sentieiro Carles Sierra Lu´ıs Torgo

Univ. Minho Univ. Nova de Lisboa Univ. Nova de Lisboa Univ. Lisboa Univ. Coimbra Univ. Porto LORIA-INRIA, France Univ. S. Paulo, Brazil ´ Univ. Evora IST, Lisboa Univ. Porto Univ. Coru˜ na, Spain European Commission (EU) Univ. Nova de Lisboa Univ. F. Pernambuco, Brazil Univ. of Economics, Czech Rep. IST. Lisboa Univ. Catalunia, Spain Univ. Porto

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Organization

List of Reviewers Salvador Abreu Alexandre Agustini Jos´e Alferes Lu´ıs Antunes Paulo Azevedo Ant´ onio L. Bajuelos Pedro Barahona Orlando Belo M´ ario R. Benevides Carlos L. Bento Olivier Boissier Rachel Bourne Olivier Bournez Andrea Bracciali Pavel Brazdil M. Paula Brito Sabine Broda Antoni Brogi Francisco Bueno Michele Bugliesi Daniel Cabeza Rui Camacho Margarida Cardoso Gladys Castillo Luis F. Castro H´elder Coelho Lu´ıs Correia Manuel E. Correia Joaquim P. Costa Vitor S. Costa Carlos V. Dam´asio Gautam Das Gael H. Dias Frank Dignum Virginea Dignum Jurgen Dix Agostino Dovier

Jesus C. Fernandez Jos´e L. Ferreira Marcelo Finger Miguel Filgueiras Jos´e M. Fonseca Dalila Fontes Michael Fink Michael Fisher Ana Fred Jo˜ ao Gama Pablo Gamallo Gabriela Guimar˜ aes Nick Jennings Al´ıpio Jorge Claude Kirchner J¨ org Keller Norbert Kuhn King-Ip Lin Vitor Lobo Alneu A. Lopes Lu´ıs S. Lopes Gabriel P. Lopes Inˆes Lynce Luis M. Macedo Benedita Malheiro Margarida Mamede Nuno C. Marques Jo˜ ao Marques-Silva Jo˜ ao P. Martins Luis C. Matos Carolina Monard Nelma Moreira Fernando Moura-Pires Jo˜ ao Moura Pires Gholamreza Nakhaeizadeh Susana Nascimento Jos´e Neves

Vitor Nogueira Eug´enio Oliveira Ana Paiva Jo˜ ao P. Pedroso Francisco C. Pereira Lu´ıs M. Pereira Bernhard Pfahringer Alessandra di Pierro Jorge S. Pinto Foster Provost Paulo Quaresma Elisa Quintarelli Luis P. Reis Solange O. Rezende Ana P. Rocha Ant´ onio J. Rodrigues Irene Rodrigues Sabina Rossi Diana Santos Sergey Semenov Carles Sierra Jaime Sichman Jo˜ ao M. Silva Carlos Soares Terrance Swift Paulo Teles F. P. Terpstra Ana P. Tom´ as Lu´ıs Torgo Tarma Uustalu Vasco T. Vasconcelos Gerard Widmer Marijana Zekic-Susac ˇ Jan Zizka

Table of Contents

Invited Speakers Agent Programming in Ciao Prolog . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Francisco Bueno

1

Multi-relational Data Mining: A perspective . . . . . . . . . . . . . . . . . . . . . . . . . . Peter A. Flach

3

A Comparison of GLOWER and other Machine Learning Methods for Investment Decision Making . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vasant Dhar

5

Extraction of Knowledge from Databases edited by Fernando Moura-Pires, Gabriela Guimar˜ aes, Al´ıpio Jorge, Pavel Brazdil Parallel Implementation of Decision Tree Learning Algorithms . . . . . . . . . . Nuno Amado, Jo˜ ao Gama, Fernando Silva

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Reducing Rankings of Classifiers by Eliminating Redundant Classifiers . . . Pavel Brazdil, Carlos Soares, Rui Pereira

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Non-parametric Nearest Neighbor with Local Adaptation . . . . . . . . . . . . . . Francisco J. Ferrer-Troyano, Jes´ us S. Aguilar-Ruiz, Jos´e C. Riquelme

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Selection Restrictions Acquisition from Corpora . . . . . . . . . . . . . . . . . . . . . . . Pablo Gamallo, Alexandre Agustini, Gabriel P. Lopes

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Classification Rule Learning with APRIORI-C . . . . . . . . . . . . . . . . . . . . . . . Viktor Jovanoski, Nada Lavraˇc

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Proportional Membership in Fuzzy Clustering as a Model of Ideal Types . S. Nascimento, B. Mirkin, F. Moura-Pires

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Evolution of Cubic Spline Activation Functions for Artificial Neural Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Helmut A. Mayer, Roland Schwaiger

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Multilingual Document Clustering, Topic Extraction and Data Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Joaquim Silva, Jo˜ ao Mexia, Carlos A. Coelho, Gabriel Lopes

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Organization

Sampling-Based Relative Landmarks: Systematically Test-Driving Algorithms Before Choosing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Carlos Soares, Johann Petrak, Pavel Brazdil Recursive Adaptive ECOC Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Elizabeth Tapia, Jos´e Carlos Gonz´ alez, Javier Garc´ıa-Villalba, Julio Villena

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A Study on End-Cut Preference in Least Squares Regression Trees . . . . . . 104 Luis Torgo

Artificial Intelligence Techniques for Financial Time Series Analysis edited by Lu´ıs Torgo The Use of Domain Knowledge in Feature Construction for Financial Time Series Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 Pedro de Almeida, Lu´ıs Torgo Optimizing the Sharpe Ratio for a Rank Based Trading System . . . . . . . . . 130 Thomas Hellstr¨ om

Multi-agent Systems: Theory and Applications edited by Eug´ enio Oliveira Choice: The Key for Autonomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 Luis Antunes, Jo˜ ao Faria, Helder Coelho Dynamic Evaluation of Coordination Mechanisms for Autonomous Agents 155 Rachel A. Bourne, Karen Shoop, Nicholas R. Jennings Evolving Multi-agent Viewpoints - an Architecture . . . . . . . . . . . . . . . . . . . . 169 Pierangelo Dell’Acqua, Jo˜ ao Alexandre Leite, Lu´ıs Moniz Pereira Enabling Agents to Update Their Knowledge and to Prefer . . . . . . . . . . . . . 183 Pierangelo Dell’Acqua, Lu´ıs Moniz Pereira Modelling Agent Societies: Co-ordination Frameworks and Institutions . . . 191 Virginia Dignum,, Frank Dignum Argumentation as Distributed Belief Revision: Conflict Resolution in Decentralised Co-operative Multi-agent Systems . . . . . . . . . . . . . . . . . . . . . . 205 Benedita Malheiro, Eug´enio Oliveira Scheduling, Re-scheduling and Communication in the Multi-agent Extended Enterprise Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 Joaquim Reis, Nuno Mamede

Organization

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Electronic Institutions as a Framework for Agents’ Negotiation and Mutual Commitment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 Ana Paula Rocha, Eug´enio Oliveira An Imitation-Based Approach to Modeling Homogenous Agents Societies Goran Trajkovski

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Logics and Logic Programming for Artificial Intelligence edited by Salvador Abreu, Jos´ e Alferes Situation Calculus as Hybrid Logic: First Steps . . . . . . . . . . . . . . . . . . . . . . . 253 Patrick Blackburn, Jaap Kamps, Maarten Marx A Modified Semantics for LUPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 Jo˜ ao Alexandre Leite On the Use of Multi-dimensional Dynamic Logic Programming to Represent Societal Agents’ Viewpoints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276 Jo˜ ao Alexandre Leite, Jos´e J´ ulio Alferes, Lu´ıs Moniz Pereira A Procedural Semantics for Multi-adjoint Logic Programming . . . . . . . . . . 290 Jes´ us Medina, Manuel Ojeda-Aciego, Peter Vojt´ aˇs Representing and Reasoning on Three-Dimensional Qualitative Orientation Point Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298 Julio Pacheco, Maria Teresa Escrig, Francisco Toledo Encodings for Equilibrium Logic and Logic Programs with Nested Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306 David Pearce, Hans Tompits, Stefan Woltran A Context-Free Grammar Representation for Normal Inhabitants of Types in TAλ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 Sabine Broda, Lu´ıs Damas Permissive Belief Revision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335 Maria R. Cravo, Jo˜ ao P. Cachopo, Ana C. Cachopo, Jo˜ ao P. Martins

Constraint Satisfaction edited by Pedro Barahona Global Hull Consistency with Local Search for Continuous Constraint Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349 Jorge Cruz, Pedro Barahona Towards Provably Complete Stochastic Search Algorithms for Satisfiability 363 Inˆes Lynce, Lu´ıs Babtista, Jo˜ ao Marques-Silva

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A Combined Constraint-Based Search Method for Single-Track Railway Scheduling Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 Elias Oliveira, Barbara M. Smith

Planning A Temporal Planning System for Time-Optimal Planning . . . . . . . . . . . . . . 379 Antonio Garrido, Eva Onaind´ıa, Federico Barber SimPlanner: An Execution-Monitoring System for Replanning in Dynamic Worlds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393 Eva Onaind´ıa, Oscar Sapena, Laura Sebastia, Eliseo Marzal Hybrid Hierarchical Knowledge Organization for Planning . . . . . . . . . . . . . . 401 Bhanu Prasad STeLLa: An Optimal Sequential and Parallel Planner . . . . . . . . . . . . . . . . . . 417 Laura Sebastia, Eva Onaind´ıa, Eliseo Marzal

Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417

Agent Programming in Ciao Prolog Francisco Bueno and the CLIP Group Facultad de Inform´ atica – UPM [email protected]

The agent programming landscape has been revealed as a natural framework for developing “intelligence” in AI. This can be seen from the extensive use of the agent concept in presenting (and developing) AI systems, the proliferation of agent theories, and the evolution of concepts such as agent societies (social intelligence) and coordination. Although a definition of what is an agent might still be controversial, agents have particular characteristics that define them, and are commonly accepted. An agent has autonomy, reactivity (to the environment and to other agents), intelligence (i.e., reasoning abilities). It behaves as an individual, capable of communicating, and capable of modifying its knowledge and its reasoning. For programming purposes, and in particular for AI programming, one would need a programming language/system that allows to reflect the nature of agents in the code: to map code to some abstract entities (the “agents”), to declare well-defined interfaces between such entities, their individual execution, possibly concurrent, possibly distributed, and their synchronization, and, last but not least, to program intelligence. It is our thesis that for the last purpose above the best suited languages are logic programming languages. It is arguably more difficult (and unnatural) to incorporate reasoning capabilities into, for example, an object oriented language than to incorporate the other capabilities mentioned above into a logic language. Our aim is, thus, to do the latter: to offer a logic language that provides the features required to program (intelligent) agents comfortably. The purpose of this talk, then, is not to introduce sophisticated reasoning theories or coordination languages, but to go through the (low-level, if you want) features which, in our view, provide for agent programming into a (high-level) language, based on logic, which naturally offers the capability of programming reasoning. The language we present is Ciao, and its relevant features are outlined below. Most of them have been included as language-level extensions, thanks to the extensibility of Ciao. Hopefully, the Ciao approach will demonstrate how the required features can be embedded in a logic programming language in a natural way, both for the implementor and for the programmer. State and Its Encapsulation: From Modules to Objects The state that is most relevant for programming intelligence is the state of knowledge. Classically, a logic program models a knowledge state, and, also, logic languages provide the means 

Daniel Cabeza, Manuel Carro, Jes´ us Correas, Jos´e M. G´ omez, Manuel Hermenegildo, Pedro L´ opez, Germ´ an Puebla, and Claudio Vaucheret

P. Brazdil and A. Jorge (Eds.): EPIA 2001, LNAI 2258, pp. 1–2, 2001. c Springer-Verlag Berlin Heidelberg 2001 

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Francisco Bueno and the CLIP Group

to manipulate and change this state: the well-known assert/retract operations. These can be used for modeling knowledge evolution. On the other hand, state of data and its evolution are arguably best modeled with objects. Also, objects are a basic construct for capturing “individuality” in the sense of agents. What is needed is a neat differentiation between the code that represents the state of knowledge and the code that represents the evolution of knowledge. A first step towards this is providing state encapsulation. This can be achieved with a well-defined, well-behaved module system. This is one of the main principles that has informed the design of Ciao. Having a language with modules and encapsulated state, the step towards objects is an easy one: the only extra thing needed is instantiation. Once we add the ability to create instances of modules, we have classes. This has been the approach in O’Ciao, the Ciao sublanguage for object orientation. Concurrency and Distribution These two features are provided in Ciao at two levels. At the language level, there are constructs for concurrent execution and for distributed execution. At the level of “individual entities”, concurrency and distribution comes through via the concept of active modules/objects. Reactivity and Autonomy: Active Modules/Objects A module/object is active when it can run as a separate process. This concept provides for “autonomy” at the execution level. The active module service of Ciao allows starting and/or connecting (remote) processes which “serve” a module/object. The code served can be conceptually part of the application program, or it can be viewed alternatively as a program component: a completely autonomous, independent functionality, which is given by its interface. Active modules/objects can then be used as “watchers” and “actors” of and on the outside world. The natural way to do this is from a well-defined, easyto-use foreign language interface that allows to write drivers that interact with the environment, but which can be viewed as logic facts (or rules) from the programmer’s point of view. An example of this is the SQL interface of Ciao to sql-based external databases. And More Adding more capabilities to the language, in particular, adding more sophisticated reasoning schemes, requires that the language be easily extensible. Extensibility has been another of the guidelines informing the design of Ciao: the concept of a package is a good example of this. Packages are libraries that allow syntactic, and also semantic, extensions of the language. They have been already used in Ciao, among other things (including most of the abovementioned features), to provide higher order constructions like predicate abstractions, and also fuzzy reasoning abilities.

Multi-relational Data Mining: A Perspective Peter A. Flach Department of Computer Science, University of Bristol Woodland Road, Bristol BS8 1UB, United Kingdom [email protected], www.cs.bris.ac.uk/˜flach/

Abstract. Multi-relational data mining (MRDM) is a form of data mining operating on data stored in multiple database tables. While machine learning and data mining are traditionally concerned with learning from single tables, MRDM is required in domains where the data are highly structured. One approach to MRDM is to use a predicate-logical language like clausal logic or Prolog to represent and reason about structured objects, an approach which came to be known as inductive logic programming (ILP) [18,19,15,16,13,17,2,5]. In this talk I will review recent developments that have led from ILP to the broader field of MRDM. Briefly, these developments include the following: – the use of other declarative languages, including functional and higher-order languages, to represent data and learned knowledge [9,6,1]; – a better understanding of knowledge representation issues, and the importance of data modelling in MRDM tasks [7,11]; – a better understanding of the relation between MRDM and standard singletable learning, and how to upgrade single-table methods to MRDM or downgrade MRDM tasks to single-table ones (propositionalisation) [3,12,10,14]; – the study of non-classificatory learning tasks, such as subgroup discovery and multi-relational association rule mining [8,4,21]; – the incorporation of ROC analysis and cost-sensitive classification [20].

References 1. A. F. Bowers, C. Giraud-Carrier, and J. W. Lloyd. Classification of individuals with complex structure. In Proceedings of the 17th International Conference on Machine Learning, pages 81–88. Morgan Kaufmann, June 2000. 2. L. De Raedt, editor. Advances in Inductive Logic Programming. IOS Press, 1996. 3. L. De Raedt. Attribute value learning versus inductive logic programming: The missing links (extended abstract). In D. Page, editor, Proceedings of the 8th International Conference on Inductive Logic Programming, volume 1446 of Lecture Notes in Artificial Intelligence, pages 1–8. Springer-Verlag, 1998. 4. Luc Dehaspe and Hannu Toivonen. Discovery of relational association rules. In Saso Dzeroski and Nada Lavrac, editors, Relational Data Mining, pages 189–212. Springer-Verlag, September 2001. 5. Saso Dzeroski and Nada Lavrac, editors. Relational Data Mining. Springer-Verlag, Berlin, September 2001. 6. P.A. Flach, C. Giraud-Carrier, and J.W. Lloyd. Strongly typed inductive concept learning. In D. Page, editor, Proceedings of the 8th International Conference on Inductive Logic Programming, volume 1446 of Lecture Notes in Artificial Intelligence, pages 185–194. SpringerVerlag, 1998. P. Brazdil and A. Jorge (Eds.): EPIA 2001, LNAI 2258, pp. 3–4, 2001. c Springer-Verlag Berlin Heidelberg 2001 

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7. Peter A. Flach. Knowledge representation for inductive learning. In Anthony Hunter and Simon Parsons, editors, Symbolic and Quantitative Approaches to Reasoning and Uncertainty (ECSQARU’99), volume 1638 of Lecture Notes in Artificial Intelligence, pages 160–167. Springer-Verlag, July 1999. 8. Peter A. Flach and Nicolas Lachiche. Confirmation-guided discovery of first-order rules with tertius. Machine Learning, 42(1/2):61–95, January 2001. 9. J. Hern´andez-Orallo and M.J. Ram´ırez-Quintana. A strong complete schema for inductive functional logic programming. In S. Dˇzeroski and P. Flach, editors, Proceedings of the 9th International Workshop on Inductive Logic Programming, volume 1634 of Lecture Notes in Artificial Intelligence, pages 116–127. Springer-Verlag, 1999. 10. Stefan Kramer, Nada Lavrac, and Peter Flach. Propositionalization approaches to relational data mining. In Saso Dzeroski and Nada Lavrac, editors, Relational Data Mining, pages 262–291. Springer-Verlag, September 2001. 11. Nicolas Lachiche and Peter Flach. A first-order representation for knowledge discovery and bayesian classification on relational data. In Pavel Brazdil and Alipio Jorge, editors, PKDD2000 workshop on Data Mining, Decision Support, Meta-learning and ILP : Forum for Practical Problem Presentation and Prospective Solutions, pages 49–60. 4th International Conference on Principles of Data Mining and Knowledge Discovery, September 2000. 12. Wim Van Laer and Luc De Raedt. How to upgrade propositional learners to first order logic: A case study. In Saso Dzeroski and Nada Lavrac, editors, Relational Data Mining, pages 235–261. Springer-Verlag, September 2001. 13. N. Lavraˇc and S. Dˇzeroski. Inductive Logic Programming: Techniques and Applications. Ellis Horwood, 1994. 14. Nada Lavraˇc and Peter A. Flach. An extended transformation approach to inductive logic programming. ACM Transactions on Computational Logic, 2(4):458–494, October 2001. 15. S. Muggleton. Inductive logic programming. New Generation Computing, 8(4):295–317, 1991. 16. S. Muggleton, editor. Inductive Logic Programming. Academic Press, 1992. 17. S. Muggleton and L. De Raedt. Inductive logic programming: Theory and methods. Journal of Logic Programming, 19/20:629–679, 1994. 18. G.D. Plotkin. Automatic Methods of Inductive Inference. PhD thesis, Edinburgh University, 1971. 19. E.Y. Shapiro. Algorithmic Program Debugging. The MIT Press, 1983. 20. Ashwin Srinivasan. Context-sensitive models in inductive logic programming. Machine Learning, 43(3):301–324, September 2001. 21. Stefan Wrobel. Inductive logic programming for knowledge discovery in databases. In Saso Dzeroski and Nada Lavrac, editors, Relational Data Mining, pages 74–101. Springer-Verlag, September 2001.

A Comparison of GLOWER and Other Machine Learning Methods for Investment Decision Making Vasant Dhar Stern School of Business, New York University 44 West 4th Street, Room 9-75, New York NY 10012 [email protected] Abstract. Prediction in financial domains is notoriously difficult for a number of reasons. First, theories tend to be weak or non-existent, which makes problem formulation open ended by forcing us to consider a large number of independent variables and thereby increasing the dimensionality of the search space. Second, the weak relationships among variables tend to be nonlinear, and may hold only in limited areas of the search space. Third, in financial practice, where analysts conduct extensive manual analysis of historically well performing indicators, a key is to find the hidden interactions among variables that perform well in combination. Unfortunately, these are exactly the patterns that the greedy search biases incorporated by many standard rule learning algorithms will miss. One of the basic choices faced by modelers is on the choice of search method to use. Some methods, notably, tree induction provide explicit models that are easy to understand. This is a big advantage of such methods over, say, neural nets or na¨ıve Bayes. My experience in financial domains is that decision makers are more likely to invest capital using models that are easy to understand. More specifically, decision makers want to understand when to pay attention to specific market indicators, and in particular, in what ranges and under what conditions these indicators produce good risk- adjusted returns. Indeed, many professional traders have remarked that they are occasionally inclined to make predictions about market volatility and direction, but cannot specify these conditions precisely or with any degree of confidence. For this reason, rules generated by pattern discovery algorithms are particularly appealing in this respect because they can make explicit to the decision maker the particular interactions among the various market indicators that produce desirable results. They can offer the decision maker a "loose theory" about the problem that is easy to critique. In this talk, I describe and evaluate several variations of a new genetic learning algorithm (GLOWER) on a variety of data sets. The design of GLOWER has been motivated by financial prediction problems, but incorporates successful ideas from tree induction and rule learning. I examine the performance of several GLOWER variants on a standard financial prediction problem (S&P500 stock returns), using the results to identify one of the better variants for further comparisons. I introduce a new (to KDD) financial prediction problem (predicting positive and negative earnings surprises), and experiment with GLOWER, contrasting it with tree- and rule-induction approaches as well as other approaches such as neural nets and na¨ıve Bayes. The results are encouraging, showing that GLOWER has the ability to uncover effective patterns for difficult problems that have weak structure and significant nonlinearities. Finally, I shall discuss open issues such as the difficulties of dealing with non stationarity in financial markets. P. Brazdil and A. Jorge (Eds.): EPIA 2001, LNAI 2258, p. 5, 2001. c Springer-Verlag Berlin Heidelberg 2001 

Parallel Implementation of Decision Tree Learning Algorithms Nuno Amado, Jo˜ ao Gama, and Fernando Silva LIACC - University of Porto R.Campo Alegre 823, 4150 Porto {namado,jgama,fds}@ncc.up.pt

Abstract. In the fields of data mining and machine learning the amount of data available for building classifiers is growing very fast. Therefore, there is a great need for algorithms that are capable of building classifiers from very-large datasets and, simultaneously, being computationally efficient and scalable. One possible solution is to employ parallelism to reduce the amount of time spent in building classifiers from very-large datasets and keeping the classification accuracy. This work first overviews some strategies for implementing decision tree construction algorithms in parallel based on techniques such as task parallelism, data parallelism and hybrid parallelism. We then describe a new parallel implementation of the C4.5 decision tree construction algorithm. Even though the implementation of the algorithm is still in final development phase, we present some experimental results that can be used to predict the expected behavior of the algorithm.

1

Introduction

Classification has been identified as an important problem in the areas of data mining and machine learning. Over the years different models for classification have been proposed, such as neural networks, statistical models as linear and quadratic discriminants, decision trees, and genetic algorithms. Among these models, decision trees are particularly suited for data mining and machine learning. Decision trees are relatively faster to build and obtain similar, sometimes higher, accuracy when compared with other classification methods [7,9]. Nowadays there is an exponential growing on the data stored in computers. Therefore, it is important to have classification algorithms computationally efficient and scalable. Parallelism may be a solution to reduce the amount of time spent in building decision trees using larger datasets and keep the classification accuracy [4,5,11,12]. Parallelism can be easily achieved by building the tree decision nodes in parallel or by distributing the training data. However, implementing parallel algorithms for building decision trees is a complex task due to the following reasons. First, the shape of the tree is highly irregular and it is determined only at runtime, beyond the fact that the amount of processing used for each node varies. Hence, any static allocation scheme will probably suffer from a high load imbalance problem. Second, even if the successors of a node are processed P. Brazdil and A. Jorge (Eds.): EPIA 2001, LNAI 2258, pp. 6–13, 2001. c Springer-Verlag Berlin Heidelberg 2001 

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in parallel, their construction needs part of the data associated to the parent. If the data is dynamically distributed by the processors witch are responsible for different nodes then it is necessary to implement data movements. If the data is not properly distributed then the performance of the algorithm can suffer due to a loss of locality [5,12]. Decision trees are usually built in two phases: tree construction and simplification phases. With no doubt, the most computational expensive phase of the algorithm is the tree construction phase[2,9,10,12]. Therefore, in this work, for the description of the parallel construction tree algorithms we only consider the first phase. In the reminder of the paper we first overview some strategies for implementing parallel decision tree algorithms, and then describe our parallel implementation of the C4.5 decision tree construction algorithm. We then present some preliminary results and draw some conclusions.

2

Related Work

This section overviews some strategies for implementing decision tree construction algorithms in parallel using task parallelism, data parallelism and hybrid parallelism. Task parallelism. The construction of decision trees in parallel by following a task-parallelism approach can be viewed as dynamically distributing the decision nodes among the processors for further expansion. A single processor using all the training set starts the construction phase. When the number of decision nodes equals the number of processors the nodes are split among them. At this point each processor proceeds with the construction of the decision sub-trees rooted at the nodes of its assignment. This approach suffers, in general, from bad load balancing due to the possible different sizes of the trees constructed by each processor. Also, for the implementations presented in [4], they require the whole training set to be replicated in the memory of all the processors. Alternatively, they require a great amount of communications for each processor to have access to the examples kept in the other’s memory. Data parallelism. The use of data parallelism in the design of parallel decision tree construction algorithms can be generally described as the execution of the same set of instructions (algorithm) by all processors involved. The parallelism is achieved by distributing the training set among the processors where each processor is responsible for a distinct set of examples. The distribution of the data can be performed in two different ways, horizontally or vertically. The parallel strategy based on vertical data distribution[5] consists in splitting the data by assigning a distinct set of attributes to each processor. Each processor keeps in its memory only the whole values for the set of attributes assigned to him and the values of the classes. During the evaluation of the possible splits each processor is responsible only for the evaluation of its attributes. Parallelism with vertical data distribution can still suffer from load imbalance due to the evaluation of continuous attributes which requires more processing than the evaluation of discrete attributes.

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The parallel strategy based on horizontal data distribution consists in distributing the examples evenly by the processors. Each processor keeps in its memory only a distinct subset of examples of the training set. The possible splits of the examples associated to a node are evaluated by all the processors, which communicate between them to find the global values of the criteria used and, by this, the best split. Each processor performs locally the split. In [11], the authors describe the implementation of two algorithms with horizontal data distribution: SLIQ and SPRINT systems. For the evaluation of a split based on a continuous attribute, these systems have the set of examples sorted by the values of the attribute. In order to avoid sorting the examples every time a continuous attribute is evaluated, they use separate lists of values for each attribute, which are sorted once at the beginning of the tree construction. SLIQ also uses a special list, called the class list, which has the values of the class for each example and stays resident in memory during all the tree construction process. In the parallel implementation of SLIQ the training set is distributed horizontally among the processors where each processor is responsible for creating its own attribute lists. In SPRINT, the class list is eliminated by adding the class label in the attribute lists entries. The index in the attribute lists is now the index of the example in the training set. The evaluation of the possible splits is also performed by all processors, which communicate between them to find the best split. After finding the best split, each processor is responsible for splitting its own attribute lists. Both systems report good performance and scalability results, being also capable of processing very-large datasets. However, the operation to perform the split of the set of examples associated with a node requires high communication load in both systems. Hybrid parallelism. The parallel decision tree construction algorithms, which use hybrid parallelism, can be characterized as using both data parallelism with horizontal or vertical distribution and task parallelism. The implementation of hybrid parallel algorithms is strongly motivated by the choice between the distribution of the amount of processing at each node and the required volume of communications. For the nodes covering a significant amount of examples, is used data parallelism to avoid the problems already stated of load imbalance and of poor use of parallelism associated with task parallelism. But, for the nodes covering fewer examples the time used for communications can be higher than the time spent in processing the examples. To avoid this problem, when the number of examples associated to a node is lower than a specific value, one of the processors continues alone the construction of the tree rooted at the node (task parallelism). Two parallel decision tree construction algorithms using hybrid parallelism are described in [6,12].

3

C4.5 Parallel Implementation

In this section, we describe a new parallel implementation of the C4.5 decision tree construction algorithm. This implementation follows an horizontal data parallelism strategy similar to that used by the parallel implementation of SLIQ [11],

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but modified for the C4.5 algorithm. Our parallel implementation was designed to be executed in a distributed memory environment where each of the k processors has its own private memory. It addresses two fundamental issues: load balance and locality. An uniform load balance is achieved by distributing horizontally the examples equally among the k processors and using a new breadth-first strategy for constructing the decision tree. As in the parallel version of SLIQ, each processor is responsible for building its own attribute lists and class lists from the subset of examples assigned to it. The entries in the class lists keep, for each example, the class label, the weight (used in the C4.5 algorithm for dealing with unknown values), the corresponding global index of the example in the training set and a pointer to the node in the tree to which the example belongs. The attribute lists also have an entry for each example with the attribute value and an index pointing to the example corresponding entry in the class list. The continuous attribute lists are globally sorted by the values of the attribute using the sorting algorithm described in [3]. Each processor has now, for each continuous attribute, a list of sorted values where the first processor has the lower values of the attribute, the second has the attribute values higher then the first processor and lower then the third, and so on. Because of the global sort of the continuous attributes, a processor can have attribute values that do not correspond to any of the examples initially assigned to it. After the sort, each processor updates its class list with the examples information corresponding to the new values of the continuous attributes. Several authors[2,10] pointed out one of the efficiency limitations of C4.5: the repetitive sorting of the examples covered by a node every time a continuous attribute is evaluated. This limitation is eliminated with the implementation of the attribute lists where the continuous attributes are sorted only once. The main problems in the parallel tree construction process reside in performing the split and in finding the best split for the set of examples covered by a node. For these two steps, communication among processors is necessary in order to determine the best global split and the assignments of examples to the new subsets resulting from the split. In the parallel version of the algorithm each processor has a distinct subset of values of the continuous attributes in their globally sorted lists. Before each processor starts evaluating the possible splits of the examples, the distributions must be initialized to reflect the examples assigned to the other processors. Each processor finds its distributions of the local set of examples for each attribute and sends them to the other processors. For the nominal attributes, these distributions are gathered in all processors. All processors compute the gain for nominal attributes. For continuous attributes the gain of a possible split, is found based upon the distributions before and after the split point. When a processor receives the distributions from another it initializes, for each continuous attribute, the distributions before the split point with the distributions of the processors with lower rank. The distributions after the split point are initialized with those from the processors with higher rank. After evaluating all possible divisions of their

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local set of examples, the processors communicate among themselves in order to find the best split from the k local best splits found by each one. As soon as the best split is found, the split is performed by creating the child nodes and dividing the set of examples covered by the node. This step requires for each processor to update the pointers to the nodes in their class lists. The attribute lists are divided in many lists, as a result of the split, and each of those sublists are assigned to every new child node. For the split each processor scans its local list of the attribute chosen and depending on the value of the attribute, each entry is moved to the correspondent sublist, and the pointer to the node in the class list is updated. For dividing the remaining attribute lists the pointers to the nodes in the class list are used. But, before that, the class lists in each process must be updated. For the entries in the class list of one processor, whose values for the chosen attribute are kept in another processor, must be updated with the information of the node to which the corresponding examples were assigned by the other processor. For each example in the set covered by the node, the index, weight and the node to which they were assigned are gathered in all processors allowing each processor to update its local class list and divide the attribute lists. When dividing the attribute lists, each processor finds its local class distributions for each attribute in the new sets of examples assigned to the child nodes. Still on this phase, the distributions are scattered allowing for each processor to know the global class distributions used later during the splits evaluation phase. Our parallel decision tree algorithm described in this work preserves most of the main features of C4.5. One of the most important is the ability to deal with unknown attribute values. Furthermore, since the same evaluation criteria and splits were considered in the parallel version, it obtains the same decision trees and classification results as those obtained by C4.5. Our parallel system modifies the C4.5 algorithm in order to use attribute lists and class lists. These are fundamental data structures to achieve parallelism as used in SLIQ strategy. The main reason for using separate lists for the attributes is to avoid sorting the examples every time a continuous attribute is evaluated. The several sorts performed by C4.5 during the evaluation of the attributes are one of its efficiency limitations [2,10], and, if they were kept in the parallel version then they would strongly limit the performance of the algorithm. Hence, by using separate lists for the attributes makes it possible to globally sort the continuous attributes only once at the beginning of the tree construction process. The SPRINT strategy was developed to overcome the use of centralized structures such as the class list. It avoids the class lists by extending the attribute lists with two extra fields, the class label and the global index of the example in the training set. The main disadvantage stated in [11] for the use of the class list is that it can limit the size of the training set that can be used with the algorithm, due to the fact that it must stay resident in memory during the execution of the algorithm. Suppose now we have a training set with N examples and A attributes and the entry values of the attribute lists and class list require one word of memory. Suppose also that we have k processors available for the execu-

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tion of the algorithms. In this situation, SPRINT will need 3 ∗ A ∗ N/k memory words in each processor to store the training set divided equally among the k processors. For the algorithm described in this work the worst situation happens when, due to the global sort of the continuous attribute lists, the class list must store the information for all examples in the training set. In this situation the amount of memory necessary to store the training set in each processor will be 2 ∗ A ∗ N/k + 3 ∗ N memory words. It is easy to observe that when the number of attributes is three times greater then the number of available processors (A > 3∗k) it is better to use, in terms of memory, the class list then the attribute lists. Another disadvantaged stated in [11] relatively to the use of the class list is the time required to update it during the split. In the implementation of SLIQ, the class list is entirely replicated in the memory of each processor. After the split each processor has to update the entire list, which limits the performance of the algorithm. Similarly to SLIQ and SPRINT, in the parallel version of C4.5 for the split the processors exchange the global indexes of the examples covered by a node with the information to which child node they were assigned. Each processor keeps a list of pointers to the entries of the class list sorted by the examples indexes in order to improve the searches when updating the class list with the information gathered from the other processors.

4

Experimental Results

Our parallel implementation is still being refined, therefore the results are only preliminary and we believe are subject to further improvement. However, they can be used to predict the expected behavior of the parallel algorithm. As mentioned before, our decision tree algorithm uses the same criteria and procedures used in the C4.5 algorithm. Therefore, they produce the same decision trees with equal classification accuracy. Consequently, we evaluate the performance of our system only in terms of execution time required for the construction of the decision tree. Again, the prune phase of the algorithm was not taken into account for the time measured in the experiments as it is negligible. The parallel version of C4.5 was implemented using the standard MPI communication primitives [8]. The use of standard MPI primitives allows the implementation of the algorithm to be highly portable to clusters of machines, that is to distributed memory environments. The experiments presented here were conducted on a PC server with four Pentium Pro CPUs and 256MB of memory running Linux 2.2.12 from the standard RedHat Linux release 6.0 Distribution. Each CPU in the PC server runs at 200MHz and contains 256Kb of cache memory. All the time results presented here are the average result of three executions of the algorithm. All experiments used the Synthetic data set from Agrawal et. al. [1]. This dataset has been previously used for testing parallel decision tree construction algorithms such as the systems SLIQ and SPRINT [11,12]. Each example in the dataset has 9 attributes, where 5 of them are continuous and 3 are discrete. The

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Fig. 1. Speedup results.

Fig. 2. Scale-up results.

values of the attributes are randomly generated. Agrawal et. al. also describe 10 classification functions based on the values of these attributes and with different complexities. For the datasets used in the experiments it was only considered one of those functions, named Function2. The first set of experiments measured the performance, in terms of speedup, of the algorithm. For each experiment we kept constant the total size of the training set and varying the number of processors from 1 to 4. Figure 1 illustrates the speedup results for training sets of 100k, 200k and 400k examples. Our algorithm overall shows good speedup results and, as expected, the best results were obtained for the largest dataset used (with 400K examples). The slowdown observed for the largest processor configuration is mainly due to the high communication costs in the split phase. The next set of experiments aimed to test the scale-up characteristics of the algorithm. In these experiments, for each scale-up measure, the size of the training set (100k examples) in each processor was kept constant while the processors configuration varied from 1 to 4. Figure 2 shows that our algorithm achieves good scale-up behavior. Again, high communication overheads in the splitting phase influence scale-up capacity as the processors increase.

Parallel Implementation of Decision Tree Learning Algorithms

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13

Conclusion

In this work we overviewed some parallel algorithms for constructing decision trees and proposed a new parallel implementation of the C4.5 decision tree construction algorithm. Our parallel algorithm uses a strategy similar to that of SLIQ but adapted for the C4.5 algorithm. Furthermore, it preserves the main features of C4.5, such as the ability to deal with unknown attribute values. As a result, our system builds the same decision trees, as those obtained by C4.5, with the same classification accuracy. Based in the preliminary results presented, the algorithm shows good speedup and scale-up performance indicating that it can be used to build decision trees from very-large datasets. However some work has yet to be done. The results obtained when measuring the speedup characteristics of the algorithm indicate that the communications overhead is a key factor in limiting the performance of the algorithm. Acknowledgements This work was partially supported by funds granted to LIACC through the Programa de Financiamento Plurianual, Funda¸c˜ao de Ciˆencia e Tecnologia, Programa POSI and FEDER. J.Gama acknowledges Metal and Sol-Eu-Net projects.

References 1. R. Agrawal, T. Imielinski, and A. Swami. Database mining: A performance perspective. In Special Issue on Learning and Discovery in Knowledge-Based Databases, number 5(6), pages 914–925. IEEE, 1993. 2. J. Catlett. Megainduction: Machine learning on very large databases. PhD thesis, University of Sydney, 1991. 3. D. J. DeWitt, J. F. Naughton, and D. A. Schneigder. Parallel sorting on a sharednothing architecture using probabilistic splitting. In Proc. of the 1st Int’l Conf. on Parallel and Distributed Information Systems, 1991. 4. J. Darlington et. al. Parallel induction algorithms for data mining. In Proc. of 2nd Intelligent Data Analysis Conference. Springer Verlag, LNCS 1280, 1997. 5. A. A. Freitas and S. H. Lavington. Mining Very Large Databases with Parallel Processing. Kluwer Academic Publishers, 1998. 6. R. Kufrin. Decision trees on parallel processors. Parallel Processing for Artificial Intelligence, Elsevier, 3:279–306, 1997. 7. D. Michie, D. J. Spiegelhalter, and C. C. Taylor. Machine Learning, Neural and Statistical Classification. Ellis Horwood, 1994. 8. P. S. Pacheco. Parallel Programming with MPI. Morgan Kaufmann Pubs., 1997. 9. J. R. Quinlan. C4.5: Programs for Machine Learning. Morgan Kaufmann Publishers, Inc., 1992. 10. S. Ruggieri. Efficient c4.5. Technical report, Universit di Pisa, 2000. 11. J. C. Shafer, R. Agrawal, and M. Mehta. SPRINT: A scalable parallel classifier for data mining. In Proc. 22nd Int. Conf. Very Large Databases, pages 544–555. Morgan Kaufmann, 3–6 1996. 12. A. Srivastava, E. Han, V. Kumar, and V. Singh. Parallel formulations of decisiontree classification algorithms. Data Mining and Knowledge Discovery, 3, 1999.

Reducing Rankings of Classifiers by Eliminating Redundant Classifiers Pavel Brazdil1 , Carlos Soares1 , and Rui Pereira2 1

LIACC / FEP, University of Porto, Rua do Campo Alegre, 823, 4150-180 Porto, Portugal, {pbrazdil,csoares}@liacc.up.pt 2 Infopulse, Portugal, [email protected] Abstract. Several methods have been proposed to generate rankings of supervised classification algorithms based on their previous performance on other datasets [8,4]. Like any other prediction method, ranking methods will sometimes err, for instance, they may not rank the best algorithm in the first position. Often the user is willing to try more than one algorithm to increase the possibility of identifying the best one. The information provided in the ranking methods mentioned is not quite adequate for this purpose. That is, they do not identify those algorithms in the ranking that have reasonable possibility of performing best. In this paper, we describe a method for that purpose. We compare our method to the strategy of executing all algorithms and to a very simple reduction method, consisting of running the top three algorithms. In all this work we take time as well as accuracy into account. As expected, our method performs better than the simple reduction method and shows a more stable behavior than running all algorithms. Keywords: meta-learning, ranking, algorithm selection

1

Introduction

There is a growing interest in providing methods that would assist the user in selecting appropriate classification (or other data analysis) algorithms. Some meta-learning approaches attempt to suggest one algorithm while others provide a ranking of the candidate algorithms [8,4]. The ranking is normally used to express certain expectations concerning performance (e.g. accuracy). The algorithm that appears in a certain position in the ranking is expected to be in some way better (or at least not worse) than the ones that appear afterwards. So, if the user is looking for the best performing algorithm, he can just follow the order defined by the ranking and try the corresponding algorithms out. In many cases the user may simply use the algorithm at the top of the ranking. However, the best performing algorithm may appear further on in the ranking. So, if the user is interested to invest more time in this, he can run few more algorithms and identify the algorithm that is best. Therefore our aim is (a) to come up with a ranking that includes only some of the given candidate algorithms, (b) not to decrease the chance that the best performing algorithm is excluded from the ranking. In this paper we describe an extension to the basic ranking method that has been designed for this aim. P. Brazdil and A. Jorge (Eds.): EPIA 2001, LNAI 2258, pp. 14–21, 2001. c Springer-Verlag Berlin Heidelberg 2001 

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In the next section we briefly review the basic ranking method. Section 3 describes the method used to exclude items from a given ranking. Section 4 presents the evaluation method adopted, while the following section describes the experimental setting and results. In Section 6 some alternative evaluation methods are briefly outlined and the last section presents the conclusions.

2

Constructing Rankings of Classifiers on Past Experience

Earlier we have proposed a method [8] that divides the problem of generating a ranking into two distinct phases. In the first one we employ a k-Nearest Neighbor method to identify datasets similar to the one at hand. This is done on the basis of different data characterization measures. In the second phase we consider the performance of the given classification algorithms on the datasets identified. This method is based on the Adjusted Ratio of Ratios (ARR), a multicriteria evaluation measure combining accuracy and time to assess relative performance. In ARR the compromise between the two criteria involved is given by the user in the form “the amount of accuracy I’m willing to trade for a 10 times speed-up is AccD%”. The ARR of algorithm ap when compared to algorithm aq on data set di is defined as follows: di = ARRap,aq

 1 + log

Adi ap Adi aq di Tap di Taq



∗ AccD

di where Adi ap and Tap are the accuracy and time of ap on di, respectively. Assuming without loss of generality that algorithm ap is more accurate but slower than di will be 1 if ap is AccD% algorithm aq on data set di, the value of ARRap,aq more accurate than aq for each order of magnitude that it is slower than aq. di will be larger than one if the advantage in accuracy of ap is AccD% ARRap,aq for each additional order of magnitude in execution time and vice-versa. The individual ARR measures are used as a basis for generating a ranking. Basically, the method aggregates the information for different datasets by calculating overall means of individual algorithms:   di aq di ARRap,aq ARRap = (1) n(m − 1) where ARRap represents the mean of individual ARR measures for algorithm ap, n represents the number of datasets and m the number of algorithms. The values of ARRap are then examined and the algorithms ordered according to these values. As it has been shown this method provides quite good rankings overall and is quite competitive when compared to other approaches, such as DEA [4]. One disadvantage of this method is that it does not provide any help as to how many algorithms the user should actually try out. This problem is addressed in the next section.

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Reducing Rankings of Classifiers by Eliminating Redundant Classifiers

There are really two reasons why we would want to eliminate algorithms from a given ranking. The first one is that the ranking recommended for a given dataset may include one or more algorithms that have proven to be significantly worse than others in similar datasets in the past and, thus, have virtually no chance of achieving better results than its competitors on the current dataset. These algorithms can thus be dropped. The second one is that the given ranking may include one or more clones of a given algorithm, that are virtually indistinguishable from it, or other algorithms with very similar performance. These algorithms can again be dropped. We may ask why we would want to include clones in the candidate set in the first place. The answer is that recognizing clones is not an easy matter. Different people may develop different algorithms and give them different names. These, in some cases, may turn out to be quite similar in the end. There is another reason for that. We may on purpose decide to include the same algorithm several times with different parameter settings. We must thus have a way to distinguish useful variants from rather useless clones. Our objective here is to describe a method that can be used to do that. Suppose a given ranking R consists of n classifiers, C1 ...Cn . Our aim is to generate a reduced ranking R´, which contains some of the items in R. The method considers all algorithms in the ranking, following the order in which they appear. Suppose, we have come to algorithm Ci . Then the sequence of subsequent algorithms Cj (where j > i) is then examined one by one. The aim is to determine whether each algorithm Cj should be left in the ranking, or whether it should be dropped. This decision is done on the basis of past results on datasets that are similar to the one at hand, i.e. datasets where the performance of the algorithms is similar to the performance that is expected on the new dataset. If the algorithm Cj has achieved significantly better performance than Ci on some datasets (shortly Cj  Ci ) the algorithm is maintained. If it did not, then two possibilities arise. The first one is that Cj is significantly worse than Ci (Cj  Ci ) on some datasets, and comparable to Ci on others. In this case Cj can be dropped. The second possibility is that neither algorithm has significant advantage over the other (Cj ≈ Ci ), indicating that they are probably clones. In this case too, Cj can be dropped. This process is then repeated until all combinations have been explored. Here performance is judged according to the ARR measure presented earlier, which combines both accuracy and time. The historical data we use contains information on different folds of cross validation procedure. It is thus relatively di is consistently easy to conduct a statistical test determining whether ARRCj,Ci greater than 1 on different folds, indicating that Cj is significantly better than Ci on dataset di. After the reduction process has terminated, the resulting ranking will contain the first item that was in R, plus a few more items from this ranking. Note that this need not be a sequence of several consecutive items. Should the best

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performing algorithm have a clone under a different name, this clone will be left out. Reducing a subsequence of algorithms is beneficial in general, as it reduces the time the user needs to spend experimenting. However, this process involves certain risks. If the sequence is reduced too much, the optimal classifier may be missed out. If on the other hand the sequence is longer than required, the total time required to determine which algorithms is best increases. It is therefore necessary to have a way of evaluating different alternatives and comparing them. This topic is described in the next section.

4

Comparing Different Rankings of Uneven Length

Let us now consider the next objective - how to compare two rankings and determine which one is better. In our previous work [1,8,9] we have used a method that involves calculating a rank correlation coefficient to a ranking, constructed simply by running the algorithms on the dataset at hand. This method has one disadvantage - it does not enable us to compare rankings of different sizes. We have therefore decided to use another method here. We evaluate a reduced ranking as if it was a single algorithm with the accuracy of the most accurate algorithm included in the ranking and with total time equal to the sum of the times of all algorithms included. Given that ARR was the performance measure used to construct and reduce the rankings, it makes sense to use the same scheme in the evaluation.

5

Experimental Evaluation

The meta-data used was obtained from the METAL project (http://www.metalkdd.org). It contains results of 10 algorithms on 53 datasets. We have used three decision tree classifiers, C5.0 tree, C5.0 with boosting [7] and Ltree, which is a decision tree which can introduce oblique decision surfaces [3]. We have also used a linear discriminant (LD) [6], two neural networks from the SPSS Clementine package (Multilayer Perceptron and Radial Basis Function Network) and two rule-based systems, C5.0 rules and RIPPER [2]. Finally, we used the instancebased learner (IBL) and naive bayes (NB) implementations from the MLC++ library [5]. As for the datasets, we have used all datasets from the UCI repository with more than 1000 cases, plus the Sisyphus data and a few applications provided by DaimlerChrysler. The algorithms were executed with default parameters and the error rate and time were estimated using 10-fold cross-validation. Not all of the algorithms were executed on the same machine and so we have employed a time normalization factor to minimize the differences. The rankings used to test the reduction algorithm were generated with the ranking method reviewed briefly in Section 2. Three settings for the compromise between accuracy and time were tested, with AccD ∈ {0.1%, 1%, 10%}, corresponding to growing importance of time.

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Pavel Brazdil, Carlos Soares, and Rui Pereira Table 1. ARR scores for different values of AccD. AccD methods 10 100 1000 reduced 1.1225 1.0048 1.0037 top 3 1.1207 0.9999 0.9889 all 0.8606 0.9975 1.0093

The parameters used in the ranking reduction method were the following: – Performance information for the ten nearest neighbors (datasets) was used to determine the redundancy of an algorithm, corresponding to approximately 20% of the total number of datasets. Although the method seems to be relatively insensitive to the number of neighbors, this percentage has obtained good results in previous experiments [8]. – An algorithm is dropped if it is not significantly better than another algorithm retained in the ranking on at least 10% of datasets selected (i.e. one dataset, since ten neighbors are used). – The significance of differences between two algorithms has been checked with the paired t test with a confidence level of 95%. We have compared our method with the full ranking and with a reduced ranking obtained by selecting the top three algorithms in the full ranking.

Fig. 1. Average ARR scores over 53 dataset for different values of AccD.

As can be seen in Table 1 and Figure 1 the method proposed always performs better than the simple reduction method that uses the top three algorithms in the full ranking. As for the choice of executing all the algorithms, when time is given great importance, this option is severely penalized in terms of the ARR score. When accuracy is the dominant criterion, executing all the algorithms represents the option. This result is of course to be expected, since this strategy consists of

Reducing Rankings of Classifiers by Eliminating Redundant Classifiers

19

Table 2. Complete and reduced rankings for the segmentdataset for two different values of AccD. The algorithms eliminated in the reduced ranking are indicated by a ’*’. AccD rank 1 2 3 4 5 6 7 8 9 10

10% C5.0 tree LD C5.0 rules C5.0 w/ boosting Ltree IBL NB RIPPER MLP RBFN

* * * * * * * *

1% C5.0 w/ boosting C5.0 rules C5.0 tree Ltree IBL LD NB * RIPPER * MLP RBFN *

executing all algorithms with the aim of identifying the best option. So, our method is suitable if time matters at least a bit. One interesting observation is that the method presented always obtains an average ARR larger than 1. This means that, for all compromises between accuracy and time, as defined by the AccD parameter, it generates recommendations that are advantageous either in terms of accuracy, or in terms of time, when compared to the average of the other two methods. We wanted to analyze some of the reduced ranking to see how many algorithms were actually dropped and which ones. Table 2 presents the recommendation that was generated for the segment dataset. When time is considered very important (AccD = 10%, equivalent to a compromise between 10x speed up and a 10% drop in accuracy), only two algorithms were retained in the ranking: C5.0 tree and LD. All the others marked with * have been dropped. This result corresponds quite well to our intuitions. Both C5.0tree and linear discriminant are known to be relatively fast algorithms. It is conceivable that this does not vary from dataset to dataset1 and hence variations in accuracy on different datasets did not affect things much. The situation is quite different if we give more importance to accuracy. Let us consider, for instance the case when AccD = 1%. Here 7 out of 10 algorithms were retained, including MLP which appeared in the 9th position in the original ranking. This is justified by the historical evidence that the method takes into account when giving this recommendation. Each of the algorithms retained must have done well at least on one dataset. It appears that mlcnb, ripper and RBFN do not satisfy this condition and hence were left out2 . 1 2

Although this may not be true for datasets with an extremely large number of attributes, we have used none of those. All results were obtained with default parameter settings. However, the performance of some algorithms is highly dependent on the parameter setting used. If parameter tuning was performed, some of the algorithms that were left out could be competitive in relation to others. This issue was ignored in this study.

20

6

Pavel Brazdil, Carlos Soares, and Rui Pereira

Discussion

The evaluation measure presented can be improved. We can try to determine whether the ARR measure associated with one reduced ranking is higher than (or equal to, or lower than) the ARR measure associated with another plan. In addition, it is possible to carry out statistical tests with the aim of determining whether these differences are significant. This analysis can be carried out for different setting of the constant AccD determining the relative importance of time. This procedure can thus be used to identify the algorithms lying on, or near the, so called, efficiency frontier [4]. Furthermore, note that this method can be used to compare reduced rankings of different lengths. However, if we wanted to evaluate not only the final outcome, but also some intermediate results, this could be done as follows. In this setting, a reduced ranking can be regarded as a plan to be executed sequentially. Suppose a given plan Pi consists of n1 items (classifiers) and plan Pj of n2 items, where, say, n2 < n1. The first n2 comparisons can be carried out as described earlier, using the ARR measure. After that we simply complete the shorter plan with n1 − n2 dummy entries. Each entry just replicates the accuracy characterizing the plan. It is assumed that no time is consumed in this process.

7

Conclusions

We have presented a method to eliminate the algorithms in a ranking that are expected to be redundant. The method exploits past performance information for those algorithms. The method presented addresses one shortcoming of existing ranking methods [8,4], that don’t indicate, from the ranking of candidate algorithms, which ones are really worth trying. As expected, the experiments carried out show that our method performs better than the simple strategy of selecting the top three algorithms. Also, when time is very important, our method represents a significant improvement compared to running all algorithms. It is interesting to note that when accuracy is very important, although running all algorithms is the best strategy, the difference to our method is small. Here we have concentrated on accuracy and time. It would be interesting to take other evaluation criteria into account, e.g., interpretability of the models. Acknowledgments We would like to thank all the METAL partners for a fruitful working atmosphere, in particular to Johann Petrak for providing the scripts to obtain the meta-data and to J¨ org Keller, Iain Paterson and Helmut Berrer for useful exchange of ideas. The financial support from ESPRIT project METAL, project ECO under PRAXIS XXI, FEDER, FSE, Programa de Financiamento Plurianual de Unidades de I&D and Faculty of Economics is gratefully acknowledged.

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References 1. P. Brazdil and C. Soares. A comparison of ranking methods for classification algorithm selection. In R.L. de M´ antaras and E. Plaza, editors, Machine Learning: Proceedings of the 11th European Conference on Machine Learning ECML2000, pages 63–74. Springer, 2000. 2. W.W. Cohen. Fast effective rule induction. In A. Prieditis and S. Russell, editors, Proceedings of the 11th International Conference on Machine Learning, pages 115– 123. Morgan Kaufmann, 1995. 3. J. Gama. Probabilistic linear tree. In D. Fisher, editor, Proceedings of the 14th International Machine Learning Conference (ICML97), pages 134–142. Morgan Kaufmann, 1997. 4. J. Keller, I. Paterson, and H. Berrer. An integrated concept for multi-criteria ranking of data-mining algorithms. In J. Keller and C. Giraud-Carrier, editors, MetaLearning: Building Automatic Advice Strategies for Model Selection and Method Combination, 2000. 5. R. Kohavi, G. John, R. Long, D. Mangley, and K. Pfleger. MLC++: A machine learning library in c++. Technical report, Stanford University, 1994. 6. D. Michie, D.J. Spiegelhalter, and C.C. Taylor. Machine Learning, Neural and Statistical Classification. Ellis Horwood, 1994. 7. R. Quinlan. C5.0: An Informal Tutorial. RuleQuest, 1998. http://www.rulequest.com/see5-unix.html. 8. C. Soares and P. Brazdil. Zoomed ranking: Selection of classification algorithms based on relevant performance information. In D.A. Zighed, J. Komorowski, and J. Zytkow, editors, Proceedings of the Fourth European Conference on Principles and Practice of Knowledge Discovery in Databases (PKDD2000), pages 126–135. Springer, 2000. 9. C. Soares, P. Brazdil, and J. Costa. Measures to compare rankings of classification algorithms. In H.A.L. Kiers, J.-P. Rasson, P.J.F. Groenen, and M. Schader, editors, Data Analysis, Classification and Related Methods, Proceedings of the Seventh Conference of the International Federation of Classification Societies IFCS, pages 119–124. Springer, 2000.

Non–parametric Nearest Neighbor with Local Adaptation Francisco J. Ferrer–Troyano, Jes´ us S. Aguilar–Ruiz, and Jos´e C. Riquelme Department of Computer Science, University of Sevilla Avenida Reina Mercedes s/n, 41012 Sevilla, Spain {ferrer,aguilar,riquelme}@lsi.us.es

Abstract. The k–Nearest Neighbor algorithm (k-NN) uses a classification criterion that depends on the parameter k. Usually, the value of this parameter must be determined by the user. In this paper we present an algorithm based on the NN technique that does not take the value of k from the user. Our approach evaluates values of k that classified the training examples correctly and takes which classified most examples. As the user does not take part in the election of the parameter k, the algorithm is non–parametric. With this heuristic, we propose an easy variation of the k-NN algorithm that gives robustness with noise present in data. Summarized in the last section, the experiments show that the error rate decreases in comparison with the k-NN technique when the best k for each database has been previously obtained.

1

Introduction

In Supervised Learning, systems based on examples (CBR, Case Based Reasoning) are object of study and improvement from their appearance at the end of the sixties. These algorithms extract knowledge by means of inductive processes from the partial descriptions given by the initial set of examples or instances. Machine learning process is usually accomplished in two functionally different phases. In the first phase of Training a model of the hyperspace is created by the labelled examples. In the second phase of Classification the new examples are classified or labelled based on the constructed model. The classifier approached in this paper belongs to the family of the nearest neighbor algorithm (from here on NN) where the training examples are the model itself. NN assigns to each new query the label of its nearest neighbor among those that are remembered from the phase of Training (from here on the set T). In order to improve the accuracy with noise present in data, the k-NN algorithm introduces a parameter k so that for each new example q to be classified the classes of the k nearest neighbors of q are considered: q will be labelled with the majority class or, in case of tie, it is randomly broken. Another alternative consists in assigning that class whose average distance is the smallest one or introducing a heuristically obtained threshold k1 < k so that the assigned class will be that with a number of associated examples greater than this threshold [12]. Extending the classification criterion, the k-NNwv algorithms (Nearest P. Brazdil and A. Jorge (Eds.): EPIA 2001, LNAI 2258, pp. 22–29, 2001. c Springer-Verlag Berlin Heidelberg 2001 

Non–parametric Nearest Neighbor with Local Adaptation

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5

1 4

Fig. 1. The chosen value for k is decisive to classify a new example q by k-NN when this example is near the decision boundaries. For this example, the smaller value of the parameter k that classifies q correctly is 5.

Neighbor Weighted Voted) assign weights to the prediction made by each example. These weights can be inversely proportional to the distance with respect to the example to be classified [5,7]. Therefore, the number k of examples observed and the metric used to classify a test example are decisive parameters. Usually k is heuristically determined by the user or by means of cross-validation [11]. The usual metrics of these algorithms are the Euclidean distance for continuous attributes and the Overlap distance for nominal attributes (both metrics were used in our experiments). In the last years have appeared interesting approaches that test new metrics [15] or new data representations [3] to improve accuracy and computational complexity. Nevertheless, in spite of having a wide and diverse field of application, to determine with certainty when k-NN obtains higher accuracy than NN [2] and viceversa [8] is still an open problem. In [6] it was proven that when the distance among examples with the same class is smaller than the distance among examples of different class, the probability of error for NN and k-NN tends to 0 and , respectively. But, not always this distribution for input data appears, reason why k-NN and k-NNwv can improve the results given by NN with noise present in the data. In [13] the experimental results give rise to the two following hypotheses: a) Noisy data need large values for k; b) The performance of k-NN is less sensitive to the choice of a metric. Figure 1 illustrates this fact when the values of two attributes from the Iris database are projected on the plane. The X-axis measures the length of the petal and the Y-axis measures the width of the petal. In [14] a study of the different situations in which k-NN improves the results of NN is exposed, and four classifiers are proposed (Locally Adaptive Nearest Neighbor, localKN Nks ) where for each new example q to be classified the parameter k takes a value kq which is similar to the values that classified the M nearest neighbors eq of q. Using a similar approach to Wettschereck’s, we propose a classification criterion for new examples by taking different values for k

24

Francisco J. Ferrer–Troyano, Jes´ us S. Aguilar–Ruiz, and Jos´e C. Riquelme

according to the most frequent ones that classified the original examples correctly. To calculate such values the proximity of each example to its enemy is analysed, being the enemy the nearest neighbor with different class. A priori, if the example to be classified is near examples having different classes among them, it might be classified by few values. But if this example is surrounded by neighbors with the same class, it could be classified by different values. This paper presents a method that reduces and classifies according to such a criterion with no need to analyse each particular case. In this way, the impure regions and the border instances are better analysed in order to provide greater robustness with noise present in the data. In section 2 the proposed method and their computational complexity are detailed. Section 3 describes the experiments and the results from the UCI repository [4] and section 4 summarizes the conclusions.

2 2.1

Description of the Algorithm Approach

By means of the k-NN algorithm, if a new example is near the decision boundaries, the resulting class depends on the parameter k. At worst, the percentages of examples of each class are similar at these regions. In such situation, the set formed by classifying values kei associated with each example ei at this region can be large or zero, i.e. some examples will not have any associated value kei which classify it correctly by k-NN. So, this information (the classifying values associated with the nearest neighbors of a new query q) can be not relevant to classify a new query q by k-NN. We not assume that it is possible to determine the values of the parameter k which allow to classify the examples in overlapped regions. However, we assume that it is possible to improve the accuracy if several times the k-NN algorithm is evaluated on these regions. The idea is as simple as to give more than one opportunity to the example that is to be classified . If the example to be classified is a central example this criterion will not have any effect. If it is a border example, the accuracy can improve. Thus, the disturbing effect caused by the noise and the proximity to enemies can be smoothed. The consequences of such a bias can be explained in three cases: – If q is a central example, the majority class might almost always be the same one for each evaluation. – If q is a noise example, either there will not be an associated value kq that classifies q correctly or kq will be large. – If q is a border example, several evaluations can avoid the errors of classification. Figures 2 and 3 illustrate these facts by means of projections on the plane of the values of two attributes of the Horse-Colic database. In the first case (Figure 2) the value of k is slight relevant whereas in the second case (Figure 3) such

Non–parametric Nearest Neighbor with Local Adaptation

Fig. 2. Horse Colic database. If the new example to be classified is central, the majority class in each evaluation might be the same almost always.

25

Fig. 3. Horse Colic database. If the new example to be classified is a border example, several evaluations of the k-NN algorithm can avoid some errors.

value is critical. Therefore, our problem is to find either the limits [kqmin , kqmax ] between which the k-NN algorithm will be applied for each new example q or the values, which are not necessarily continuous, {kq1 , kq2 , . . .} from which is calculated the majority class. The method has been denominated f N N (k– Frequent Nearest Neighbors) since it takes the most frequent values of k among those that classified correctly the examples of each database. In this process, there are no parameters given by the user since these values are calculated locally for each database. 2.2

The Algorithm

Let n be the number of examples of the Training set T . Let kN N (e, i) the ith nearest neighbor of an example e within T . We denote majorityClass(e, i..j) as the majority class between the ith and the j th neighbors of e. fNN associates with each example ei two values: 1. kCM ini : The smallest k that classifies correctly the example ei by using the k-NN algorithm, such that (see Figure 4): ∀j ∈ [1, kCM ini ) | Class (kN N (ei , j)) = Class (ei ) ⇒ ⇒ majorityClass (ei , 1..j) = Class (ei )

(1)

2. kCM axi : If kCM ini was found, then kCM axi ≥ kCM ini and: ∀j ∈ [kCM ini , kCM axi ] ⇒ Class (ei ) = Class (kN N (ei , j))

(2)

With these values, a new value kLim is calculated which satisfies the following property: ∀ei ∈ T, j ∈ [min(kCM ini ), kLim] ⇒ ∃ek ∈ T | kCM ink = j

(3)

26

Francisco J. Ferrer–Troyano, Jes´ us S. Aguilar–Ruiz, and Jos´e C. Riquelme e (A ) K C M in p o s . c la s s B 1

3

B

2

C

4

A

5

C

6

A

7

B

8

A

9

A

K C M a x 1 0

1 1

1 2

A

A

A

1 3

C

m a jo r ity C la s s ( e , 1 ..4 ) = B m a jo r ity C la s s ( e , 1 ..6 ) = B m a jo r ity C la s s ( e , 1 ..7 ) = B m a jo r ity C la s s ( e , 1 ..8 ) = A

Fig. 4. Example of kCM in and kCM ax for an example e with class A. The ties are broken with the nearest class. Majority class is not A from k = 1 to k = 8. When k = 9 the majority class is A (kCM ine = 9). All the examples have class A from k = 9 to k = 12. Finally, the thirteenth neighbor of e has class C, so that kCM axe = 12.

where min(kCM ini ) is the least kCM ini value of each example. Those examples ei that either have not any associated value kCM ini or have an associated value kCM ini > kLim are considered outliers and they are removed. The resulting reduced set (from here on Tf ) will be used as Training model for our algorithm. In order to classify a new example q, the k-NN algorithm is applied several times to the same example q by varying the value of k. These values belong the interval [min(kCM ini ), kLim]. The assigned label will be that among the nearest to q that is most frequentin the kT evaluations of k-NN. Thus, the computational  complexity of fNN is: Θ n2 · (log n + 1) + n · (log n + δ + 2) + kLim2 . In the first phase the set Tf is generated. The n − 1 nearest neighbors for the n examples of the Training set are ordered (Θ (n · (n + n · log n))). So, for each example it is computed the distance to all the neighbors (Θ (n)) and then the associated list is ordered (Θ (n log n)). After this procedure kLim is found (Θ (n · δ) , min(kCM ini ) ≤ δ ≤ kLim) and the outliers  are removed (Θ (n)). In the second phase a test example is classified (Θ n · (log n + 1) + kLim2 ). The pseudo code for the fNN algorithm is shown in Figure 5 where n is the original number of examples and c the number of different labels for the class.

3

Results

To carry out the method and the test, the Euclidean distance for continuous attributes and the Overlap distance for the nominal attributes were used. The values of the continuous attributes were normalized in the interval [0,1]. Examples with missing-class was removed and attributes with missing-values was treated with the mean or mode, respectively. fNN was tested on 20 databases from the Machine Learning Database Repository at the University of California, Irvine [4]. In order to reduce statistical variation, each experiment was executed

Non–parametric Nearest Neighbor with Local Adaptation

27

function fNN(Train:SET; query:INSTANCE) return (label:Integer) var T_f: Set; k,k_Lim,label: Integer; k_Vect: VECTOR[n][2] Of Integer frequencies: VECTOR[c] Of Integer beginF // Calculating kCMin, kCMax for each example. Calculate_MinMax_Values_K(Train, k_Vect) // Finding the limits for the evaluations of kNN. Calculate_Limits(k_Vect,k_Lim) // Removing the examples whose kCMin does not belong to [1,k_Lim]. T_f:= Delete_Outliers(Train, k_Lim) for k:= Min(kCMin) to k_Lim label:= Classify_KNN(query,T_f,k) frequencies[label]:= frequencies[label]+ 1/Average_Dist(query,label,k) return(frequencies.IndexOfMaxElement()) endF

Fig. 5. Pseudo code for fNN.

by means of 10-folds cross-validation. fNN was compared with k-NN using 25 different values of k (the odd numbers belonging to interval [1, 51]). This limit was fixed after observing for all databases how the accuracy decreased from a value near the best k for each database (being 33 the maximum value for Heart Cleveland) database. In Table 1 is reported the main results obtained. The averageaccuracy with the associated standard deviation and the computational cost by means of fNN is showed in Columns 2a and 2b respectively. The k-NN algorithm is included for comparison using the best k for each database (Column 3a) and the best average-value (k=1) for all databases (Column 1a). Both computational cost for k-NN were very similar and they are showed in Column 1b. Column 3b shows the best value of k for each database by k-NN. Column 2c show the size of Tf regarding the Training set and Column 2d show the values of kLim for each database, i.e. the limit for k by fNN. The databases marked with * mean an improvement of fNN regarding 1-NN by means of t-Student statical test using α = 0.05. We can observe in Table 1 that fNN obtained better precision than 1-NN for 13 databases where the best k for the k-NN algorithm was a high value, so that: – If KLim < kbest for k-NN, then fNN provides higher accuracy than 1-NN. – The percentage of examples that are excluded from Tf is a minimum error bound for k-NN.

4

Conclusions

An easy variation of the k-NN algorithm has been explained and evaluated in this paper. Experiments with commonly used databases indicate that exits do-

28

Francisco J. Ferrer–Troyano, Jes´ us S. Aguilar–Ruiz, and Jos´e C. Riquelme

Table 1. Results for 20 databases from the UCI repository by using 10-folds crossvalidation. Column 1 shows the average accuracy with the standard deviation and the computational cost by k-NN with k=1 (the best value for all databases). Column 2 shows the same percentages obtained by fNN, the percentage of examples retained from the Training set and the value of kLim, i.e. the limit for k by fNN . Column 3 shows the best accuracy with the standard deviation by the k-NN algorithm when the best k is found. This best k was looked for in the odd numbers belonging to interval [1,51].

Domain Anneal Balance Scale* B. Cancer (W) Credit Rating* German Credit Glass Heart D. (C)* Hepatitis* Horse Colic Ionosphere Iris Pima Diabetes Primary Tumor* Sonar Soybean Vehicle Voting Vowel Wine Zoo* Average

1-NN Pred. Acc. Time 91.76 ±2.4 1.10 77.76 ±4.8 0.25 95.56 ±2.2 0.20 80.72 ±2.2 0.56 72.29 ±2.9 1.42 70.19 ±2.0 0.04 74.92 ±2.5 0.09 81.29 ±0.8 0.03 67.93 ±3.0 0.22 86.61 ±1.9 0.29 95.33 ±0.8 0.01 71.21 ±5.0 0.56 35.69 ±1.3 0.05 86.54 ±1.5 0.16 90.92 ±3.5 0.65 70.06 ±3.0 1.12 92.18 ±1.6 0.07 99.39 ±0.9 1.19 96.07 ±1.1 0.03 97.03 ±0.6 0.01 81.67 ±2.2 0.40

fNN Pred. Acc. Time %Ret. 90.32 ±1.8 15.7 96.5 89.44 ±1.5 4.0 89.7 96.57 ±1.7 2.91 92.1 87.11 ±1.8 7.59 91.9 74.61 ±3.4 18.2 89.1 69.16 ±1.3 0.64 84.4 81.52 ±2.0 1.32 89.3 87.11 ±0.9 0.43 88.5 69.02 ±1.6 2.90 83.7 85.18 ±2.0 3.66 91.1 96.00 ±0.8 0.29 95.6 74.09 ±3.9 7.62 87.7 42.19 ±1.5 0.81 54.9 86.06 ±1.2 1.91 94.1 91.07 ±2.9 8.42 95.9 69.97 ±2.9 13.5 89.9 92.64 ±1.3 1.18 95.1 98.79 ±1.3 16.1 99.1 96.63 ±0.7 0.54 98.1 93.07 ±1.1 0.19 95.6 83.53 ±1.8 5.39 90.11

kLim 9 11 9 7 21 9 13 9 11 13 1 15 11 5 13 13 3 1 5 1 9

best k-NN Pred. Acc. best k 91.76 ±2.4 1 89.76 ±1.4 21 96.85 ±2.0 17 87.68 ±1.6 13 73.09 ±4.2 17 70.19 ±2.0 1 83.17 ±2.7 33 85.16 ±1.0 7 70.38 ±2.6 7 86.61 ±1.9 1 97.33 ±0.8 15 75.52 ±4.2 17 43.07 ±1.5 29 86.54 ±1.5 1 90.92 ±3.5 1 70.06 ±3.0 1 93.56 ±1.0 5 99.39 ±0.9 1 97.75 ±0.7 31 97.03 ±0.6 1 84.29 ±2.0 11

mains where classification is very sensitive to the parameter k by using the k-NN algorithm. For these input data, we could summarize several aspects: – Without the need of parameter, fNN is a reduction and classification technique that keeps the average accuracy of the k-NN algorithm. – kLim and the size of Tf compared to the size of T are an approximated indicator for the percentage of examples that cannot be correctly classified by the k-NN algorithm. – The reduction of the database is very similar to the reduction that makes CNN [15], so that fNN is less restrictive than CNN. With large databases, this reduction can accelerate the learning process for the k-NN algorithm.

Non–parametric Nearest Neighbor with Local Adaptation

5

29

Future Work

Actually we are testing fNN with other classifiers. Particularly, we have chosen two systems, C4.5 [9] and HIDER [10], which generate decision trees and axis– parallel decision rules, respectively. Due to fNN makes a previous reduction, we have chosen the method EOP [1], which reduces databases conserving the decision boundaries that are parallel to the axis.

Acknowledgments The research was supported by the Spanish Research Agency CICYT under grant TIC99-0351. We thank the anonymous reviewers for providing helpful advice and suggestions that improved this work.

References 1. J. S. Aguilar, J. C. Riquelme, and M. Toro. Data set editing by ordered projection. In Proceedings of the 14th European Conference on Artificial Intelligence, pages 251–255, Berlin, Germany, August 2000. 2. D. W. Aha, D. Kibler, and M. K. Albert. Instance-based learning algorithms. Machine Learning, 6:37–66, 1991. 3. S. Arya, D. M. Mount, N. S. Netanyahu, R. Silverman, and A. Wu. An optimal algorithm for nearest neighbor searching. In Proceedings of 5th ACM SIAM Symposium on discrete Algorithms, pages 573–582, 1994. 4. C. Blake and E. K. Merz. Uci repository of machine learning databases, 1998. 5. S. Cost and S. Salzberg. A weighted nearest neighbor algorithm for learning with symbolic features. Machine Learning, 10:57–78, 1993. 6. T. M. Cover and P. E. Hart. Nearest neighbor pattern classification. IEEE Transactions on Information Theory, IT-13(1):21–27, 1967. 7. S.A. Dudani. The distance-weighted k-nearest-neighbor rule. IEEE Transactions on Systems, Man and Cybernetics, SMC-6, 4:325–327, 1975. 8. R. C. Holte. Very simple classification rules perform well on most commonly used datasets. Machine learning, 11:63–91, 1993. 9. J. R. Quinlan. C4.5: Programs for machine learning. Morgan Kaufmann, San Mateo, California, 1993. 10. J. C. Riquelme, J. S. Aguilar, and M. Toro. Discovering hierarchical decision rules with evolutive algorithms in supervised learning. International Journal of Computers, Systems and Signals, 1(1):73–84, 2000. 11. M. Stone. Cross-validatory choice and assessment of statistical predictions. Journal of the Royal Statistical Society B, 36:111–147, 1974. 12. I. Tomek. An experiment with the edited nearest-neighbor rule. IEEE Transactions on Systems, Man and Cybernetics, 6(6):448–452, June 1976. 13. C. Wettschereck. A Study of Distance-Based Machine Learning Algorithms. PhD thesis, Oregon State University, 1995. 14. D. Wettschereck and T.G. Dietterich. Locally adaptive nearest neighbor algorithms. Advances in Neural Information Processing Systems, (6):184–191, 1994. 15. D. R. Wilson and T. R. Martinez. Improved heterogeneous distance functions. Journal of Artificiall Intelligence Research, 6(1):1–34, 1997.

Selection Restrictions Acquisition from Corpora Pablo Gamallo , Alexandre Agustini



, and Gabriel P. Lopes

CENTRIA, Departamento de Inform´ atica Universidade Nova de Lisboa, Portgual {gamallo,aagustini,gpl}@di.fct.unl.pt

Abstract. This paper describes an automatic clustering strategy for acquiring selection restrictions. We use a knowledge-poor method merely based on word cooccurrence within basic syntactic constructions; hence, neither semantic tagged corpora nor man-made lexical resources are needed for generalising semantic restrictions. Our strategy relies on two basic linguistic assumptions. First, we assume that two syntactically related words impose semantic selectional restrictions to each other (cospecification). Second, it is also claimed that two syntactic contexts impose the same selection restrictions if they cooccur with the same words (contextual hypothesis). In order to test our learning method, preliminary experiments have been performed on a Portuguese corpus.

1

Introduction

The general aim of this paper is to describe a particular corpus-based method for semantic information extraction. More precisely, we implement a knowledgepoor system that uses syntactic information to acquire selection restrictions and semantic preferences constraining word combination. According to Gregory Grefenstette [9,10], knowledge-poor approaches use no presupposed semantic knowledge for automatically extracting semantic information. They are characterised as follows: no domain-specific information is available, no semantic tagging is used, and no static sources as machine readable dictionaries or handcrafted thesauri are required. Hence, they differ from knowledgerich approaches in the amount of linguistic knowledge they need to activate the semantic acquisition process. Whereas knowledge-rich approaches require previously encoded semantic information (semantic tagged corpora and/or man-made lexical resources [17,6,1]), knowledge-poor methods only need a coarse-grained notion of linguistic information: word cooccurrence. In particular, the main aim of knowledge-poor approaches is to calculate the frequency of word cooccurrences within either syntactic constructions or sequences of n-grams in order to extract semantic information such as selection restrictions [19,11,3], and word ontologies [12,15,9,13]. Since these methods do not require previously defined semantic knowledge, they overcome the well-known drawbacks associated with handcrafted thesauri and supervised strategies.  

Research supported by the PRAXIS XXI project, FCT/MCT, Portugal Research sponsored by CAPES and PUCRS - Brazil

P. Brazdil and A. Jorge (Eds.): EPIA 2001, LNAI 2258, pp. 30–43, 2001. c Springer-Verlag Berlin Heidelberg 2001 

Selection Restrictions Acquisition from Corpora

31

Nevertheless, our method differs from standard knowledge-poor strategies on two specific issues: both the way of extracting word similarity and the way of defining syntactic contexts. We use the contextual hypothesis to characterise word similarity and the co-specification hypothesis to define syntactic contexts. 1.1

The Contextual Hypothesis

In most knowledge-poor approaches to selection restriction learning, the process of inducing and generalising semantic information from word cooccurrence frequencies consists in automatically clustering words considered as similar. The best-known strategy for measuring word similarity is based on Harris’ distributional hypothesis. According to this assumption, words cooccurring in similar syntactic contexts are semantically similar and, then, should be clustered into the same semantic class. However, the learning methods based on the distributional hypothesis may lead to cluster in the same class words that fill different selection restrictions. Let’s analyse the following examples taken from [20]: (a) John worked till late at the council (b) John worked till late at the office (c) the council stated that they would raise taxes (d) the mayor stated that he would raise taxes On the basis of the distributional hypothesis, since council behaves similarly to office and mayor they would be clustered together into the same word class. Nevertheless, the bases for the similarity between council and office are different from those relating council and mayor. Whereas council shares with office syntactic contexts associated mainly with LOCATIONS (e.g., the argument of work at in phrases (a) and (b)), council shares with mayor contexts associated with AGENTS (e.g., the subject of state in phrases (c) and (d)). That means that a polysemous word like council should be clustered into various semantic word classes, according to its heterogeneous syntactic distribution. Each particular sense of the word is related to a specific type of distribution. Given that the clustering methods based on the distributional hypothesis solely take into account the global distribution of a word, they are not able to separate and acquire its different contextual senses. In order to extract contextual word classes from the appropriate syntactic constructions, we claim that similar syntactic contexts share the same semantic restrictions on words. Instead of computing word similarity on the basis of the too coarse-grained distributional hypothesis, we measure the similarity between syntactic contexts in order to identify common selection restrictions. More precisely, we assume that two syntactic contexts occurring with (almost) the same words are similar and, then, impose the same semantic restrictions on those words. That is what we call contextual hypothesis. Semantic extraction strategies based on the contextual hypothesis may account for the semantic variance of words in different syntactic contexts. Since these strategies are concerned with the extraction of semantic similarities between syntactic contexts, words will be

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Pablo Gamallo, Alexandre Agustini, and Gabriel P. Lopes

clustered with regard to their specific syntactic distribution. Such clusters represent context-dependent semantic classes. Except the cooperative system Asium introduced in [4,5,2], few or no research on semantic extraction have been based on such a hypothesis. 1.2

Co-specification

Traditionally, a binary syntactic relationship is constituted by both the word that imposes linguistic constraints (the predicate) and the word that must fill such constraints (its argument). In a syntactic relationship, each word plays a fixed role. The argument is perceived as the word specifying or modifying the syntactic-semantic constraints imposed by predicate, while the latter is viewed as the word specified or modified by the former. However, recent linguistic research assumes that the two w ords related by a syntactic dependency are mutually specified [16,8]. Each word imposes semantic conditions on the other word of the dependency, and each word elaborates them. Consider the relationship between the polysemic verb load and the polysemic noun books in the non ambiguous expression to load the books. On the one hand, the polysemic verb load conveys at least two alternate meanings: “bringing something to a location” (e.g., Ann loaded the hay onto the truck ), and “modifying a location with something” (e.g., Ann loaded the truck with the hay). This verb is disambiguated by taking into account the sense of the words with which it combines within the sentence. On the other hand, the noun book(s) is also a polysemic expression. Indeed, it refers to different types of entities: “physical objects” (rectangular book ), and “symbolic entities” (interesting book ). Yet, the constraints imposed by the words with which it combines allows the noun to be disambiguated. Whereas the adjective rectangular activates the physical sense of book, the adjective interesting makes reference to its symbolic content. In to load the books, the verb load activates the physical sense of the noun, while books leads load to refer to the event of bringing something to a location. The interpretation of the complex expression is no more ambiguous. Both expressions, load and books, cooperate to mutually restrict their meaning. The process of mutual restriction between two related words is called by Pustejovsky “co-specification” or “co-composition” [16]. Co-specification is based on the following idea. Two syntactically dependent expressions are no longer interpreted as a standard pair “predicate-argument”, where the predicate is the active function imposing the semantic preferences on a passive argument, which matches such preferences. On the contrary, each word of a binary dependency is perceived simultaneously as a predicate and an argument. That is, each word both imposes semantic restrictions and matches semantic requirements. When one word is interpreted as an active functor, the other is perceived as a passive argument, and conversely. Both dependent expressions are simultaneously active and passive compositional terms. Unlike most work on selection restrictions learning, our notion of “predicate-argument” frame relies on the active process of semantic co-specification, and not on the trivial operation of argument specification. This trivial operation only permits the one-way specification and disambiguation of

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33

the argument by taking into account the sense of the predicate. Specification and disambiguation of the predicate by the argument is not considered. In this paper, we describe a knowledge-poor unsupervised method for acquiring selection restrictions, which is based on the contextual and the cospecification hypotheses. The different parts of this method will be outlined in the next section.

2

System Overview

To evaluate the hypotheses presented above, a software package was developed to support the automatic acquisition of semantic restrictions. The system is constituted by four related modules, illustrated in Figure 1. In the following paragraphs we merely outline the overall functionalities of these modules. Then, in the remainder of the paper, we describe accurately the specific objects and processes of each module. Parsing: The raw text is tagged [14] and partially analysed [18]. Then, an attachment heuristic is used to identify binary dependencies. The result is a list of cooccurrence triplets containing the syntactic relationship and the lemmas of the two related head words. This module will be described in section 3.1 Extracting: The binary dependencies are used to extract the syntactic contexts. Unlike most work on selection restrictions learning, the characterisation of syntactic contexts relies on the dynamic process of co-specification. Then, the word sets that appear in those contexts are also extracted. The result is a list of contextual word sets. This module will be analysed in section 3.2. Filtering: Each pair of contextual word sets are statistically compared using a variation of the weighted Jaccard Measure [9]. For each pair of contextual sets considered as similar, we select only the words that they share. The result is a list of semantically homogenous word sets, called basic classes. Section 4.1 describes this module. Clustering: Basic classes are successively aggregated by a conceptual clustering method to induce more general classes, which represent extensionally the selection restrictions of syntactic contexts. We present this module in section 4.2. Finally, the classes obtained by clustering are used to update the subcategorisation information in the dictionary.1 The system was tested over the Portuguese text corpora P.G.R.2 . Some results are analysed in section 4.3. The fact of using specialised text corpora makes 1

2

The first tasks, tagging and parsing, are based on a non domain-specific dictionary for Portuguese, which merely contains morphosyntactic information. The subcategorisation restrictions extracted by our method are used to extend the morphosyntactic information of the dictionary. P.G.R. (Portuguese General Attorney Opinions) is constituted by case-law documents.

34

Pablo Gamallo, Alexandre Agustini, and Gabriel P. Lopes T a g g in g a n d S h a llo w P a rs in g A tta c h m e n t h e u ris tic s : id e n tify in g b in a r y d e p e n d e n c ie s P A R S IN G

e x tra c tio n o f s y n ta c tic c o n te x ts e x tra c tio n o f c o n te x tu a l w o r d s e ts E X T R A C T IN G

id e n tify in g s im ila r c o n te x tu a l s e ts e x tra c tio n o f b a s ic c la s s e s b y in te rs e c tin g s im ila r c o n te x tu a l s e ts F IL T E R IN G

c a lc u la tin g th e w e ig th o f b a s ic c la s s e s b u ild in g n e w c la s s e s a t le v e l n C L U S T E R IN G

D ic tio n a r y u p d a te

Fig. 1. System modules

easier the learning task, given that we have to deal with a limited vocabulary with reduced polysemy. Furthermore, since the system is not dependent of a specific language such as Portuguese, it could be applied to whatever natural language.

3

Identification of Binary Dependencies and Extraction of Syntactic Contexts

Binary dependencies and syntactic contexts are directly associated with the notion of selection restrictions. Selection restrictions are the semantic constraints that a word needs to match in order to be syntactically dependent and attached to another word. According to the co-specification hypothesis, two dependent words can be analysed as two syntactic contexts of specification. So, before describing how selection restrictions are learned, we start by defining first how binary dependencies are identified, and second how syntactic contexts are extracted from binary dependencies. 3.1

Binary Dependencies

We assume that basic syntactic contexts are extracted from binary syntactic dependencies. We use both a shallow syntactic parser and a particular attachment heuristic to identify binary dependencies. The parser produces a single partial syntactic description of sentences, which are analysed as sequences of basic chunks (NP, PP, VP, . . . ). Then, attachment is temporarily resolved by a simple heuristic based on right association (a chunk tend to attach to another chunk immediately to its right). Finally, we consider that the word heads of two

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35

attached chunks form a binary dependency. It can be easily seen that syntactic errors may appear since the attachment heuristic does not take into account distant dependencies.3 For reasons of attachment errors, it is argued here that the binary dependencies identified by our basic heuristic are mere hypotheses on attachment; hence they are mere candidate dependencies. Candidate dependencies will be checked by taking into account further information on the attached words. In particular, a candidate dependency will be checked and finally verified only if the two attached words impose selection restrictions to each other. Therefore, the test confirming or not a particular attachment relies on the semantic information associated with the related words. Let’s describe first the internal structure of a candidate dependency between two words. A candidate syntactic dependency consists of two words and the hypothetical grammatical relationship between them. We represent a dependency as the following binary predication: (r; w1↓ , w2↑ ). This binary predication is constituted by the following entities: – the binary predicate r, wich can be associated to specific prepositions, subject relations, direct object relations, etc.; – the roles of the predicate, “↓ ” and “↑ ”, which represent the head and complement roles, respectively; – the two words holding the binary relation: w1 and w2. Binary dependencies denote grammatical relationships between the head and its complement. The word indexed by “↓ ” plays the role of head, whereas the word indexed by “↑ ” plays the role of complement. Therefore, w1 is perceived as the head and w2 as the complement. Furthermore, the binary dependencies (i.e., grammatical relationships) we have considered are the following: subject (noted subj ), direct object (noted dobj ), prepositional object of verbs, and prepositional object of nouns, both noted by the specific preposition. 3.2

Extraction of Syntactic Contexts and Co-specification

Syntactic contexts are abstract configurations of specific binary dependencies. We use λ-abstraction to represent the extraction of syntactic contexts. A syntactic context is extracted by λ-abstracting one of the related words of a binary dependency. Thus, two complementary syntactic context can be λ-abstracted from the binary predication associated with a syntactic dependency: [λx↓ (r; x↓ , w2↑ )] and [λx↑ (r; w1↓ , x↑ )]. The syntactic context of word w2, [λx↓ (r; x↓ , w2↑ )], can be defined extensionally as the set of words that are the head of w2. The exhaustive enumeration of every word that can occur with that syntactic frame enables us to characterise extensionally its selection restrictions. Similarly, The syntactic context of word 3

The errors are caused, not only by the too restrictive attachment heuristic, but also by further misleadings, e.g., words missing from the dictionary, words incorrectly tagged, other sorts of parser limitations, etc.

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Pablo Gamallo, Alexandre Agustini, and Gabriel P. Lopes

w1, [λx↑ (r; w1↓ , x↑ )], represents the set of words that are complement of w1. This set is perceived as the extensional definition of the selection restrictions imposed by the syntactic context. Consider Table 1. The left column contains expressions constituted by two words syntactically related by a particular type of syntactic dependency. The right column contains the syntactic contexts extracted from these expressions. For instance, from the expression presidente da rep´ ublica (president of the republic), we extract two syntactic contexts: both [λx↓ (de; x↓ , rep´ ublica↑ )], where rep´ ublica plays the role of complement, ↑ and [λx (de; presidente↓ , x↑ )], where presidente is the head. Table 1. Syntactic contexts extracted from binary expressions Binary Expressions

Syntactic Contexts

presidente da rep´ ublica

[λx↓ (de;x↓ ,repu ´ blica↑ )], [λx↑ (de;presidente↓ ,x↑ )]

(president of the republic) nomea¸ c˜ ao do presidente

[λx↓ (de;x↓ ,presidente↑ )], [λx↑ (de;nomea¸ c˜ a o↓ ,x↑ )]

(nomination for president) nomeou o presidente

[λx↓ (dobj;x↓ ,presidente↑ )], [λx↑ (dobj;nomear ↓ ,x↑ )]

(nominated the president) discutiu sobre a nomea¸ c˜ ao

[λx↓ (sobre;x↓ ,nomea¸ c˜ a o↑ )], [λx↑ (sobre;discutir↓ ,x↑ )]

(disscussed about the nomination)

Since syntactic configurations impose specific selectional preferences on words, the words that match the semantic preferences (or selection restrictions) required by a syntactic context should constitute a semantically homogeneous word class. Consider the two contexts extracted from presidente da rep´ ublica. On the one hand, context [λx↑ (de; presidente↓ , x↑ )] requires a particular noun class, namely human organizations. In corpus P.G.R., this syntactic context selects for nouns such as rep´ ublica (republic), governo (government), instituto (institute), conselho (council ),. . . On the other hand, context [λx↓ (r; x↓ , rep´ u blica↑ )] requires nouns denoting either human beings or organizations: presidente (president), ministro (minister of state), assembleia (assembly), governo, (government) procurador (attorney), procuradoria-geral (attorneyship) , minist´ erio (state department), etc. It follows that the two words related by a syntactic dependency are mutually determined. The context constituted by a word and a specific function imposes semantic conditions on the other word of the dependency. The converse is also true. As has been said, the process of mutual restriction between two related words is called co-specification. In presidente da rep´ ublica, the context constituted by the noun presidente and the grammatical function head somehow restricts the sense of rep´ ublica. Conversely, both the noun rep´ ublica and the role of complement also restrict the sense of presidente: u blica↑ )] selects for presidente – [λx↓ (de; x↓ , rep´ ↑ – [λx (de; presidente↓ , x↑ )] selects for rep´ ublica

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37

In our system, the extraction module consists of the two following tasks: first, the syntactic contexts associated with all candidate binary dependencies are extracted. Then, the set of words appearing in those syntactic contexts are selected. The words appearing in a particular syntactic context form a contextual word set. Contextual word sets are taken as the input of the processes of filtering and clustering; these processes will be described in the next section. Let’s note finally that unlike the Grefenstette’s approach [9], information on co-specification is available for the characterisation of syntactic contexts. In [7], a strategy for measuring word similarity based on the co-specification hypothesis was compared to the Grefensetette’s strategy. Experimental tests demonstrated that co-specification allows a finer-grained characterisation of syntactic contexts.

4

Filtering and Clustering

According to the contextual hypothesis introduced above, two syntactic contexts that select for the same words should have the same extensional definition and, then, the same selection restrictions. So, if two contextual word sets are considered as similar, we infer that their associated syntactic contexts are semantically similar and share the same selection restrictions. In addition, we also infer that these contextual word sets are semantically homogeneous and represent a contextually determined class of words. Let’s take the two following syntactic contexts and their associated contextual word sets:   ↑ ↓ , x↑ ) = {article law norm precept statute . . .} λx↑ (of ; inf ringement λx (dobj; inf ringe↓ , x↑ ) = {article law norm principle right . . .} Since both contexts share a significant number of words, it can be argued that they share the same selection restrictions. Furthermore, it can be inferred that their associated contextual sets represent the same context-dependent semantic class. In our corpus, context [λx↑ (dobj; violar↓ , x↑ )] (to infringe) is not only a o↓ , x↑ )] (infringemen t of ), considered as similar to context [λx↓ (dobj; viola¸c˜ ↓ but also to other contexts such as: [λx (dobj; respeitar↓ , x↑ )] (to respect) and [λx↑ (dobj; aplicar↓ , x↑ )] (to apply). In this section, we will specify the procedure for learning context-dependent semantic classes from the previously extracted contextual sets. This will be done in two steps: – Filtering: word sets are automatically cleaned by removing those words that are not semantically homogenous. – Conceptual clustering: the previously cleaned sets are successively aggregated into more general clusters. This allows us to build more abstract semantic classes and, then, to induce more general selection restrictions. 4.1

Filtering

As has been said in the introduction, the cooperative system Asium is also based on the contextual hypothesis [4,5]. This system requires the interactive participation of a language specialist in order to filter and clean the word sets when

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Pablo Gamallo, Alexandre Agustini, and Gabriel P. Lopes

they are taken as input of the clustering strategy. Such a cooperative method proposes to manually remove from the sets those words that have been incorrectly tagged or analysed. Our strategy, by contrast, intends to automatically remove incorrect words from sets. Automatic filtering consists of the following subtasks: First, each word set is associated with a list of its most similar sets. Intuitively, two sets are considered as similar if they share a significant number of words. Various similarity measure coefficients were tested to create lists of similar sets. The best results were achieved using a particular weighted version of the Jaccard coefficient, where words are weighted considering their dispersion (global weight) and their relative frequency for each context (local weight). Word dispersion (global weight) disp takes into account how many different contexts are associated with a given word and the word frequency in the corpus. The local weight is calculated by the relative frequency f r of the pair word/context. The weight of a word with a context cntx is computed by the following formula: W (wordi , cntxj ) = log2 (f rij ) ∗ log2 (dispi ) where f rij =

f requency of wordi with cntxj sum of f requencies of words occurring in cntxj

and

 dispi =

j

f requency of wordi with cntxj

number of contexts with wordi

So, the weighted Jaccard similarity WJ between two contexts m and n is computed by4 :  (W (cntxm , wordi ) + W (cntxn , wordi )) i  W J(cntxm , cntxn ) = common j (W (cntxm , wordj ) + W (cntxn , wordj )) Then, once each contextual set has been compared to the other sets, we select the words shared by each pair of similar sets, i.e., we select the intersection between each pair of sets considered as similar. Since words that are not shared by two similar sets could be incorrect words, we remove them. Intersection allows us to clear sets of words that are not semantically homogenous. Thus, the intersection of two similar sets represents a semantically homogeneous class, which we call basic class. Let’s take an example. In our corpus, the most similar set to [λx↑ (de; viola¸c˜ao↓ , x↑ )] (infringement of )) is [λx↑ (dobj; violar↓ , x↑ )] (infringe) . Both sets share the following words: sigilo princ´ ıpios preceito plano norma lei estatuto disposto disposi¸ c˜ ao direito conven¸ c˜ ao artigo (secret principle precept plan norm law statute rule precept right convention article) 4

common means that just common words to both contexts m and n are computed

Selection Restrictions Acquisition from Corpora

39

This basic class does not contain incorret words such as vez, flagrantemente, obriga¸ c˜ ao, interesse (time, notoriously, obligation, interest), which were oddly associated to the context [λx↑ (de; viola¸c˜ao↓ , x↑ )], but which does not appear in context [λx↑ (dobj; violar↓ , x↑ )]. This class seems to be semantically homogenous because it contains only words referring to legal documents. Once basic classes have been created, they are used by the conceptual clustering algorithm to build more general classes. Note that this strategy do not remove neither infrequent nor very frequent words. Frequent and infrequent words may be semantic significant provided that they occur with similar syntactic contexts. 4.2

Conceptual Clustering

We use an agglomerative (bottom-up) clustering for successivelly aggregating the previously created basic classes. Unlike most research on conceptual clustering, aggregation does not rely on a statistical distance between classes, but on empirically set conditions and constraints [21]. These conditions will be discussed below. Figure 2 shows two basic classes associated with two pairs of similar syntactic contexts. [CON T Xi ] represents a pair of syntactic contexts sharing the words preceito, lei, norma (precept, law, norm, and [CON T Xj ] represents a pair of syntactic contexts sharing the words preceito, lei, direito (precept, law, right). Both basic classes are obtained from the filtering process described in the previous section. Figure 3 illustrates how basic classes are aggregated into more general clusters. If two classes fill the conditions that we will define later, they can be merged into a new class. The two basic classes of the example are clustered into the more general class constituted by preceito, lei, norma, direito. Such a generalisation leads us to induce syntactic data that does not appear in the corpus. Indeed, we induce both that the word norma may appear in the syntactic contexts represented by [CON T Xj ], and that the word direito may be attached to the syntactic contexts represented by [CON T Xi ].

[ C O N T X ij]

[C O N T X i ] p re c e ito

le i

n o rm a

le i

p re c e ito

d ire ito

n o rm a [C O N T X i ]

[C O N T X j ]

p re c e ito

le i

d ire ito

[C O N T X j ]

Fig. 2. Basic classes

Fig. 3. Agglomerative clustering

Two basic classes are compared and then aggregated into a new more general class if they fulfil three specific conditions:

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Pablo Gamallo, Alexandre Agustini, and Gabriel P. Lopes

1. They must have the same number of words. We consider that two classes are compared in a more efficient manner when they have the same number of elements. Indeed, nonsensical results could be obtained if we compare large classes, which still remain polysemic and then heterogeneous, to the small classes that are included in them. 2. They must share n−1 words. Two classes sharing n−1 words are aggregated into a new class of n + 1 members. Indeed, two classes with the same number of elements only differing in one word may be considered as semantically close. 3. They must have the highest weight. The weight of a class corresponds to the number of occurrences of the class as a subset of other classes (within n + 20 supersets). Intuitively, the more a class is included in larger classes, the more semantically homogeneous it should be. Only those classes with the highest weight will be compared and aggregated. Note that clustering does not rely here on a statistical distance between classes. Rather, clustering is guided by a set of constraints, which have been empirically defined considering linguistic data. Due to the nature of these constraints, the clustering process should start with small size classes with n elements, in order to create larger classes of n + 1 members. All classes of size n that fulfil the conditions stated above are aggregated into n + 1 clusters. In this agglomerative clustering strategy, level n is defined by the classes with n elements. The algorithm continues merging clusters at more complex levels and stops when there are no more clusters fulfilling the three conditions. 4.3

Tests and Evaluation

We used a small corpus with 1,643,579 word occurrences, selected from the caselaw P.G.R. text corpora. First, the corpus was tagged by the part-of- speech tagger presented in [14]. Then, it was analysed in sequences of basic chunks by the partial parser presented in [18]. The chunks were attached using the right association heuristic so as to create binary dependencies. 211,976 different syntactic contexts with their associated word sets were extracted from these dependencies. Then, we filter these contextual word sets by using the method described above so as to obtain a list of basic classes. In order to test our clustering strategy, we start the algorithm with basic classes of size 4 (i.e., classes with 4 elements). We have 7, 571 basic classes with 4 elements, but only a small part of them fills the clustering conditions so as to form 1, 243 clusters with 5 elements. At level 7, there are still 600 classes filling the clustering conditions, 263 at level 9, 112 at level 11, 38 at level 13, and finally only 1 at level 19. In table 2, we show some of the clusters generated by the algorithm at different intermediate levels.5 Note that some words may appear in different clusters. For instance, cargo (task/post) is associated with nouns referring to activities (e.g., actividade, 5

In the left column, the first number represents the weight of the set, i.e., its occurrences as subset of larger supersets; the second number represents class cardinality.

Selection Restrictions Acquisition from Corpora

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Table 2. Some clusters at levels 6, 7, 8, 9, 10, and 11 0006 (06) aludir citar enunciar indicar mencionar referir allude cite enunciate indicate mention refer 0009 (07) considerar constituir criar definir determinar integrar referir consider constitute create define determinate integrate refer 0002 (07) actividade atribui¸ c˜ ao cargo fun¸ c˜ ao fun¸ c˜ oes tarefa trabalho activity attribution position/task function functions task work 0003 (08) administra¸ c˜ ao cargo categoria exerc´ ıcio fun¸ c˜ ao lugar regime servi¸ co administration post rank practice function place regime service 0002 (09) abono indemniza¸ c˜ ao multa pens˜ ao propina remunera¸ c˜ ao renda san¸ c˜ ao vencimento bail compensation fine pension fee remuneration rent sanction salary 0007 (10) administra¸ c˜ ao autoridade comiss˜ ao conselho direc¸ c˜ ao estado governo ministro tribunal ´ org˜ ao administration authority commission council direction state government minister tribunal organ 0026 (11) al´ ınea artigo c´ odigo decreto diploma disposi¸ c˜ ao estatuto legisla¸ c˜ ao lei norma regulamento paragraph article code decret diploma disposition statute legislation law norm regulation

trabalho, tarefa (activity, work, task )), as well as with nouns referring to the positions where those activities are produced (e.g., cargo, categoria, lugar (post, rank, place)). The sense of polysemic words is represented by the natural attribution of a word to various clusters. Table 3. Some clusters generated at level 12 0002 (12) administra¸ c˜ ao associa¸ c˜ ao autoridade comiss˜ ao conselho direc¸ c˜ ao entidade estado governo ministro tribunal ´ org˜ ao administration association authority commission council direction entity state government minister government tribunal organ 0002 (12) administra¸ c˜ ao assembleia autoridade comiss˜ ao conselho direc¸ c˜ ao director estado governo ministro tribunal ´ org˜ ao administration assembly authority commission council direction director state government minister government tribunal organ 0002 (12) assembleia autoridade cˆ amara comiss˜ ao direc¸ c˜ ao estado europol governo minist´ erio pessoa servi¸ co ´ org˜ ao assembly authority chamber commission direction state europol government state department person service organ 0002 (12) administra¸ c˜ ao autoridade comiss˜ ao conselho direc¸ c˜ ao empresa estado gest˜ ao governo minist´ erio servi¸ co ´ org˜ ao administration authority commission council direction firm state management gouvernment state department person service organ

Since this clustering strategy have been conceived to assure the semantic homogeneity of clusters, it does not really assure that each cluster represents an independent semantic class. Hence, two or more clusters can represent the same contextual-based class and, then, the same semantic restriction. Let’s see

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Pablo Gamallo, Alexandre Agustini, and Gabriel P. Lopes

Table 3. Intuitively, the four clusters, which have been generated at level 12, refer to a general semantic class: agentive entities. Yet, the algorithm is not able to aggregate them into a more general cluster at level 13, since they do not fill condition 2. Further work should refine the algorithm in order to solve such a problem. Note that the algorithm does not generate ontological classes like human beings, institutions, vegetables, dogs,. . . but context-based semantic classes associated with syntactic contexts. Indeed, the generated clusters are not linguisticindependent objects but semantic restrictions taking part in the syntactic analysis of sentences. This way, the words autoridade, pessoa, administra¸ c˜ ao, etc. (authority, person, administration) belong to the same contextual class because they share a great number of syntactic contexts, namely they appear as the subject of verbs such as aprovar, revogar, considerar, . . . (approve, repeal, consider ). Those nouns do not form an ontological class but rather a linguistic class used to constrain the syntactic word combination. More precisely, we may infer that the following syntactic contexts:  ↑  ↓ ↑ λx↑ (subj; aprovar↓ , x↑ ) λx↑ (subj; revogar , x↓ ) ↑  λx (subj; considerar , x ) share the same selection restrictions since they are used to build a contextbased semantic class constituted by words like autoridade, pessoa, administra¸ ca ˜o, . . . As has been said, the acquired selection restrictions should be used to check the attachment hypotheses concerning the candidate dependencies previously extracted.

5

Conclusion and Further Work

This paper has presented a particular unsupervised strategy to automatically learn context-based semantic classes used as restrictions on syntactic combinations. The strategy is mainly based on two linguistic assumptions: co-specification hypothesis, i.e., the two related expressions in a binary dependency impose semantic restrictions to each other, and contextual hypothesis, i.e., two syntactic contexts share the same semantic restrictions if they cooccur with the same words. The system introduced in this paper will be applied to attachment resolution in syntactic analysis. The degree of efficacy in such a task may serve as a reliable evaluation for measuring the soundness of our learning strategy. This is part of our current work.

References 1. Roberto Basili, Maria Pazienza, and Paola Velardi. Hierarchical clustering of verbs. In Workshop on Acquisition of Lexical Knowledge from Text, pages 56–70, Ohio State University, USA, 1993.

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2. Gilles Bisson, Claire N´edellec, and Dolores Canamero. Designing clustering methods for ontology building: The mo’k workbench. In Internal rapport, citerseer.nj.nec.com/316335.html, 2000. 3. Ido Dagan, Lillian Lee, and Fernando Pereira. Similarity-based methods of word coocurrence probabilities. Machine Learning, 43, 1998. 4. David Faure and Claire N´edellec. Asium: Learning subcategorization frames and restrictions of selection. In ECML98, Workshop on Text Mining, 1998. 5. David Faure. Conception de m´ ethode d’aprentissage symbolique et automatique pour l’acquisition de cadres de sous-cat´ egorisation de verbes et de connaissances s´emantiques a ` partir de textes : le syst` eme ASIUM. PhD thesis, Universit´e Paris XI Orsay, Paris, France, 200. 6. Francesc Ribas Framis. On learning more appropriate selectional restrictions. In Proceedings of the 7th Conference of the European Chapter of the Association for Computational Linguistics, Dublin, 1995. 7. Pablo Gamallo, Caroline Gasperin, Alexandre Agustini, and Gabriel P. Lopes. Syntactic-based methods for measuring word similarity. In Text, Speech, and Discourse (TSD-2001). Berlin:Springer Verlag (to appear), 2001. 8. Pablo Gamallo. Construction conceptuelle d’expressions complexes: traitement de la combinaison nom-adjectif. PhD thesis, Universit´e Blaise Pascal, ClermontFerrand, France, 1998. 9. Gregory Grefenstette. Explorations in Automatic Thesaurus Discovery. Kluwer Academic Publishers, USA, 1994. 10. Gregory Grefenstette. Evaluation techniques for automatic semantic extraction: Comparing syntatic and window based approaches. In Branimir Boguraev and James Pustejovsky, editors, Corpus processing for Lexical Acquisition, pages 205– 216. The MIT Press, 1995. 11. Ralph Grishman and John Sterling. Generalizing automatically generated selectional patterns. In Proceedings of the 15th International on Computational Linguistics (COLING-94), 1994. 12. D. Hindle. Noun classification form predicate-argument structures. In Proceedings of the 28th Meeting of the ACL, pages 268–275, 1990. 13. Dekang Lin. Automatic retrieval and clustering of similar words. In COLINGACL’98, Montreal, 1998. 14. Nuno Marques. Uma Metodologia para a Modela¸c˜ ao Estat´istica da Subcategoriza¸c˜ ao Verbal. PhD thesis, Universidade Nova de Lisboa, Lisboa, Portugal, 2000. 15. Fernando Pereira, Naftali Tishby, and Lillian Lee. Distributional clustering of english words. In Proceedings of the 30th Annual Meeting of the Association of Comptutational Linguistics, pages 183–190, Columbos, Ohio, 1993. 16. James Pustejovsky. The Generative Lexicon. MIT Press, Cambridge, 1995. 17. Philip Resnik. Semantic similarity in taxonomy: An information-based measure and its application to problems of ambiguity in natural language. Journal of Artificial Intelligence Research, 11:95–130, 1999. 18. V. Rocio, E. de la Clergerie, and J.G.P. Lopes. Tabulation for multi-purpose partial parsing. Journal of Grammars, 4(1), 2001. 19. Satoshi Sekine, Jeremy Carrol, Sofia Ananiadou, and Jun’ichi Tsujii. Automatic learning for semantic collocation. In Proceedings of the 3rd Conference on Applied Natural Language Processing, pages 104–110, 1992. 20. Tokunaga Takenobu, Iwayama Makoto, and Tanaka Hozumi. Automatic thesaurus construction based on grammatical relations. In Proceedings of IJCAI-95, 1995. 21. Luis Talavera and Javier B´ejar. Integrating declarative knowledge in hierarchical clustering tasks. In Intelligent Data Analysis, pages 211–222, 1999.

Classification Rule Learning with APRIORI-C Viktor Jovanoski and Nada Lavraˇc J. Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia {Viktor.Jovanoski, Nada.Lavrac}@ijs.si

Abstract. This paper presents the APRIORI-C algorithm, modifying the association rule learner APRIORI to learn classification rules. The algorithm achieves decreased time and space complexity, while still performing exhaustive search of the rule space. Other APRIORI-C improvements include feature subset selection and rule post-processing, leading to increased understandability of rules and increased accuracy in domains with unbalanced class distributions. In comparison with learners which use the covering approach, APRIORI-C is better suited for knowledge discovery since each APRIORI-C rule has high support and confidence.

1

Introduction

Mining of association rules has received a lot of attention in recent years. Compared to other machine learning techniques, its main advantage is a low number of database passes done when searching the hypothesis space, whereas its main disadvantage is time complexity. One of the best known association rule learning algorithms is APRIORI [3,4]. This algorithm was extensively studied, adapted to other areas of machine learning and data mining, and successfully applied in many problem domains [5,15,1,14,2]. An association rule R has the form X ⇒ Y, f or X, Y ⊆ I, where I is a set of all items1 , and X and Y are itemsets. If f req(X) denotes the number of transactions that are supersets of itemset X, and N the number of all transactions, then Support(X) = f req(X) . Each rule is associated with its confidence N ) f req(X∪Y ) and support: Conf idence(R) = f req(X∪Y . f req(X) , and Support(R) = N This paper presents our algorithm APRIORI-C, based on APRIORI, whose modifications enable it to be used for classification. The basic APRIORI-C algorithm is described in Section 2. Given that the idea of using association rules for classification is not new [13], the main contribution of this paper are substantially decreased memory consumption and time complexity (described in Section 2), further decreased time-complexity by feature subset selection (Section 3), and improved understandability of results by rule post-processing (Section 4). 1

In machine learning terminology, an item is a binary feature. In association rule learning, a binary attribute Ai = vj is generated for each value vj of a discrete attribute Aj . For numeric attributes, items are formed by attribute discretization. Throughout this paper, items and features are used as synonyms.

P. Brazdil and A. Jorge (Eds.): EPIA 2001, LNAI 2258, pp. 44–51, 2001. c Springer-Verlag Berlin Heidelberg 2001 

Classification Rule Learning with APRIORI-C

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45

The Core of APRIORI-C

Association rule learning can be adapted for classification purposes by implementing the following steps: 1. Discretize continuous attributes. 2. For each discrete attribute with N values create N items: for a discrete value vi , i-th item of this attribute is assigned value 1, others are assigned value 0. In the case of a missing value, all items are assigned value 0. 3. Run an association rule learning algorithm. 4. Collect rules whose right-hand side consist of a single item, representing a value of the target attribute. 5. Use this set of rules to classify unclassified examples. To classify an unclassified example with all the rules found by the algorithm, first, sort rules according to some criteria, next, go through the list of all rules until the first rule that covers the example is found, and finally, classify the example according to the class at the right-hand side of this rule. If no rule covers the example, mark the example as unclassified. The above modifications are straightforward. Nevertheless, to better adapt the algorithm to classification purposes, APRIORI-C includes the following optimizations: Classification rule generation Rules with a single target item at the righthand side can be created during the search. To do so, the algorithm needs to save only the supported itemsets of sizes k and k + 1. This results in decreased memory consumption (improved by factor 10). Notice, however, that this does not improve the algorithm’s time complexity. Prune irrelevant rules Classification rule generation can be supressed if one of the existing generalizations of the rule has support and confidence above the given thresholds. To prevent rule generation, the algorithm simply excludes the corresponding itemset from the set of supported k+1-itemsets. Time and space complexity reduction are considerable (improved by factor 10 or more). Prune irrelevant items If an item cannot be found in any of the itemsets containing the target item, then it is impossible to create a rule containing this item. Hence, APRIORI-C prunes the search by discarding all itemsets containing this item. The above optimizations assume that we want to find only rules which have a single item, called a target item, at their right-hand side. Consequently, one has to run the algorithm for each target item, representing each individual class. The algorithm, named APRIORI-C, is outlined in Figure 1. APRIORI-C was evaluated on 17 datasets from the UCI ML databases repository (ftp://ftp.ics.uci.edu/pub/machine-learning-databases/). Most datasets contain continuous attributes which had to be discretized. This was done by using the K-Means clustering algorithm [16,7], which was an arbitrary choice.

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for each target item T k=1 C1 = set of all 1-itemsets check the support of all itemsets in C1 delete unsupported itemsets from C1 while Ck not empty do build all potentially supported k+1-itemsets put them into Ck+1 check their support delete unsupported itemsets from Ck+1 find all rules that have target item T at their right-hand side delete all itemsets that were used for constructing rules detect irrelevant items and delete irrelevant itemsets k =k+1 end while endfor Fig. 1. The APRIORI-C algorithm.

In the experiments, MinConfidence was set to 0.9, MinSupport to 0.03 and MaxRuleLength to 5. This setting works well for most of the datasets. For few other datasets, MinSupport had to be set to a higher value, e.g., 0.05 or even 0.1, to prevent combinatorial explosion. In contrast, for some other datasets the algorithm didn’t find any rule, hence MinSupport was set to 0.01. Using 10-fold cross-validation, the accuracy of APRIORI-C was compared to the accuracies of other machine learning algorithms (results reported in [18], using default parameter settings; notice that the accuracy of these algorithms could be further improved by parameter tuning). Results in Table 1 show that in datasets with few or no continuous attributes, APRIORI-C is at least as good as other algorithms, sometimes even slightly better (glass, tic-tac-toe and vote). However, APRIORI-C performs poorly on the datasets containing continuous attributes (e.g., balance, waveform and wine). Except for APRIORI-C, all the other algorithms handle continuous attributes by themselves and not in pre-processing. The poor results can be mainly attributed to the suboptimal discretization currently used in APRIORI-C.

3

Pre-processing by Feature Subset Selection

The most serious problem of APRIORI-C is that increased number of features results in an exponential increase in time complexity. Attribute correlations can also seriously affect the performance and accuracy. To deal with these problems, feature subset selection was employed to select a feature subset, sufficient for the learner to construct a classifier of similar accuracy in shorter time. The following four approaches were tested: statistical correlation, odds ratio, and two variants of the RELIEF algorithm [11,17,12]. Experiments showed that in the association rule learning context, feature subset selection needs to be sensitive to the difference in the meaning of attribute values 0 and 1: while value 1 is favorable for rule construction, value 0 is not used in a constructed rule, it just prohibits rule construction.

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Table 1. Results of APRIORI-C compared to other algorithms. Dataset australian balance breast-w bridges-td car diabetes echocardiogram german glass hepatitis hypothyroid image iris tic-tac-toe vote waveform wine

C4.5 CN2 kNN Ltree LBayes APRIORI-C 0.85 0.83 0.85 0.87 0.86 0.86 0.77 0.81 0.80 0.93 0.87 0.72 0.94 0.94 0.95 0.94 0.97 0.92 0.85 0.85 0.85 0.85 0.88 0.83 0.92 0.95 0.94 0.88 0.86 0.85 0.74 0.74 0.73 0.75 0.77 0.72 0.65 0.66 0.69 0.64 0.71 0.65 0.72 0.73 0.70 0.73 0.75 0.70 0.70 0.65 0.70 0.68 0.63 0.77 0.79 0.80 0.85 0.82 0.85 0.80 0.99 0.99 0.97 0.99 0.96 0.95 0.97 0.86 0.97 0.97 0.92 0.77 0.95 0.93 0.95 0.97 0.98 0.96 0.85 0.98 0.91 0.82 0.70 0.99 0.96 0.95 0.90 0.95 0.9 0.96 0.76 0.69 0.81 0.85 0.86 0.34 0.94 0.93 0.97 0.97 0.99 0.88

Statistical Correlation In association rule learning, strong correlations among items cause drastic increase of the number of supported itemsets. Correlated items were removed by first testing all the pairs of non-target items and removing one of them if the correlation was above the user defined threshold M axCorr. The algorithm complexity is O(n2 ) w.r.t. the number of items. Odds Ratio For target class C1 , union of all the non-target classes C2 , and n training examples, Odds ratio is computed for each feature F as follows: |C1 ) OddsRatio(F ) = log odds(F odds(F |C2 ) , where odds(F ) equals 1− 12 n 1 n2

if p(F ) = 1; and finally, equals

p(F ) 1−p(F )

1 n2 1 n2

1−

if p(F ) = 0; equals

if p(F ) = 0 and p(F ) = 1. Prob-

abilities are estimated using the relative frequency. Features are then sorted in the descending order of odds ratio values and the number of items is selected w.r.t the RatioOfSelectedItems parameter. Given that Odds ratio distinguishes between attribute values 1 and 0, it performs very well (see also results in [17]). VRELIEF in VRELIEF2 In the RELIEF algorithm below [12], q is a list of quality estimations, SampleSize is the user-defined number of randomly selected examples, and drx,i is the distance between examples r and x for item Ii . for each item Ii do q[Ii ] = 0 for j = 1 to Sample size do randomly select an example r find nearest hit t and nearest miss s for each item Ii do drs,i −drt,i q[Ii ]:=q[Ii ]+ Samplesize sort items according to measure q select the best items

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RELIEF is an excellent algorithm for feature subset selection, but in our problem it performs poorly since it makes no distinction between attribute values 0 and 1. Consequently, the original RELIEF distance function was changed: VRELIEF assigns higher quality to an item with value 1 for examples of the same class. Despite the significant accuracy increase, the algorithm often selects items that cause unnecessary increase in time complexity. Hence, the distance function in VRELIEF2 was changed so that items that increase the complexity without increasing accuracy receive lower quality estimation. The distance computations for training examples, labeled a and b, and values of the tested items for these two examples, are shown below: Class membership Class(a)=+ Class(b)=+ Class(a)=+ Class(b)=Class(a)=- Class(b)=+ Class(a)=- Class(b)=-

RELIEF VRELIEF valuea /valueb valuea /valueb 1/1 0/1 1/0 0/0 1/1 0/1 1/0 0/0 0 1 1 0 1 0 0 -1 0 1 1 0 0 -1 1 0 0 1 1 0 0 1 -1 0 0 1 1 0 -1 0 0 1

VRELIEF2 valuea /valueb 1/1 0/1 1/0 0/0 2 0 0 -2 -1 -2 2 0 -1 2 -2 0 -2 -1 -1 2

Results Algorithms Odds Ratio, VRELIEF and VRELIEF2 were tested with values of parameter RatioOfSelectedItems set to 0.2, 0.4, 0.6 and 0.8. Algorithm Statistical Correlation was tested with values of parameter M axCorr set to 0.2, 0.4, 0.6 and 0.8. For each value of the parameter, 10-fold cross-validation was performed and statistical t-test computed to see whether the best algorithm is significantly better than the others, both concerning the accuracy and complexity. Below is the summary of results: – The Odds Ratio algorithm is a good choice for nearly every value of the RatioOfSelectedItems parameter. Other algorithms often come close, but never surpass it. The values around 0.4 of this parameter usually suffice for achieving the same accuracy as if no feature subset selection were performed. – The Statistical correlation algorithm is often useful for cleaning the dataset as it only reduces the time complexity and retains the quality of results. The values around 0.5 of the M axCorr parameter are usually sufficient to drastically decrease the time complexity while retaining the same accuracy. Notice that this algorithm can easily be used in combination with other algorithms. – The VRELIEF and VRELIEF2 algorithms produce worse results in terms of accuracy when compared to Odds Ratio but they are better at decreasing the time complexity. The difference in performance between VRELIEF and VRELIEF2 is statistically insignificant.

4

Post-processing by Rule Subset Selection

Rule redundancy It is common that many subsets of the set of constructed rules cover almost the same training examples. Rule overflow The induced classifier is often not understandable since it includes too many rules. The user’s upper limit of understanding is a classifier with 10–15 rules. Depending on the choice of parameters, the original algorithm often created classifiers with more than 100 rules (even more than 500).

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Limited rule coverage The classifier often gives no answer, since no rule in the classifier fires for an instance to be classified. This problem is very serious when dealing with highly unbalanced class distributions. Majority class domination When class distribution is unbalanced, the rules classifying to the majority class prevail: there are so many of those, that rules for the minority class hardly make it into the classifier. This causes poor accuracy when classifying instances of the minority class. To deal with the above problems, APRIORI-C performs rule post-processing to select a rule subset with a comparable classification accuracy.

The default Rule Assignment After the algorithm selects the rules to be used in a classifier, some unclassified examples will probably remain in the set of training examples L. These unclassified examples contribute the majority of wrong classifications. Previous research confirmed that the probability of a wrong classification is much lower than the probability of the disability to classify an example. The simplest approach is to add a rule at the end of the rule list that will unconditionally classify an example to the majority class of the unclassified examples. The same approach, solving the problem of limited rule coverage, is used in the CN2 algorithm [8].

Select N Best Rules (and Select N Best Rules for Each Class) This algorithm uses the covering approach for rule subset selection. The number of rules to be selected is specified by the user-defined value of parameter N . The algorithm first selects the best rule (with highest support), then eliminates all the covered examples, sorts the remaining rules and again selects the best rule. This is repeated until the number of selected rules reaches the value of the parameter N or until there are no more rules to select or until there are no more examples to cover. The algorithm returns a sorted list of rules, and adds the default rule. select N C = {} put all rules into T put all the examples into L sort the rules in T according to their support and confidence in L while | C |< N and | L |> 0 and | T |> 0 do remove best rule r from T and add it to C remove the examples, covered by rule r, from L recalculate support and confidence of rules in T end while build the default rule and add it to C output = C This algorithm solves the problem of rule redundancy and rule overflow. Clearly, it also gives classifiers that execute faster. But it remains vulnerable to the problem of unbalanced class distribution. To solve this problem, the algorithm can be modified to select N rules for each class (if so many rules exist for each class). In this way the rules for the minority class also find their way into the constructed classifier.

Results Each algorithm was tested with several values of parameter N : 1, 2, 5, 10, 15 and 20. The main observations, confirmed by statistical tests, are outlined below: – Algorithms USE N BEST RULES and USE N BEST RULES FOR EACH CLASS do not differ in accuracy. Only when there are significant differences in class distributions, the USE N BEST RULES FOR EACH CLASS algorithm performs better.

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Next, both algorithms increase their accuracy significantly when using the default rule. This increase gets smaller with increasing value of parameter N , but it still remains noticeable. Finally, both algorithms achieve good results in terms of accuracy and understandability when the value of parameter N reaches 10. Accuracy results are comparable to the original algorithm. – We have implemented and tested also the CONFIRMATION RULE SUBSET SELECTION algorithm [9] which also employs a greedy approach, but without removing the covered examples. The accuracy of this algorithm is always slightly lower than the accuracy of the other two algorithms, since this algorithm does not build the default rule. – When comparing classifiers without the default rule, all algorithms achieve similar performance. This is probably due to the good quality of the rule set given as input to all the algorithms.

5

Conclusions

Using association rules for classification purposes has been addressed also by other researchers. Liu et al. [13] address the same problem. Their approach is similar to ours, but their algorithm for selecting rules to generate a classifier is more complicated and slower. They perform no feature subset selection and no post-processing. Bayardo and Agrawal [5,6] address the problem of mining constraint association rules. Implementing an efficient search for association rules given item constraints (useful for interactive mining) is described by Goethals and Bussche [10]. Their method of pruning is closely related to the APRIORI-C method of eliminating irrelevant itemsets. This paper presents a new algorithm from the field of association rule learning that successfully solves classification problems. The APRIORI-C algorithm is a modification of the well-known APRIORI algorithm, making it more suitable for building rules for classification, due to the decreased time and space complexity, whereas the algorithm still exhaustively searches the rule space. Feature subset selection is best done using Odds Ratio, whereas post-processing is best done using the SELECT N BEST RULES or the SELECT N BEST RULES FOR EACH CLASS algorithms (for N = 10), together with the default rule. In UCI domains APRIORI-C achieved results comparable to algorithms that have been designed for classification purposes. Given comparable accuracy, the advantage of APRIORI-C is that each of its rules represents a reasonable “chunk” of knowledge about the problem. Namely, each individual rule is guaranteed to have high support and confidence. This is important for knowledge discovery, as shown in the CoIL challenge: despite average classification accuracy, the induced rules were evaluated as very useful for practice. Most of the practically useful rules (or, better yet, conclusions) reported in the CoIL challenge were discovered by APRIORI-C as well.

Acknowledgements The work was supported by the Slovenian Ministry of Education, Science and Sport, and the IST-1999-11495 project Data Mining and Decision Support for Business Competitiveness: A European Virtual Enterprise.

References 1. K. Ali, S. Manganaris and R. Shrikant. Partial Classification using Association Rules. In Proceedings of the Third International Conference on Knowledge Discovery and Data Mining KDD 1997, Newport Beach, California.

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2. R. Agrawal, J.Gehrke, D. Gunopulos and P. Raghavan. Authomatic Subspace Clustering of High Dimensional Data for Data Mining Applications. In Proceedings of ACM SIGMOD Conference on Management of Data, 1998. 3. R. Agrawal, T. Imielinski and R. Shrikant. Mining Association Rules between Sets of Items in Large Databases. In Proceedings of ACM SIGMOD Conference on Management of Data, Washington, D.C., 1993. pp. 207-216. 4. R. Agrawal and R. Srikant. Fast Algorithms for Mining Association Rules. In Proc. of the 20th Int’l Conference on Very Large Databases, Santiago, Chile, September 1994. pp. 207-216. 5. R. J. Bayardo Jr., R. Agrawal and D. Gunopulos. Constraint-Based Rule Mining in large, Dense Databases. In Proceedings of the 15th International Conference on Data Engineering, 1999. pp. 188-197. 6. R. J. Bayardo Jr. and R. Agrawal. Mining the most Interesting Rules. In Proceedings of the 5th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 1999. pp. 145-154. 7. P. S. Bradley, U. M. Fayyad. Refining Initial Points for K-Means Clustering. In Proceedings of International Conference on Machine Learning ICML’98. pp. 91-99. 8. P. Clark and T. Niblett. The CN2 induction algorithm. Machine Learning 3: 261283, 1989. 9. D. Gamberger, N. Lavraˇc, C. Groselj. Diagnostic Rules of Increased Reliability for Critical Medical Applications. In Proceedings of Artificial Intelligence in Medicine. Joint European Conference on Artificial Intelligence in Medicine and Medical Decision Making, AIMDM’99, Aalborg, Denmark, June 1999. 10. B. Goethals and J. v.d.Bussche. On Supporting Interactive Association Rule Mining. In Proceedings of the Second International Conference on Data Warehousing and Knowledge Discovery, Lecture Notes in Computer Science Springer-Verlag, September 4-6, 2000, London-Greenwich, United Kingdom. 11. D. Koller, M. Sahami. Toward Optimal Feature Selection. In ICML-96: Proceedings of the Thirteenth International Conference on Machine Learning, pp. 284-292, San Francisco, CA: Morgan Kaufmann. 12. I. Kononenko. On Biases in Estimating Multi-Valued Attributes. In Proceedings of the 14th International Joint Conference on Artificial Intelligence IJCAI-95, pp. 1034-1040, 1995. 13. B. Liu, W. Hsu and Y. Ma. Integrating Classification and Association Rule Mining. Proceedings of the Fourth International Conference on Knowledge Discovery and Data Mining KDD’98, New York, USA, 1998. 14. H. Mannila and H. Toivonen. Discovering Generalized Episodes using Minimal Occurences, In Proceedings of the Second International Conference on Knowledge Discovery and Data Mining KDD96, 1996. 15. N. Megiddo and R. Shrikant. Discovering Predictive Association Rules. In Proceedings of the Fourth International Conference on Knowledge Discovery and Data Mining KDD’98, New York, USA, 1998. 16. M. Meila, D. Heckerman. An Experimantal Comparison of Several Clustering and Initialisation Methods. Technical report MSR-TR-98-06, Microsoft research, 1998. 17. D. Mladeni´c. Feature Subset Selection in Text-Learning. In Proceedings of 10th European Conference on Machine Learning ECML’98. pp. 121-129. 18. L. Todorovski and S. Dˇzeroski. Combining Multiple Models with Meta Decision Trees. In Proc. ECML2000 Workshop on Meta-learning: Building Automatic Advice Strategies for Model Selection.

Proportional Membership in Fuzzy Clustering as a Model of Ideal Types S. Nascimento1,2 , B. Mirkin3 , and F. Moura-Pires4 1

3

Faculdade de Psicologia e Ciˆencias da Educa¸ca ˜o–LEAD, UL 2 Dep. Inform´ atica and CENTRIA, FCT-UNL PORTUGAL School of Computer Science and Information Systems, Birkbeck College London, UK 4 ´ Departamento de Inform´ atica, Universidade de Evora PORTUGAL

Abstract. The goal of this paper is to further investigate the extreme behaviour of the fuzzy clustering proportional membership model (FCPM) in contrast to the central tendency of fuzzy c-means (FCM). A data set from the field of psychiatry has been used for the experimental study, where the cluster prototypes are indeed extreme, expressing the concept of ‘ideal type’. While augmenting the original data set with patients bearing less severe syndromes, it is shown that the prototypes found by FCM are changed towards the more moderate characteristics of the data, in contrast with the almost unchanged prototypes found by FCPM, highlighting its suitability to model the concept of ‘ideal type’. Keywords: Fuzzy clustering; fuzzy model identification; proportional membership; ideal type.

1

Introduction

In previous work [1], [2], the fuzzy clustering proportional membership model (FCPM) was introduced and studied. In contrast to other fuzzy clustering approaches, FCPM is based on the assumption that the cluster structure is reflected in the data from which it has been constructed. More specifically, the membership of an entity in a cluster expresses the proportion of the cluster prototype reflected in the entity, according to FCPM. One of the phenomena observed in an extensive experimental study performed with simulated data, was that the cluster prototypes tend to express an extreme rather than average behaviour within a cluster [2]. The other approaches such as fuzzy c-means (FCM) tend to produce clusters whose prototypes are averaged versions of the relevant entities (up to degrees of the relevance) [3]-[5]. The goal of this paper is to further investigate this property of FCPM. Having a cluster structure revealed in a data set, we question how sensible is this cluster structure with regard to augmenting of the data set by entities that bear more or less similarity to the cluster prototypes. We take a specific data set [6] from the field of psychiatry where the cluster prototypes are indeed extreme to express P. Brazdil and A. Jorge (Eds.): EPIA 2001, LNAI 2258, pp. 52–62, 2001. c Springer-Verlag Berlin Heidelberg 2001 

Proportional Membership in Fuzzy Clustering as a Model of Ideal Types

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severe syndromes of mental conditions and we augment this set with patients bearing less severe syndromes and explore whether the prototypes are changed or not. Yes, they are changed towards the more moderate characteristics with FCM. However, there is almost no change under FCPM, which shows that this domain may be a natural habitat of the FCPM approach.

2 2.1

The Fuzzy Clustering Proportional Membership Model (FCPM) The Proportional Membership Model

In the clustering model, we assume the existence of some prototypes, offered by the knowledge domain, that serve as “ideal” patterns to data entities. To relate the prototypes to observations, we assume that the observed entities share parts of the prototypes. The underlying structure of this model can be described by a fuzzy c-partition defined in such a way that the membership of an entity to a cluster expresses proportion of the cluster’s prototype reflected in the entity (proportional membership). This way, the underlying structure is substantiated in the fitting of data to the “ideal” patterns. To be more specific, let X = [xkh ] denote a n × p entity-to-feature data table where each entity, described by p features, is defined by the row-vector xk = [xkh ] ∈ p (k = 1 · · · n ; h = 1 · · · p). Let data matrix X be preprocessed into Y = [ykh ] by shifting the origin to the gravity center of all the entities (rows) in Y and rescaling features (columns) by their ranges. This data set can be structured according to a fuzzy c-partition which is a set of c clusters, any cluster i (i = 1, · · · , c) being defined by: 1) its prototype, a row-vector vi = [vih ] ∈ p , and 2) its membership values {uik } (k = 1 · · · n), so that the following constraints hold for all i and k: 0 ≤ uik ≤ 1 c uik = 1.

(1a) (1b)

i=1

Let us assume that each entity yk of Y is related to each prototype vi up to its membership degree uik ; that is, uik expresses the proportion of vi which is present in yk in such a way that approximately ykh = uik vih for every feature h. More formally, we suppose that ykh = uik vih + εikh ,

(2)

where the residual values εikh are as small as possible. These equations provide a feedback from a cluster structure to the data. According to (2), a clustering criterion can be defined to fit each data point to each of the prototypes up to the degree of membership. This goal is achieved by minimizing all the residual values εikh via one of the least-squares criteria

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S. Nascimento, B. Mirkin, and F. Moura-Pires

Em (U, V ) =

p c n

2 um ik (ykh − uik vih ) ,

(3)

i=1 k=1 h=1

subject to constraints (1a) and (1b), where m = 0, 1, 2 is a pre-specified parameter. The equations in (2) along with the least-squares criteria (3) to be minimized by unknown parameters U and V = (v1 , v2 , . . . , vc ) ∈ cp for Y given, are designated as the generic FCPM model. The models corresponding to m = 0, 1, 2 are denoted as FCPM-0, FCPM-1, and FCPM-2, respectively [2]. In FCPM, both, prototypes and memberships, are reflected in the model of data generation. The equations (2) can be considered as a device to reconstruct the data from the model. The clustering criteria follow the least-squares framework to warrant that the reconstruction is as exact as possible. Other scalarizations of the idea of minimization of the residuals can be considered as well. 2.2

Ideal Type and FCPM

Each prototype, vi , according to (2), is an “ideal” point such that any entity, yk , bears a proportion of it, uik , up to the residuals. The proportion, uik , is considered as the value of membership of yk to the cluster i, representing thus, the extent entity yk is characterized by the corresponding “ideal” point vi . This allows us to consider this model as relevant to the concept of ideal type in logics. M. Weber [1864-1920] defines that ‘The ideal type is such a combination of characteristics that no real entity can satisfy all of them, though the entities can be compared by their proximity to the ideal type’ (quoted from [6]). An ideal type represents a concept self-contained and entirely separated from all the other (ideal) types. As our simulation experiments have shown, the model indeed tends to reveal somewhat extreme points as the cluster prototypes, especially when FCPM-2 is employed [2]. This will be further explored in the remainder. 2.3

FCPM and FCM

The criteria (3) can be expressed in terms of the distances between observed entities yk and cluster prototypes vi as follows: Em (U, V ) =

c n

um ik d(yk , uik vi )

(4)

k=1 i=1

where d(a, b) is the Euclidean distance (squared) between p-dimensional vectors a and b. This shows that these criteria are parallel, to an extent, to those minimized in the popular fuzzy c-means method (FCM) [3]: Bm (U, V ) =

c n k=1 i=1

um ik d(yk , vi ).

(5)

Proportional Membership in Fuzzy Clustering as a Model of Ideal Types

55

The major difference is that FCPM takes the distances between entities yk and their ‘projections’ on the axes joining 0 and cluster prototypes while FCM takes the distances between yk and prototypes themselves. This leads to the following differences in respective algorithms and solutions: 1. The alternating optimization algorithm is straightforward in FCM because its criterion (5) very well separates the sets of variables related to centroids and to membership. On the contrary, the alternating optimization in FCPM requires some work when optimizing the membership, because it is not separated from centroids in (4). 2. FCM gives poor results when m = 0 or m = 1 [3], while these values of m are admissible in FCPM and lead to interesting results [2]. In particular, in FCPM-0 each entity is considered as a part of each prototype, leading to such effects as automatically adjusting the number of clusters to smaller values. On the other hand, in FCPM-1 and FCPM-2 larger proportions uik have larger weights over the smaller ones, thus overcoming the rigidity of FCPM-0. We will stick to the most contrasting of these models, FCPM-2, in this paper. 3. FCM tends to produce prototypes as averaged versions of their clusters, while FCPM would tend keep prototypes outside of the data cloud. 4. In FCPM, the following phenomenon occurs which has no analogues in FCM. Given centroids vi , minimizing (4) over uik would tend to minimize distances d(yk , uik vi ) by projecting yk onto axes joining 0 and vi thus leading to uik vi being these projections. This would require a careful choice of the location of the origin of the space in FCPM, which is irrelevant in FCM. In particular, putting the origin into the gravity center (grand mean) point would make all potential extreme prototypes much differing from each other in the framework of FCPM. Figure 1 illustrates this aspect geometrically. Consider two data points, y1 and y2 , and a prototype, v1 , in the original reference frame (Figure 1A). It is apparent from the figure that the projection of each data point onto prototype v1 , u11 v1 and u12 v1 correspond to close values. Let us consider the reference frame centered on the mean of the data, y, instead (Figure 1B). Now, the prototype is v1 , and the projections, u11 v1 and u12 v1 , of each data point, become much more distinct from each other. A similar construction may be devised for prototype v2 and v2 in each reference frame. Moreover, if the original reference frame is used, one may question the utility of having two prototypes (v1 and v2 ), whereas in the transformed reference frame the corresponding prototypes (v1 and v2 ) become very much distinct. 2.4

FCPM Algorithm

An FCM like alternating optimization (AO) algorithm has been developed in order to minimize the FCPM criteria [2]. Each iteration of the algorithm consists of two steps as follows.

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Fig. 1. How the distinction between prototypes vi and corresponding projections, uik vi , of data points yk are affected by the choice of the origin of the space in the framework of FCPM model. A. Data points and prototypes in the original reference frame; B. Same data points and prototypes in the transformed reference frame, where its relative position to the original reference frame is depicted in A.

First, given a prototype matrix V , the optimal membership values are found by minimizing one of the criteria (3). In contrast to FCM, minimization of each criteria subject to constraints (1a) and (1b) is not an obvious task; it requires an iterative solution on its own. The gradient projection method [8],[9] has been selected for finding optimal membership values (given the prototypes). It can be proven that the method converges fast for FCPM-0 with a constant (anti)gradient stepsize. Let us denote the set of membership vectors satisfying conditions  (1a) and

(t) (t) (1b) by Q. The calculations of the membership vectors uk = uik are based

 (t) (t) on vectors dk = dik : (t)

(t−1)

dik = uik



−

(6) (m+1)

2αm (m + 2) vi , vi  uik

−

m−1 2(m + 1) vi , yk  um ik + m yk , yk  uik

 (t)

where αm is a stepsize parameter of the gradient method. Then, uk is to be (t) (t) taken as the projection of dk in Q, denoted by PQ (dk )1 . The process stops 1

(t)

The projection PQ (dk ) is based on an algorithm we developed for projecting a (t) (t) vector dk over the simplex of membership vectors uk ; its description is omitted here.

Proportional Membership in Fuzzy Clustering as a Model of Ideal Types

57

when the condition U (t) − U (t−1) ≤ ε is fulfilled, with |·|err an appropriate matrix norm. Second, given a membership matrix U , the optimal prototypes are determined according to the first-degree optimum conditions as m+1 (t) ykh uik   m+2 , n (t) u k=1 ik

n



k=1

(t)

vih =

(7)

with m = 0, 1, 2. Thus, the algorithm consists of “major” iterations of updating matrices U and V and “minor” iterations of recalculation of membership values in the gradient projection method within each of the “major” iterations. The algorithm starts with a set V (0) of c arbitrarily specified prototype points in p and U (0) ; it stops when the difference between successive prototype matrices becomes small or a maximum number of iterations t1 max is reached (in our experiments t1 max = 100). The algorithm converges only locally (for FCPM-1 and FCPM-2). Moreover, with a “wrong” number of clusters pre-specified, FCPM-0 may not converge at all due to its peculiar behaviour: it may shift some prototypes to infinity [2].

3 3.1

Experimental Study Contribution Weights

The concept of ‘importance weight’ of a variable is useful in cluster analysis. In particular the following relative contributions of a variable h to a cluster i, w(h|i) and to the overall data scatter, w(h), will be considered in this study [6], [7]: v2 w(h|i) = ih (8) v 2ih h c

v 2ih ni

w(h) = i=1 k,h

2 ykh

(9)

 where v ih denotes the gravity center of (hard) cluster i, i.e. v ih = k∈Ci ykh /ni , with Ci = {k : uik = 1}, and ni = |Ci | , the number of entities belonging to cluster i. Note that the farther v ih is from zero (which, due to our data standardization is the grand mean), the easier is to separate that cluster from the other ones in terms of variable h, which is reflected in the weight values. Due to this, w(h|i) might be viewed as a measure of the “degree of interestingness” of variable h in cluster i with regard to its “standard” mean value. Let us define the ‘most contributing’ features within a cluster and to the overall data structure,  as the ones greater than the averages of (8) and (9),  w (h|i) /p and h h w (h) /p respectively, which may act as frontier values.

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Table 1. Relative contributions of the 17 psychosomatic variables (h1 -h17 ) to classes D, M , Ss and Sp ; and to the data scatter according to the original partition structure. The features values higher than corresponding averages are marked. h h1 h2 h3 h4 h5 h6 h7 h8 h9 h10 h11 h12 h13 h14 h15 h16 h17 w

3.2

D w(h|D) 4.27 2.36 2.28 2.70 14.17 1.30 1.18 9.95 15.60 3.44 1.76 1.76 16.88 1.36 0.59 0.00 5.44 5.00

M w(h|M ) 3.87 1.67 16.17 0.00 3.44 3.76 0.67 13.99 4.94 1.39 0.53 0.71 6.26 0.46 0.49 8.39 16.40 4.89

Ss Sp General w(h|Ss ) w(h|Sp ) w(h) 0.22 0.04 2.07 3.75 2.19 2.02 7.31 0.03 5.58 0.54 1.49 1.06 1.00 2.19 5.07 4.42 1.41 2.20 1.70 0.99 0.92 12.76 8.93 9.57 0.59 2.28 5.74 4.28 8.37 3.43 2.79 16.40 3.97 1.00 12.50 3.02 0.13 6.12 7.00 3.01 5.35 1.92 0.70 6.45 1.54 20.92 1.27 5.64 11.14 2.00 7.45 4.50 4.60 4.01

Fuzzy Clustering of Mental Disorders Data

A mental disorders data set [6] was chosen, consisting of 44 patients, described by seventeen psychosomatic features (h1 -h17 ). The features are measured on a severity rating scale taking values of 0 to 6. The patients are partitioned into four classes of mental disorders: depressed (D), manic (M ), simple schizophrenic (Ss ) and paranoid schizophrenic (Sp ). Each class contains eleven consecutive entities that are considered ‘archetypal psychiatric patients’ of that class. The mental disorders data set shows several interesting properties. First, there is always a pattern of features (a subset of h1 -h17 ) that take extreme values (either 0 or 6) and clearly distinguish each class. Better still, some of these features take opposite values among distinct classes. However, some feature values are shared by classes leading to overlaps. Given these characteristics, each disease is characterized by ‘archetypal patients’ that show a pattern of extreme psychosomatic feature values defining a syndrome. Table 1 presents the relative weights, w (h|i) (defined by (8)), of features h1 -h17 to classes D, M , Ss and Sp and to the data scatter, w(h) (9), according to the original partition structure. The corresponding averages, w, are listed at the bottom row. All values are in percent, and the values corresponding to the ‘most contributing’ features are marked.

Proportional Membership in Fuzzy Clustering as a Model of Ideal Types

59

The algorithms FCPM-2 and FCM (with its parameter m = 2) have been run starting from the same initial points, setting the number of clusters to four (i.e. c = 4). Table 2 shows the prototypes found by FCM and FCPM-2, in the original data scale, where the marked values belong to the set of the most contributing weight features within a cluster. Comparing the results, it is clear that the feature-values of FCPM-2 prototypes are more extreme than corresponding ones obtained by FCM (which is in accordance with our previous studies [2]). Moreover, in the prototypes found by FCPM-2 some of the feature values move outside the feature scale. In fact, all these ‘extreme’ values belong to the set of features that contribute the most to the whole partition or, at least, to a cluster (Table 1). In particular, these features present the highest discriminating power to separate the corresponding cluster from the remaining ones. This property of FCPM prototypes goes in line with suggestions in data mining that the more deviant a feature is from a standard (the grand mean, in this case), the more interesting it is. Concerning the membership values found, both algorithms assign the highest belongingness of an entity to its original class, correctly clustering all entities to the corresponding class2 .

3.3

Clustering of Augmented Mental Disorders Data

In order to study FCPM-2 behaviour on revealing extreme prototypes against FCM based central prototypes, the original data set should be modified to get in less expressed cases. To achieve that, each class was augmented with six midscale patients and three light-scale patients. Each new patient, xg = [xgh ], was generated from a randomly selected original patient, xk = [xkh ], applying the transformation: xgh = round (sF · xkh ) + t (for all h = h1 , · · · , h17 ), with scalefactor sF = 0.6 to obtain a mid-scale patient and sF = 0.3 to obtain a light-scale patient. The shift parameter t is a random number between 0 or 1. Table 3 shows the prototypes (v) found in the original data set followed by corresponding ones (v ) for the augmented data, for each algorithm, where the values of features with the highest weights are also marked. Most of FCM prototypes extreme feature values (in v’s) move towards in termediate feature values (in v ’s), showing FCM tendency to reveal central prototypes. Contrastingly, in FCPM-2 prototypes, the most weighting features maintain their full-scale (i.e. extreme) values, reinforcing the ‘extreme’ nature of FCPM-2 prototypes, and consequently, their sensitivity to the most discriminating features, despite the presence of new mid- and light-scale patients. 2

The only exception occurs for entity (21) from class M , which is assigned to class Sp ; the same phenomenon is reported in [6] for other clustering algorithms as complete linkage, K-means and separate-and-conquer.

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Table 2. Cluster prototypes ( vD , vM , vSs , vSp ), revealed by FCM and FCPM-2, presented in the original space. Values corresponding to the most contributing weight features are marked. h h1 h2 h3 h4 h5 h6 h7 h8 h9 h10 h11 h12 h13 h14 h15 h16 h17

4

vD 4 4 5 2 5 2 1 0 6 2 2 1 5 3 3 2 1

F CM vM 1 2 0 3 1 5 1 6 1 4 2 1 0 4 3 0 6

vSs 3 2 5 3 1 2 2 1 2 2 2 1 2 2 3 5 0

vSp 3 4 3 4 1 4 3 5 2 5 5 4 1 5 5 2 4

vD 6 5 6 1 7 1 0 -1 8 0 1 0 7 2 2 3 -1

F CP M -2 vM vSs 0 2 1 0 -2 6 3 3 0 0 6 0 0 3 7 -1 0 1 4 1 2 1 1 0 -1 3 4 1 2 2 -1 7 8 -1

vSp 4 5 4 6 0 5 4 6 1 6 7 6 -1 6 7 1 5

Conclusion

Modelling the concept of ‘ideal type’ through the notion of ‘proportional membership’ appears to be a promising aspect to be explored in the FCPM model. The results of the experimental study clearly outline the extreme behaviour of FCPM prototypes in contrast with the central tendency of FCM prototypes, particularly when the data set was augmented with new patients more or less similar to the cluster prototypes. Since the extreme feature values of FCPM correspond to the most contributing weights, the proportional membership has a discriminating power to separate clusters from each other. Moreover, this extreme behaviour appears to be compatible with the notion of “interestingness” in data mining, since it is sensitive to the feature-values that are farthest from the average. In terms of applications, the concept of ‘ideal type’ fits to such domain areas as psychiatry or market research, where a prototype (such as mental disturbance or consumer profile, in the examples given) is well characterized by extreme conditions. Modeling such a concept through fuzzy clustering seems appealing and useful as a part of the decision making process in those application areas. The extension of this preliminary experimental study using more vast data sets is fundamental to firmly establish the found results and better outline the model properties and its relevance in the application to several domain areas.

Proportional Membership in Fuzzy Clustering as a Model of Ideal Types

61

Table 3. Prototypes found by FCM and FCPM-2, in the original data set (v’s) and in the augmented data set (v  ’s), characterizing each mental disorder: D, M , Ss and Sp . h h1 h2 h3 h4 h5 h6 h7 h8 h9 h10 h11 h12 h13 h14 h15 h16 h17

vD 4 4 5 2 5 2 1 0 6 2 2 1 5 3 3 2 1

 vD 4 4 4 2 4 2 1 0 5 2 2 1 4 2 3 2 1

vM 1 2 0 3 1 5 1 6 1 4 2 1 0 4 3 0 6

F  vM 1 2 1 3 1 4 1 5 1 3 2 2 1 4 3 1 5

CM  vSs vSs 3 2 2 2 5 4 3 2 1 1 2 2 2 2 1 1 2 2 2 2 2 2 1 1 2 2 2 2 3 2 5 3 0 1

vSp 3 4 3 4 1 4 3 5 2 5 5 4 1 5 5 2 4

 vSp 3 4 3 4 1 4 2 4 2 4 5 4 1 5 5 1 4

vD 6 5 6 1 7 1 0 -1 8 0 1 0 7 2 2 3 -1

 vD 5 5 5 1 7 1 0 -1 7 0 1 1 7 2 2 3 0

vM 0 1 -2 3 0 6 0 7 0 4 2 1 -1 4 2 -1 8

F CP  vM 0 1 -1 3 0 6 0 7 0 4 2 1 -1 4 3 -1 7

M -2  vSs vSs 2 2 0 0 6 5 3 2 0 0 0 0 3 2 -1 -1 1 1 1 1 1 0 0 0 3 2 1 1 2 1 7 6 -1 -1

vSp 4 5 4 6 0 5 4 6 1 6 7 6 -1 6 7 1 5

 vSp 4 5 4 5 0 5 4 6 1 6 7 6 0 6 7 1 4

Acknowledgments One of the authors (S.N.) acknowledges FCT-Portugal for the Ph.D. grant between 1997-1999 (PRAXIS XXI).

References 1. Nascimento, S., Mirkin, B., Moura-Pires, F.: Multiple Prototypes Model for Fuzzy Clustering. In Kok, J., Hand, D. and Berthold, M., (eds.), Advances in Intelligent Data Analysis. Third International Symposium, (IDA’99), Lecture Notes in Computer Science, 1642, Springer-Verlag. (1999) 269–279 2. Nascimento, S., Mirkin, B., Moura-Pires, F.: A Fuzzy Clustering Model of Data with Proportional Membership. The 19th International Conference of the North American Fuzzy Information Processing Society (NAFIPS 2000). IEEE (2000) 261266 3. Bezdek, J.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press, New York (1981) 4. Bezdek, J., Keller, J., Krishnapuram, R., Pal, T.: Fuzzy Models and Algorithms for Pattern Recognition and Image Processing. Kluwer Academic Publishers (1999) 5. H¨ oppner, F., Klawonn, F., Kruse, R., Runkler, T.: Fuzzy Cluster Analysis. John Wiley and Sons (1999) 6. Mirkin, B.: Mathematical Classification and Clustering. Kluwer Academic Publishers (1996) 7. Mirkin, B.: Concept Learning and Feature Selection Based on Square-Error Clustering. In Machine Learning, 25(1) (1999) 25-40

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8. Polyak, B.: Introduction to Optimization. Optimization Software, Inc., New York (1987) 9. Bertsekas, D.: Nonlinear Programming. Athena Scientific (1995)

Evolution of Cubic Spline Activation Functions for Artificial Neural Networks Helmut A. Mayer and Roland Schwaiger Department of Computer Science University of Salzburg A–5020 Salzburg, Austria {helmut,rschwaig}@cosy.sbg.ac.at

Abstract. The most common (or even only) choice of activation functions (AFs) for multi–layer perceptrons (MLPs) widely used in research, engineering and business is the logistic function. Among the reasons for this popularity are its boundedness in the unit interval, the function’s and its derivative’s fast computability, and a number of amenable mathematical properties in the realm of approximation theory. However, considering the huge variety of problem domains MLPs are applied in, it is intriguing to suspect that specific problems call for specific activation functions. Biological neural networks with their enormous variety of neurons mastering a set of complex tasks may be considered to motivate this hypothesis. We present a number of experiments evolving structure and activation functions of generalized multi–layer perceptrons (GMLPs) using the parallel netGEN system to train the evolved architectures. For the evolution of activation functions we employ cubic splines and compare the evolved cubic spline ANNs with evolved sigmoid ANNs on synthetic classification problems which allow conclusions w.r.t. the shape of decision boundaries. Also, an interesting observation concerning Minsky’s Paradox is reported.

1

Introduction

While many researchers have investigated a variety of methods to improve Artificial Neural Network (ANN) performance by optimizing training methods, learn parameters, or network structure, comparably few work has been done towards using activation functions other than the logistic function. It has been shown that a two–hidden–layer MLP with sigmoidal activation function can implement arbitrary convex decision boundaries [1]. Moreover, such an MLP is capable of forming an arbitrarily close approximation to any continous nonlinear mapping [2]. However, common to these theorems is that the number of neurons in the layers is at best bounded, but can be extremely large for practical purposes. E.g., for a one–hidden–layer MLP Barron (1993) derived a proportionality of the sum square error (SSE) to the number of neurons according to SSE ∼ √1T with T being the number of neurons (for target functions having a Fourier representation) [3]. P. Brazdil and A. Jorge (Eds.): EPIA 2001, LNAI 2258, pp. 63–73, 2001. c Springer-Verlag Berlin Heidelberg 2001 

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Helmut A. Mayer and Roland Schwaiger

If we consider the simple example of a rectangular function, it becomes obvious that a rectangular activation function can approximate this target function much easier than a sigmoidal function. 1.1

Related Work

Liu and Yao (1996) evolved the structure of Generalized Neural Networks (GNN) with two different activation function types, namely, sigmoid and Gaussian basis function. Experiments with the Heart Disease data set from the UCI machine learning benchmark repository revealed small differences in classification error slightly favoring GNNs over ANNs solely using sigmoid or Gaussian basis activation function [4]. Vecci et al. (1998) introduced the Adaptive Spline Neural Network (ASNN), where activation functions are described by Catmull–Rom cubic splines. ANN error (including a regularization term) then is not only dependent on the weights, but also on the spline parameters which together with the weights are adapated by backpropagation learning. It has been reported that ASNNs yield a performance comparable to networks using the logistic AF, while using a smaller number of hidden neurons than the conventional network [5]. Sopena et al. (1999) presented a number of experiments (with widely–used benchmark problems) showing that multilayer feed–forward networks with a sine activation function learn two orders of magnitude faster while generalization capacity increases (compared to ANNs with logistic activation function) [6].

2

Evolution of ANN Structure and Activation Functions

The technical platform for the evolution of GMLPs is the netGEN system searching a problem–adapted ANN architecture by means of an Evolutionary Algorithm (EA), and training the evolved networks using the Stuttgart Neural Network Simulator (SNNS) [7]. In order to speed up the evolutionary process, an arbitrary number of workstations may be employed to train individual ANNs in parallel. The ANN’s genetic blueprint is based on a direct encoding suggested by Miller et al. [8]. The basic structure of the genotype is depicted in Figure 1.

L e a rn P a ra m e te rs

N e u ro n P a ra m e te rs

S tru c tu re P a ra m e te rs

Fig. 1. The organization of the ANN genotype.

The binary encoded GMLP chromosome contains three main sections. The Learn Parameters encode values used for ANN training, the Neuron Parameters are used to describe the activation function of each neuron, and the Structure Parameters explicitely specify each connection of the network (direct encoding).

Evolution of Cubic Spline Activation Functions

E p o c h s

L e a rn 1

L e a rn 2

H id d e n N e u ro n s ’ A c tiv a tio n F u n c tio n s (h )

O u tp u t N e u ro n s ’ A c tiv a tio n F u n c tio n s (o )

C o n tro l P o in ts (n )

H id d e n M a rk e r

P o in t M a rk e r

x 1

y 1

P o in t M a rk e r

x 2

y 2

65

C o n tro l P o in ts (n )

P o in t M a rk e r

x n

y n

H id d e n M a rk e r

P o in t M a rk e r

x 1

y 1

P o in t M a rk e r

x n

y n

Fig. 2. Details of the learn parameter section (above) and the neuron parameter section (below) of the ANN genotype.

Figure 2 shows the details of the learn parameter and the neuron parameter section. The learn parameter section contains the number of epochs and two learning parameters for the selected training algorithm Resilient Back–propagation (RProp) [9]. The evolution of the number of epochs for ANN training is a measure to avoid overfitting with the additional benefit of another critical ANN parameter being discovered by evolution. The most interesting feature of the neuron parameter section are Markers – single bases (bits) which are a simple analogue to activators/repressors regulating the expression of wild–type genes. A hidden neuron marker determines, if the specific neuron associated with it is present in the decoded network. As the number of output neurons is usually strictly dependent on the specific problem the ANN should learn, these neurons are not controlled by markers. The activation function for each neuron is composed by a maximum number of n control points of a cubic spline. In order to also allow fewer control points, each control point is “regulated” by a point marker. It should be noted that, if a neuron marker indicates the absence (or pruning) of a particular neuron, all control points for the cubic spline activation function and all connections associated with that neuron become obsolete. As a consequence, most ANN chromosomes contain noncoding regions. When using the logistic AF, only the hidden neuron markers are contained in the neuron parameter section. ANN structure is represented by a linearized binary adjacency matrix. As in this work we are only concerned with feed–forward architectures, all elements of the upper triangle matrix must be 0, hence they are not included in the ANN genotype. Due to this linearization we are able to use the standard 2–point crossover operator for recombination. Technically, the hidden neuron markers are stored in the main diagonal of the connection matrix constructed from the genotype’s structure section as shown in Fig. 3 for an exemplary network. The maximum number of hidden neurons (neuron markers) has to be set in advance with this encoding scheme, hence, it could be labeled as Evolutionary Pruning, since the system imposes an upper bound on the complexity of the network.

66

Helmut A. Mayer and Roland Schwaiger H id d e n N e u ro n s C o n n e c tio n s to N e u ro n h 1

O u tp u t N e u ro n s

C o n n e c tio n s to N e u ro n h 2

C o n n e c tio n s to N e u ro n h m

F ro m 1 T o 1 0 2 0 3 1 4 1 5 1 2

3

4

C o n n e c tio n s to N e u ro n o 1

C o n n e c tio n s to N e u ro n o n

5

0

0

0

0

0

0

0

0

1

1

0

0

0

0

0

0

0

1

1

0

5

3

H id d e n M a rk e rs (fro m N e u ro n S e c tio n )

1

4 2

Fig. 3. Genotype/Phenotype mapping of ANN structure.

2.1

ANN Fitness Function

The ANN fitness function comprises a complexity regularization term Ec = |Ctotal |, with Ctotal being the set of all network connections. The Composite Fitness Function F is given by a weighted sum of Model Fitness and Complexity Fitness F = α1

1 1 + α2 1 + Em 1 + Ec

(1)

with α1 + α2 = 1.0, and Em being the model error. Earlier work showed that α2 in the range of 0.001 − 0.01 is sufficient to guide the evolution towards ANNs of low complexity. In effect the complexity term acts as a ”tie–breaker” between different ANNs with (nearly) identical model error, where the less complex network receives a slightly better fitness. In this work we set α1 = 0.99. 2.2

EA and ANN Parameters

The following EA and ANN parameters have been used with all the experiments in this paper: EA Parameters: Population Size = 50, Generations = 50, Crossover Probability pc = 0.6, Mutation Probability pm = 0.005, Crossover = 2–Point, Selection Method = Binary Tournament. ANN Parameters: Network Topology = Generalized Multi–Layer Perceptron, Activation Function (hidden and output neurons) = Sigmoid or evolved Cubic Splines, Output Function (all neurons) = Identity, Training = RProp, Learning Parameters Δ0 (max 1.0), Δmax (max 50.0), Number of Training Epochs (max 1000) = Evolutionary.

Evolution of Cubic Spline Activation Functions

2.3

67

Cubic Spline Parameters

A cubic spline activation function is described by n control points (xi , yi ) ∈ R where i = 1, . . . , n. These n points define n − 1 intervalls on the x-axis denoted by x ∈ [xi , xi+1 ] with xi+1 > xi . In each of these intervalls a function fi (x) is defined by fi (x) = fi (xi ) + ai (x − xi ) + bi (x − xi )2 + ci (x − xi )3

(2)

with constants ai , bi , ci ∈ R. Demanding equality of the function value, and the first and second derivative at the interval borders the constants can be determined for each interval yielding a continous and differentiable function composed of a number of cubic splines. With respect to the ANN genotype (Fig. 2) the maximum number of control points nc has to be set prior to the evolutionary run. Also, the x–, and y–range of the cubic spline activation function has to be fixed to specific intervals [xmin , xmax ] (sensitivity interval) and [amin , amax ] (activation interval), respectively. However, within these bounds the evolutionary process may freely float. For all experiments we set the number of control points nc = 8 and the activation interval [amin , amax ] = [0.0, 1.0]. The sensitivity interval depends on the specific problem.

3

Experimental Setup

The experiments have been devised in order to answer two main questions. The first one is simply, if the rather complex organization of the ANN genotype containing genetic information on the neurons’ activation function allows the evolutionary process to find any valid and reasonable networks. Thus, like cohorts of ANN researchers, we start out with the very simple but still interesting XOR problem. The second question to be adressed is the performance of a cubic spline network in comparison to a GMLP with conventional, sigmoidal AFs. Intuitively, the decision boundaries in classification problems could be modeled more easily by cubic splines of great plasticity than by the “frozen” logistic function. Thus, we choose the simple continous XOR problem with piece–wise linear decision boundaries, and the synthetic, but nevertheless hard Two Spirals problem with complex, nonlinear decision boundaries. During the evolutionary process the ANN structure is trained on a training set and evaluated on a validation set (ANN fitness). Finally, the performance of the evolved best net is measured on a test set. Each evolutionary run is repeated 20 times. For the XOR problem we use a network with two input and one output neuron. The binary output value 1 is defined by an activation of the output neuron ao > 0.5, otherwise the output is mapped to 0. All pattern sets contain the only four example patterns.

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The continous XOR (cXOR) problem is defined by a division of the unit square into four squares of identical area being separated by the lines x = 0.5 and y = 0.5. The lower left and the upper right square are labeled with binary value 1, the two remaining squares represent the class with binary value 0. The corresponding ANN has an I/O–representation identical to the simple XOR problem. The training set is composed of 100 randomly selected points in the unit square, the validation set contains 200 random patterns, and the test set is made of 10,000 equally spaced points covering the complete unit square. The task in the Two Spirals problem is to discriminate between two sets of points which lie on two distinct spirals in the plane. These spirals coil three times around the origin and around one another [10]. Training, validation, and test set comprise 194 patterns each. The basic ANN structure is defined by two input neurons and two output neurons (one for each spiral, winner takes all). For these classification problems the model error in the fitness function is simply given by Em = nevv , where ev is the number of misclassifications on the validation set, and nv its respective size.

4

Experimental Results

For the XOR problem we only evolved networks with cubic spline AFs. We set the maximum number of hidden neurons to three and the sensitivity interval of the neurons’ cubic spline AF to [−10.0, 10.0]. In order to enable a more detailed fitness assignment we used Em = M SE for the model error (Equ. 1). After 20 runs the average MSE of the single best nets of each run was 6.45 × 10−6 . Four of the best nets had a single hidden neuron, while the other 16 ANNs simply consisted of the two linear inputs and the output neuron with a cubic spline AF. These two simple structures are depicted in Figure 4.

Fig. 4. Only two evolved XOR structures (white/input neuron, black/neuron with cubic spline AF).

The details of two evolved XOR nets are shown in Fig. 5. When performing the calculations for the four possible input patterns, it can be seen that only a small portion of the sensitivity interval is used. Specifically, the big peak in each AF exceeding the activation interval seems to be useless, however, it could be argued that the steep slope provided by these peaks is profound guidance for the training algorithm. The most interesting property of these networks is that they seem to contradict the well–known fact that a single perceptron cannot learn the XOR function

Evolution of Cubic Spline Activation Functions

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(Minsky’s Paradox [11]). In a strict sense a perceptron is defined having a threshold AF, but even a logistic AF does not resolve Minsky’s Paradox. While these functions have the desirable non–linearity, they are monotonous in contrast to the non–monotonous evolved cubic spline AFs. In all the reported aftermath of Minsky’s work, it seems ironic that a simple triangle activation function would have resolved the paradox. Recently, Rueda and Oommen (2000) reported on this observation in the context of statistical pattern recognition proposing pairwise linear classifiers [12]. A non–monotonous triangle AF being a simplification of the sinusoidally shaped parts of the cubic spline AFs in Fig. 5 transforms the ANN into a pairwise linear classifier. In Table 1 the results for the continous XOR (cXOR) problem are presented.

Table 1. cXOR – Structure parameters, classification accuracy (Acc) with standard deviation (StdDev) and overall best performance of evolved ANNs (averaged on 20 runs).

AF

Structure Hidden Connections Sigmoid 2.80 10.70 Spline 2.50 9.70

cXOR Validation Set Test Set Acc StdDev Acc StdDev Best 0.9878 0.0053 0.9679 0.0065 0.9752 0.9780 0.0092 0.9583 0.0132 0.9767

Again, we set the maximum number of hidden neurons to three and the sensitivity interval of the cubic splines to [−10.0, 10.0]. The results slightly favor the sigmoid networks, however, the best overall ANN found is a cubic spline net (Fig. 6), even though the search space of the latter is much larger. While the genotype for the network with logistic AF consists of 39 bases, the cubic spline net chromosome comprises 538 bases.

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In Fig. 7 the output neuron value for the complete unit square by the best sigmoidal and the best cubic spline ANN is shown.

Fig. 7. cXOR – Output neuron activation for unit square of the best evolved sigmoid ANN (left) and the best evolved spline ANN(right)(darker = lower value).

Although, the classification results of both nets are nearly identical, it can be seen that the spline net has found a very sharp and accurate decision boundary for x = 0.5, and a more fuzzy boundary at y = 0.5. The sigmoid net exhibits uniform activations (due to monotonicity of the AF), but has slight problems to accurately model the vertical and horizontal decision boundaries. The results of GMLPs evolved for the Two Spirals problem are presented in Table 2. The upper bound of hidden neurons has been set to 16, and the sensitivity interval of cubic splines to [−100.0, 100.0]. In addition to the evolutionary runs we present results (20 different initial sets of random weights) of a standard

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Table 2. TwoSpirals – Structure parameters, classification accuracy (Acc) with standard deviation (StdDev) and overall best performance of evolved and standard (not evolved) ANNs (averaged on 20 runs). TwoSpirals Structure Validation Set Hidden Connections Acc StdDev Standard 16.00 64.00 0.6173 0.0281 Sigmoid 14.90 130.70 0.8541 0.0273 Spline 10.15 58.20 0.7090 0.0385 AF

Acc 0.6150 0.8379 0.6791

Test Set StdDev Best 0.0303 0.6701 0.0327 0.8918 0.0502 0.7887

sigmoid network with one hidden layer (16 neurons) for which the evolved learn parameters of the best evolved sigmoid net have been used. Here the performance of the evolved sigmoidal nets is clearly superior to the spline networks, but the difference in search space size (234 bases sigmoid, 2682 bases spline) might be the main reason for these results. In order to gather some evidence for this explanation, we started a single run evolving spline nets for 500 generations (instead of 50) and found a network (9 hidden, 36 connections) with an accuracy of 0.8711 and 0.8969 on validation and test set, respectively. As this single run took approx. 60 hours on 22 Linux PCs (200–800MHz Pentiums), we are working on a substantial speedup of the evolutionary process by using (very) early stopping techniques for ANN training. In Fig. 8 the classification of the unit square by the best evolved ANNs (Table 2) is depicted.

Fig. 8. TwoSpirals – Unit square classification by best evolved sigmoid ANN (left) and best evolved spline ANN (right), and the test set (middle).

Both evolved ANNs generate non–contigous subspaces for the two classes which make misclassifications inevitable. Though, the spline net has lower classification accuracy, the decision boundaries are of a shape closer resembling the spirals than those of the sigmoid net. However, the spirals are only defined in the areas shown in the middle figure (Fig.8), and these areas are classified more

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accurately by the sigmoid net. A specific source of error for the spline net is located in the upper right quadrant, where a black area is inside the inmost grey ring (falsely) covering a part of the grey spiral. As indicated above, further evolution of the complex cubic spline genes could eliminate such artefacts.

5

Summary

We have reported on experiments evolving structure and activation functions of generalized multi–layer perceptrons. We compared evolution of ANNs with the widely used logistic activation function in each hidden and output neuron to networks with cubic spline activation functions. Each neuron in the spline net can have a different nonlinear, non–monotonous activation function of (nearly) arbitrary shape. The non–monotonicity of these activation functions led the way to solve the XOR problem with only a single neuron which is impossible by using monotonous activation functions. Further experiments with the more complex two spirals problem favored the evolved sigmoid nets. However, the one order of magnitude larger genotype of the spline networks could be the main reason for this result. By inspecting the decision boundaries of the two types of networks the potential of the spline nets to model linear and circular boundaries of class subspaces with great accuracy have been demonstrated. Also, with the two spirals problem the number of hidden neurons and connections of a spline network was found to be considerably smaller than that of a sigmoid network. This is in accordance to reports on the adaptive spline neural networks presented in [5]. Continuing work will explore the use of cubic splines with improved locality, as a single mutation in a cubic spline gene can dramatically change the shape of the whole activation function. More advanced classes of cubic splines avoid this behavior, and a change of a single control point will result in only a local change of the cubic spline in the neighborhood of this point. Moreover, techniques to decrease the training time of ANNs are currently investigated so as to decrease the running time of network evolution employing the parallel netGEN system.

References 1. Lippmann, R.P.: An introduction to computing with neural nets. IEEE Acoustics, Speech and Signal Processing 4 (1987) 4–22 2. Cybenko, G.: Approximation by superpositions of a sigmoidal function. Mathematics of Control, Signals, and Systems 2 (1987) 303–314 3. Barron, A.R.: Universal approximation bounds for superpositions of a sigmoidal function. IEEE Transactions on Information Theory 39 (1993) 930–944 4. Liu, Y., Yao, X.: Evolutionary Design of Artificial Neural Networks with Different Nodes. In: Proceedings of the Third IEEE International Conference on Evolutionary Computation. (1996) 570–675 5. Vecci, L., Piazza, F., Uncini, A.: Learning and approximation capabilities of adaptive spline activation function neural networks. Neural Networks (1998) 259–270

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6. Sopena, J.M., Romero, E., Alqu´ezar, R.: Neural networks with periodic and monotonic activation functions: a comparative study in classification problems. In: Proceedings of the 9th International Conference on Artificial Neural Networks. (1999) 7. Zell, A., Mamier, G., Vogt, M., Mach, N., Huebner, R., Herrmann, K.U., Soyez, T., Schmalzl, M., Sommer, T., Hatzigeogiou, A., Doering, S., Posselt, D.: SNNS Stuttgart Neural Network Simulator, User Manual. University of Stuttgart (1994) 8. Miller, G.F., Todd, P.M., Hegde, S.U.: Designing neural networks using genetic algorithms. In Schaffer, J.D., ed.: Proceedings of the Third International Conference on Genetic Algorithms, San Mateo, California, Philips Laboratories, Morgan Kaufman Publishers, Inc. (1989) 379–384 9. Riedmiller, M., Braun, H.: A direct adaptive method for faster backpropagation learning: The RPROP algorithm. In: Proceedings of the IEEE International Conference on Neural Networks, San Francisco, CA (1993) 10. CMU-Repository: ftp://ftp.cs.cmu.edu/afs/cs.cmu.edu/ project/connect/bench/. WWW Repository, Carnegie Mellon University (1993) 11. Minsky, M.L., Papert, S.A.: Perceptrons: Introduction to Computational Geometry. Expanded edn. MIT Press (1988) 12. Rueda, L., Oommen, B.J.: The Foundational Theory of Optimal Bayesian Pairwise Linear Classifiers. In: Proceedings of Joint IAPR International Workshops SSPR 2000 and SPR 2000 (LNCS 1876), Springer (2000) 581–590

Multilingual Document Clustering, Topic Extraction and Data Transformations Joaquim Silva1 , Jo˜ ao Mexia2 , Carlos A. Coelho3 , and Gabriel Lopes1 1

DI / FCT / Universidade Nova de Lisboa Quinta da Torre, 2725 Monte da Caparica, Portugal {jfs, gpl}@di.fct.unl.pt 2 DM / FCT / Universidade Nova de Lisboa Quinta da Torre, 2725 Monte da Caparica, Portugal 3 DM / ISA / Universidade T´ecnica de Lisboa, Tapada da Ajuda, Portugal [email protected]

Abstract. This paper describes a statistics-based approach for clustering documents and for extracting cluster topics. Relevant Expressions (REs) are extracted from corpora and used as clustering base features. These features are transformed and then by using an approach based on Principal Components Analysis, a small set of document classification features is obtained. The best number of clusters is found by ModelBased Clustering Analysis. Data transformations to approximate to normal distribution are done and results are discussed. The most important REs are extracted from each cluster and taken as cluster topics.

1

Introduction

We aimed at developing an approach for automatically separating documents from multilingual corpora into clusters. We required no prior knowledge about document subject matters or language and no morphosyntactic information was used, since we wanted a language independent system. Moreover, we also wanted to extract the main topics characterizing the documents in each cluster. Clustering software usually needs a matrix of objects characterized by a set of features. In order to obtain those features, we used LocalMaxs algorithm to automatically extract REs from corpora [1]. These REs, such as Common agriculture policy, Common Customs, etc., provide important information about the content of the texts. Therefore we decided to use them as base features for clustering. The most informative REs correspond to cluster topics, as we will show. This paper is organized as follows: features extraction is explained in section 2; data transformations to approximate to normality, clustering and summarization in sections 3 and 4; section 5 presents and discusses results obtained; related work and conclusions are drawn in section 6 and 7.

P. Brazdil and A. Jorge (Eds.): EPIA 2001, LNAI 2258, pp. 74–87, 2001. c Springer-Verlag Berlin Heidelberg 2001 

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Extracting Multiword Features from Corpora

We used LocalMaxs algorithm, Symmetric Conditional Probability (SCP) statistical measure and Fair Dispersion Point Normalization (FDPN) to extract REs from any corpus. A full explanation of these tools is given in [1]. However, a brief description is presented here. Thus, let us consider that an n-gram is a string of words in any text1 . For example the word rational is an 1-gram; the string rational use of energy is a 4-gram. LocalMaxs is based on the idea that each n-gram has a kind of cohesion sticking the words together within the n-gram. Different n-grams usually have different cohesion values. One can intuitively accept that there is a strong cohesion within the n-gram (Bill, Clinton) i.e. between the words Bill and Clinton. However, one cannot say that there is a strong cohesion within the n-gram (or, if ) or within the (of, two). Thus, the SCP (.) cohesion value of a generic bigram (x, y) is obtained by SCP ((x, y)) = p(x|y).p(y|x) =

p(x, y)2 p(x).p(y)

(1)

where p(x, y), p(x) and p(y) are the probabilities of occurrence of bigram (x, y) and unigrams x and y in the corpus; p(x|y) stands for the conditional probability of occurrence of x in the first (left) position of a bigram, given that y appears in the second (right) position of the same bigram. Similarly p(y|x) stands for the probability of occurrence of y in the second (right) position of a bigram, given that x appears in the first (left) position of the same bigram. However, in order to measure the cohesion value of each n-gram of any size in the corpus, FDPN concept is applied to SCP (.) measure and a new cohesion measure, SCP f (.), is obtained. SCP f ((w1 . . . wn )) =

1 n−1

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(2)

where p((w1 . . . wn )) is the probability of the n-gram w1 . . . wn in the corpus. So, any n-gram of any length is “transformed” in a pseudo-bigram2 that reflects the average cohesion between each two adjacent contiguous sub-n-gram of the original n-gram. Then, LocalMaxs algorithm elects every n-gram whose SCP f (.)3 cohesion value is a salient one (a local maximum), (see [1] for details). See some examples of elected n-grams, i.e., REs: Human Rights, Human Rights in East Timor, politique ´energ´etique and economia energ´etica. 1 2

3

We use the notation (w1 . . . wn ) or w1 . . . wn to refer an n-gram of length n. Roughly we can say that known statistical cohesion / association measures such as Dice(.), M I(.), χ2 , etc. seem to be “tailored” to measure just 2-grams. However, by applying FDPN to those measures, it is possible to use them for measuring the cohesion values of n-grams for any value of n [1]. LocalMaxs has been used in other applications with other statistical measures, as it is shown in [1]. However, for Information Retrieval (IR) purposes, very interesting results were obtained by using SCP f (.), in comparison with other measures [2].

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2.1

The Number of Features

Document clustering usually requires a matrix of documents characterized by the smallest possible set of variables. That matrix is then conveyed to clustering software. So, a multilingual 872,795 words corpus with 324 documents4 was used in order to test our approach. LocalMaxs extracted 25,838 REs from that corpus. Obviously, we cannot use such a high number of features for distinguishing such a small number of objects (324 documents). However, these REs (base features) provide the basis for building a new and reduced set of features. 2.2

Reducing the Number of Features

Let us take the following extracted REs containing the word agricultural : agricultural products, processing of agricultural products, agricultural products receiving refunds and common agricultural policy. For document clustering purposes, there is redundancy in these REs, since, for example, whenever processing of agricultural products is in a document, agricultural products is also in the same document and it may happen that, common agricultural policy is also in that document. These redundancies can be used to reduce the number of features. Thus, according to Principal Components Analysis (PCA), often the original m correlated random variables (features) X1 , X2 , . . . , Xm can be “replaced” by a subset Y1 , Y2 , . . . , Yk of the m new uncorrelated variables (components) Y1 , Y2 , . . . , Ym , each one being a linear combination of the m original variables, i.e., those k principal components provide most of the information of the original m variables [5, pages 340-350]. The original data set, consisting of l measurements of m variables, is reduced to another one consisting of l measurements of k principal components. Principal components depend solely on the covariance matrix Σ (or the correlation matrix ρ) of the original variables X1 , . . . , Xm . Now we state RE1 , RE2 , . . . , REp as being the original p variables (REs) of the subELIF corpus. Then, for a reduced set of new variables (principal components) we would have to estimate the associated covariance matrix of the variables RE1 , . . . , REp . So, let the sample covariance matrix RE be the estimator of Σ. ⎤ ⎡ RE1,1 RE1,2 . . . RE1,p ⎢ RE1,2 RE2,2 . . . RE2,p ⎥ ⎢ ⎥ RE = ⎢ . (3) .. . . .. ⎥ . ⎣ . . . . ⎦ RE1,p RE2,p . . . REp,p where REi,k estimates the covariance Cov(REi , REk ). RE can be seen as a similarity matrix between REs. Unfortunately, due to this matrix huge size (25, 838 × 25, 838), we cannot obtain principal components using available software. Moreover it is unlikely that PCA could achieve the reduction we need: from 25, 838 original features to k < 324 (the number of documents) new features (principal components). 4

This is part of the European Legislation in Force (sub-ELIF) corpus: htp://europa.eu.int/eur-lex.

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Geometrical Representations of Document Similarity

We can associate to the jth document, the vector dTj = [x1,j , . . . , xp,j ]5 where xi,j is the original number of occurrences of the ith RE in the jth document6 . Now, we can have a smaller (324 × 324) covariance matrix ⎡ ⎤ S1,1 S1,2 . . . S1,n ⎢ S1,2 S2,2 . . . S2,n ⎥ ⎢ ⎥ S=⎢ . (4) .. . . . ⎥ ⎣ .. . .. ⎦ . S1,n S2,n . . . Sn,n where

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(5)

and x·,j , meaning the average number of occurrences per RE in the jth document, is given by7 i=p 1 x·,j = xi,j . (6) p i=1 Then S will be a similarity matrix between documents. Escoufier and L’Hermier [3] proposed an approach, based on PCA, to derive geometrical representations from similarity matrices. Since S is symmetric we have S = P ΛP T , with P orthogonal (P = [e1 , . . . , en ], the matrix of normalized eigenvectors of S) and Λ diagonal. The principal elements of Λ are the eigenvalues λ1 , . . . , λn of S and λ1 ≥ λ2 · · · ≥ λn ≥ 0. Thus S = QQT with Q = P Λ1/2 .

(7)

The elements of the ith line of Q will be the coordinates of the point associated with the ith document. We may consider only the coordinates corresponding to the leading eigenvalues. Then, to assess how much of the total information is carried out by the first k components, i.e. the first k columns of Q, we may use j=k 8

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So, by taking the first k columns of matrix Q such that P T V (k) equals, say .80 or more, we can reduce the initial large number of features to k < n new features (components). However, considering the 324 documents of the corpus, if we use the original number of occurrences of the ith RE in the jth document (xi,j ) to obtain “similarities” (see (5)), we need the first 123 components to provide 5 6 7 8

We will use p for the number of REs of the corpus and n for the number of documents. These numbers of occurrences can be transformed, as we will see in Sect. 2.4. When we replace an index by a dot, a mean value has been obtained. PTV are initials for cumulative Proportion of the Total Variance.

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0.85 of the total information, i.e. P T V (123) = 0.85. Although it corresponds to 0.4% of the initial 25, 838 features, large numbers of components must be avoided in order to minimize computational effort of the clustering process. So, to reduce this number, we need to “stimulate” similarities between documents, and therefore, the original occurrences of the REs in documents must be transformed. 2.4

Transforming the Original Number of Occurrences

As referred above, the geometrical representation may be obtained from transformed occurrences. The technique we used has four phases. In the first phase we standardize in order to correct document heterogeneity. This heterogeneity is measured by the variation between the occurrence numbers of the different REs inside each document. This variation may be assessed by 1 (xi,j − x·,j )2 p − 1 i=1 i=p

V (Dj ) =

j = 1, . . . , n

(9)

where x·,j is given by (6). The standardized values will be zi,j = (xi,j − x·,j ).[V (Dj )]−1/2

i = 1, . . . , p ; j = 1, . . . , n .

(10)

In the second phase we evaluate the variation between documents for each RE. Although, each RE associated variation must reflect how much the RE occurrences vary in different documents, due to document content, not due to document size. Therefore we use normalized values to calculate this variation: V (REi ) =

j=n 1 (zi,j − zi,· )2 n − 1 j=1

i = 1, . . . , p .

(11)

These values are important since we found that, generally, the higher the V (REi ), the more information is carried out by the ith RE. On the other hand, it was observed that REs constituted by long words, usually are more informative from the IR / Text Mining point of view (e.g. agricultural products or communaut´e economique europ´eenne are more informative than same way, plus au moins or reach the level ). Thus, in a third phase we define weighted occurrences as x∗i,j = xi,j · V (REi ) · AL(REi )

i = 1, . . . , p ; j = 1, . . . , n

(12)

where AL(REi ) is the average number of characters per word in the ith RE. Lastly, in the fourth phase we carry out a second standardization considering the weighted occurrences. This is for correcting document size heterogeneity, since we do not want that the document size affects its relative importance. Thus ∗ = (x∗i,j − x∗·,j ).[V (Dj∗ )]−1/2 zi,j

i = 1, . . . , p ; j = 1, . . . , n

1 ∗ (x − x∗·,j )2 p − 1 i=1 i,j

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i=p

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(14)

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These standardizations are transformed occurrences and are used to obtain the similarity matrix between documents, whose generic element is given by 1 ∗ ∗ ∗ ∗ (z − z·,j )(zi,l − z·,l ) p − 1 i=1 i,j i=p

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(15)

Non-informative REs

Some high-frequency REs appearing in most documents written in the same language are not informative from the Text Mining point of view, e.g., locutions such as Consid´erant que (having regard ), and in particular, or other expressions which are incorrect REs, such as of the or dans les (in the). Although these expressions are useless to identify document topics, they are informative for distinguishing different languages. As a matter of fact they occur in most documents of the same language, and their associated variation (see (11)) is usually high or very high, i.e., they are relevant to “approximate” documents of the same language for calculating similarities between documents (see (12), (13) and (15)). So, it seems that either they should be removed to distinguish topics in documents of the same language, or they should be kept for distinguishing documents of different languages. To solve this problem, we use the following criterion: the REs having at least one extremity (the leftmost or the rightmost word) that exists in at least 90 % of the documents we are working with, are removed from the initial set of REs. We follow that criterion since these expressions usually begin or end with words occurring in most documents of the same language, e.g., of, les, que, etc.. As we will see in Subsect. 3.3, the documents and REs with which the system is working, depend on the node of the clustering tree. To summarize, in this section we obtained a matrix where a small set of components characterizes a group of documents. This matrix will be used as input for clustering. For this purpose, the matrix of document similarity (S) (see (4)) was calculated. Its generic element is given by (15). Then, from S, Q was obtained by (7) and the first k columns of Q were taken, such that P T V (k) ≥ 0.80. Finally, the latter matrix will be conveyed to clustering software. Considering the initial 25, 838 REs for the 324 documents of the sub-ELIF corpus, we obtained P T V (3) = .848; P T V (5) = .932 and P T V (8) = .955.

3

Clustering Documents

We need to split documents into clusters. However we do not know how many clusters should be obtained. Moreover, though we have obtained k features (components) to evaluate the documents, we do not know neither the composition of each cluster, nor its volume, shape and orientation in the k-axes space. 3.1

The Model-Based Cluster Analysis

Considering the problem of determining the structure of clustered data, without prior knowledge of the number of clusters or any other information about

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their composition, Fraley and Raftery [4] developed the Model-Based Clustering Analysis (MBCA). By this approach, data are represented by a mixture model where each element corresponds to a different cluster. Models with varying geometric properties are obtained through different Gaussian parameterizations and cross-cluster constraints. This clustering methodology is based on multivariate normal (Gaussian) mixtures. So the density function associated to cluster c has the form exp{− 12 (xi − μc )T Σ −1 c (xi − μc )} fc (xi |μc , Σ c ) = . (16) 1 r (2π) 2 |Σ c | 2 Clusters are ellipsoidal, centered at the means μc ; element xi belongs to cluster c. The covariance matrix Σ c determines other geometric characteristics. This methodology is based on the parameterization of the covariance matrix in terms of eigenvalue decomposition in the form Σ c = λc D c Ac D Tc , where D c is the matrix of eigenvectors, determining the orientation of the principal components of Σ c . Ac is the diagonal matrix whose elements are proportional to the eigenvalues of Σ c , determining the shape of the ellipsoid. The volume of the ellipsoid is specified by the scalar λc . Characteristics (orientation, shape and volume) of distributions are estimated from the input data, and can be allowed to vary between clusters, or constrained to be the same for all clusters. Considering our application, input data is given by the k columns of matrix Q (see (7) and (8)). MBCA subsumes the approach with Σ c = λI, long known as k-means, where sum of squares criterion is used, based on the assumption that all clusters are spherical and have the same volume (see Table 1). However, in the case of kmeans, the number of clusters has to be specified in advance, and considering many applications, real clusters are far from spherical in shape. Therefore we have chosen MBCA for clustering documents. Then, function emclust has been used with S-PLUS package, which is available for Windows and Linux. During the cluster analysis, emclust shows the Bayesian Information Criterion (BIC), a measure of evidence of clustering, for each “pair” model-number of clusters. These “pairs” are compared using BIC: the larger the BIC, the stronger the evidence of clustering (see [4]). The problem of determining the number of clusters is solved by choosing the best model. Table 1 shows the different models Table 1. Parameterizations of the covariance matrix Σ c in the Gaussian model and their geometric interpretation Σc λI λc I λDAD T λc D c Ac D Tc λD c AD Tc λD c AD Tc

Distribution Volume Shape

Orientation

Spherical Spherical Ellipsoidal Ellipsoidal Ellipsoidal Ellipsoidal

Equal Variable Variable Variable

Equal Variable Equal Variable Equal Variable

Equal Equal Equal Variable Equal Equal

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used during the calculation of the best model. Models must be specified as a parameter of the function emclust. However, usually there is no prior knowledge about the model to choose. Then, by specifying all models, emclust gives us BIC values for each pair model-number of clusters and proposes the best model which indicates which cluster must be assigned to each object (document). 3.2

Assessing Normality of Data. Data Transformations

MBCA works based on the assumption of normality of data. Then, Gaussian distribution must be checked for the univariate marginal distributions of the documents on each component. Thus, a QQ-plot is made for each component. For this purpose, each of the first k columns of matrix Q (see (7) and (8)) is standardized, ordered and put on y axis of the QQ-plot. Then, standardized normal quantiles are generated and put on x axis of the QQ-plot (see [5, pages 146-162] for details). Fig. 1(a) represents the QQ-plot for the 2th component, assessing the normality of data of cluster 1.29 . This QQ-plot is representative, since most of the components for other clusters produced similar QQ-plots. Most

2 .5

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Fig. 1. QQ-plot of data for cluster 1.2 on 2nd component (a); Chi-square plot of the ordered distances for data in cluster 1.2 (b)

of the times, if QQ-plots are straight (univariate distributions are normal), the joint distribution of the k dimensions (components) are multivariate normal. However, multivariate normality must be tested. Then, a Chi-square plot is constructed for each cluster. Thus, the square distances are ordered from smallest to largest as d2(1) ≤ d2(2) ≤ · · · ≤ d2(m) , where d2(j) = (xj − xc )T S −1 c (xj − xc ). V ector xj is the jth element (document) of cluster c; xc is the means vector for is the inverse of the estimator of the the k dimensions of that cluster, and S −1 c cluster covariance matrix. Then the pairs (d2(j) , χ2k ((j − 1/2)/m)) are graphed, 9

In Sect. 5 we will deal with specific clusters.

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where m is the number of elements of the cluster and χ2k ((j − 1/2)/m) is the 100(j − 1/2)/m percentile of the Chi-square distribution with k (the number of components, see (8)) deg rees of freedom. The plot should resemble a straight line. A systematic curved pattern suggests lack of normality. Since the straightness of the univariate and multivariate plots are not perfect (see Fig. 1(a) and Fig. 1(b)), some transformations of the data were tried to approximate to normality. Transformations were applied to some of the k columns of matrix Q (see (7) and (8)): those whose QQ-plot suggested lack of normality. So, let y be an arbitrary element of a given column we want to transform. We considered the following slightly modified family of power transformations from y to y (λ) [6]:  yλ −1 λ = 0 . λ y (λ) = (17) ln y λ=0 Power transformations are defined only for positive variables. However this is not restrictive, because a single constant can be added to each element in the column if some of the elements are negative. Thus, given the elements y1 , y2 , . . . , ym in a given column, the Box-Cox [6] solution for the choice of an appropriate power λ for that column is the one which maximizes the expression l(λ) = −

 j=m  j=m 1 (λ) m ln (yj − y (λ) )2 + (λ − 1) ln yj 2 m j=1 j=1 where

y (λ)

j=m 1 (λ) = y m j=1 j

(18)

(19)

(λ)

and m is the number of elements of the cluster; yj is defined in (17). So, every element y of the ith column of matrix Q will be transformed from y to y (λ) ˆ i , i.e., the value of λ maximizing l(λ). This new according to (17) where λ = λ matrix was conveyed to clustering software. However, the results obtained were not better than using the non-transformed matrix, as we will see in Sect. 5. Therefor e, although the straightness of the plots in Fig. 1(a) and Fig. 1(b) are not perfect, as it should be to ensure normality, it is close enough to encourage us to use MBCA as an adequate approach for clustering this kind of data. 3.3

Sub-clusters

As we will see in Sect. 5, our approach organizes sub-ELIF corpus in 3 main clusters: English, Portuguese and French documents. However, we can distinguish different subjects in different documents of the same cluster. So, a hierarchical tree of clusters is built as follows: let us consider that every cluster in the tree is a node. For every node, non-informative REs are removed (see Subsect. 2.5) from the set of REs contained in the documents of that node (a subset of the original REs), in order to obtain a new similarity matrix between documents (see (15)). Then, the first k columns of the new matrix Q are taken (see (7) and (8)), and new clusters are proposed by MBCA.

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Choosing the Best Number of Clusters

As has been said, MBCA calculates the best model based on the k first columns of matrix Q (k components). A large number of components means no significant information loss, which is important for a correct clustering (best model ) to be proposed by MBCA. On the other hand, a large number of components must be avoided, since it takes MBCA to estimate large covariance matrices – during the internal computation for different models – which can be judged to be close to singularity (see [4]). Therefore, we use the following criterion: the first k components are chosen in such a way that P T V (k) ≥ 0.80 (see (8)). Then, based on those k components, MBCA produces a list of BIC values for each model: VVV (Variable volume, Variable shape, Variable Orientation), EEV etc. (see Table 1). Each list may have several local maxima. The largest local maximum over all models is usually proposed as the best model. However, a heuristic that works well in practice (see [4]) chooses the number of clusters corresponding to the first decisive local maximum over all the models considered.

4

Summarization

Summarizing a document and summarizing a cluster of documents are different tasks. As a matter of fact, documents of the same cluster have common REs such as rational use of energy or energy consumption, rather than long sentences which are likely to occur in just one or two documents. Then, summarizing topics seems adequate to disclose the core content of each cluster. Cluster topics correspond to the most important REs in the cluster. Let the cluster from where we want to extract its topics be the “target cluster”. Then, in order to extract it, first the REs of the parent node of the target cluster are ordered according to the value given by Score(REi ) assigned to the ith RE. Score(REi ) = T hr(REi ) · V (REi ) · AL(REi )  T hr(REi ) =

1 0

where

SCP f (REi ) ≥ threshold . else

(20) (21)

V (REi ) and AL(REi ) have the same meaning as in (12). Thus, T hr(·) corresponds to a filter that “eliminates” REs whose SCP f (·) cohesion value (see Sect. 2) is lower than threshold – a value empirically set to 0.015. These REs, e.g., Consid´erant que, and in particular, etc., are not informative for IR / Text Mining. Most of the times, these REs are previously eliminated when selecting the informative REs for calculating the covariance matrix; however it may not happen in case of a multilingual set of documents. (see Subsect. 2.5). So, the largest Score(REi ) corresponds to the most important RE. For example, according with this criterion, the 15 most important REs of the initial cluster (the one containing all documents) are the following: Nomenclatura Combinada (Combined Nomenclature), nomenclature combin´ee, Member States, ´ combined nomenclature, Etats membres (Member states), Council Regulation,

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produtos agr´ıcolas (agricultural products), produits agricoles, utiliza¸c˜ ao racional (rational use), nomenclature tarifaire (tariff nomenclature), autoridades aduan eiras (customs authorities), estˆ ancia aduaneira (customs office), Common Customs, indicados na coluna (indicated in column) and agricultural products. Now, taking for instance the “French documents” as the target cluster, we cannot “guarantee” that produits agricoles will be a topic, since not every French document content is about produits agricoles. On the other hand, the same topic often appears in different documents, written in different forms, (e.g. produits agricoles and Produits Agricoles). Hence, according to Score(·), the 15 most important REs of the target cluster occurring in at least 50 % of its documents are put in a list. From this list, the REs with Score(·) value not lower than 1/50 of the maximum Score(·) value obtained from that list, are considered topics.

5

Results

Sub-ELIF is a multilingual corpus with 108 documents per language. For each document there are two other documents which are translations to the other languages. From Table 2 we can see the hierarchical tree of clusters obtained by this approach. We also present the topics extracted from each cluster. Table 2. Evaluation of the clusters

Cluster

Main topic

1 2 3 1.1 1.2 1.3 2.1 2.2 2.3 3.1 3.2 3.3

european communities Comunidade Europeia Communaut´e europ´eenne rational use of energy agricultural products combined nomenclature economia de energia produtos agr´ıcolas Nomenclatura Combinada politique ´energ´etique produits agricoles nomenclature combin´ee

Correct # Total # Act. corr. # Prec. (%) Rec. (%) 108 108 108 23 27 58 23 27 58 23 27 58

108 107 109 23 27 58 26 25 56 26 27 56

108 107 108 20 21 51 21 21 52 22 21 53

100 100 99.1 86.9 77.8 87.9 80.8 84 92.9 84.6 77.8 94.6

100 99.1 100 86.9 77.8 87.9 91.3 77.8 89.7 95.7 77.8 91.4

Cluster 1: European Communities, Member States, EUROPEAN COMMUNITIES, Council Regulation, Having regard to Council Regulation, Having regard to Council and Official Journal. Cluster 2: Comunidade Europeia, Nomenclatura Combinada, COMUNIDADES EUROPEIAS and directamente aplic´ avel (directly applicable). ´ Cluster 3: Communaut´e europ´eenne, nomenclature combin´ee, Etats mem´ ´ bres, COMMUNAUTES EUROPEENNES and directement applicable.

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Cluster 1.1: rational use of energy, energy consumption and rational use. Cluster 1.2: agricultural products, Official Journal, detailed rules, Official Journal of the European Communities, proposal from the Commission, publication in the Official Journal and entirely and directly. Cluster 1.3: combined nomenclature, Common Customs, customs authorities, No 2658/87, goods described, general rules, appropriate CN, Having regard to Council Regulation, tariff and statistical and Customs Code. Cluster 2.1: economia de energia (energy saving), utiliza¸c˜ ao racional, racional da energia (rational of energy) and consumo de energia (energy consuming). Cluster 2.2: produtos agr´ıcolas, Comunidades Europeias, Jornal Oficial, directamente aplic´ avel, COMUNIDADES EUROPEIAS, Jornal Oficial das Comunidades, directamente aplic´ avel em todos os Estados-membros (directly applicable to all Member States), publica¸ca ˜o no Jornal Oficial, publica¸c˜ ao no Jornal Oficial das Comunidades and Parlamento Europeu (European Parliament). Cluster 2.3: Nomenclatura Combinada, autoridades aduaneiras (customs authorities), indicados na coluna, mercadorias descritas, informa¸c˜ oes pautais vinculativas (binding tariff informations), Aduaneira Comum (Common Customs), regras gerais, c´ odigos NC (NC codes) and COMUNIDADES EUROPEIAS. Cluster 3.1: politique ´energ´etique (energy policy), rationnelle de ´energie and l’utilization rationnelle. Cluster 3.2: produits agricoles, organisation commune, organisation commune des march´es, directment applicable, Journal officiel, Journal officiel des ´ EUROPEENNES. ´ Communaut´es and COMMUNAUTES Cluster 3.3: nomenclature combin´ee, autorit´es douani`es (customs authorities), nomenclature tarifaire, No 2658/87, marchandises d´ecrites, tarifaire et ´ EUROPEENNES. ´ statistique (tariff and statistical) and COMMUNAUTES 5.1

Discussion

MBCA (function emclust) proposed clusters 1, 2 and 3 considering EEV as the best model, (see Table 1). EEV model was also considered best model when the sub-clusters of clusters 1, 2 and 3 were calculated. Clusters were obtained with non-transformed data to approximate to normality (see Subsect. 3.2). In Table 2, column Main topic means the most relevant topic according to (20) obtained for the cluster indicated by column Cluster ; by Correct # we mean the correct number of documents in the corpus for the topic in Main topic; Total # is the number of documents considered to belong to the cluster by our approach; Act. corr. # is the number of documents correctly assigned to the cluster; Prec. (%) and Rec. (%) are Precision and Recall. Although the original texts of the sub-ELIF corpus are classified by main topic areas, e.g., Agriculture, Energy – Rational use, etc., we have removed that information from the documents before extracting the REs using LocalMaxs, as we wanted to test our approach for clustering usual documents. Although, the topics shown in the previous lists capture the core content of each cluster. However, each cluster is not a perfect “translation” of the “corresponding” clusters in the other languages. Some reasons may help to explain why. Thus, because in

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Portuguese we write Estado-Membro (just one word) for Member State, it will not be in cluster 2, since LocalMaxs does not extract unigrams. Moreover, not every RE has the same number of occurrences of the corresponding RE in the other languages. For example, there are 55 occurrences of Nomenclatura Combinada, 54 of nomenclature combin´ee, 45 of combined nomenclature and 10 of Combined Nomenclature. Then, under the criterion used for extracting topics (see Sect. 4), 45 occurrences is less than 50% of the 108 documents of the cluster 1. Therefore combined nomenclature is not considered a topic in cluster 1. As we keep the original words in text, the same topic may be shown in different forms, e.g., EUROPEAN COMMUNITIES and European Communities. Though some REs are not topics or just weakly informative expressions, such as Journal officiel or general rules, we think that about 80% of these REs can be considered correct topics / subtopics, exposing the core content of the clusters. Since our approach is not oriented for any specific language, we believe that different occurrences for the same concept in the three different languages, are the main reason for different Precision and Recall scores comparing “corresponding” clusters. Furthermore, some documents have REs written in more than one language, for example there is a “Portuguese document” containing some important REs written in French. This reduced Precision of cluster 3 and Recall of cluster 2, since this document was oddly put in cluster 3. We transformed data to approximate to normality (see Subsect. 3.2) and use it as input to clustering software. Unfortunately, this modified data caused a decrease of Precision (about 20% lower) and the number of subclusters for clusters 1, 2 and 3 were different. However, we will work again on other data transformations with larger corpora in order to obtain better results. As has been said in Sect. 3.1, the larger the BIC value, the stronger the evidence of clustering (see [4]). Then, BIC can be used to decide whether to “explore” sub-clusters or not. However, we did not work on this problem yet.

6

Related Work

Some known approaches for extracting topics and relevant information use morphosyntactic information, e.g., TIPSTER [7]. So, these approaches would need specific morphosyntactic information in order to extract topics from documents in other languages, and that information might not be available. In [8], a multidocument summarizer, called MEAD is presented. It generates summaries using cluster topic detection and tracking system. However, in this approach, topics are unigrams. Though many uniwords have precise meanings, multiword topics are usually more informative and specific than unigrams. In [9], an approach for clustering documents is presented. It is assumed that there exists a set of topics underlying the document collection to cluster, since topics are not extracted from the documents. When the number of clusters is not given to this system, it is calculated based on the number of topics.

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87

Conclusions

We presented an unsupervised statistics-based and language independent approach for document clustering and topic extraction. It was applied to a multilingual corpus, using just information extracted from it. Thousands of REs were extracted by LocalMaxs algorithm and then, transformed into a small set of new features, which – according to the results obtained – showed good document classification power. The best number of clusters was automatically calculated by MBCA and the results obtained led to a rather precise document clustering. Thus, the number of clusters was not left to the user choice, as it might correspond to an unnatural clustering. Although we tested this approach on a small corpus (872,795 words), the results are encouraging, since about 80% of the clusters REs are sufficiently informative for being taken as topics of documents. This lead us to believe that topics, rather than long sentences belonging to just one or two documents, are adequate to define clusters core content. We tried some data transformations when some distributions suggested lack of normality. However, considering the clustering software we used, the preliminary results showed that the negative effect of these data modifications seems to be more important than the positive effect they produce to make distributions more “normal (Gaussian) looking”. Although, further research is required on larger corpora to solve this and other problems.

References 1. Silva, J. F., Dias, G.,Guillor´e, S., Lopes, G. P. 1999. Using LocalMaxs Algorithm for the Extraction of Contiguous and Non-contiguous Multiword Lexical Units. Lectures Notes in Artificial Intelligence, Springer-Verlag, volume 1695, pages 113-132. 2. Silva, J. F., Lopes, G. P. 1999. A Local Maxima Method and a Fair Dispersion Normalization for Extracting Multiword Units. In Proceedings of the 6th Meeting on the Mathematics of Language, pages 369-381, Orlando. 3. Escoufier Y., L’Hermier, H. 1978. A propos de la Comparaison Graphique des Matrices de Variance. Biometrischc Zeitschrift, 20, pages 477-483. 4. Fraley, C., Raftery, A. E. 1998. How many clusters? Which clustering method? Answers via model-based cluster analysis. The computer Journal, 41, pages 578-588. 5. Johnson R. A., Wichern, D. W. 1988. Applied Multivariate Statistical Analysis, second edition. Prentice-Hall. 6. Box, G. E. P., D. R. Cox. 1964. An Analysis of Transformations, (with discussion). Journal of the Royal Statistical Society (B), 26, no. 2, pages 211-252. 7. Wilks, Y., Gaizauskas, R. 1999. Lasie Jumps the Gate. In Tomek Strzalkowski, editor, Natural Language Information Retrieval. Kluwer Academic Publishers, pages 200-214. 8. Radev, D. R., Hongyan, J., Makgorzata, B. 2000. Centroid-based summarization of multiple documents: sentence extraction, utility-based evaluation, and user studies. Proceedings of the ANLP/NAACL Workshop on Summarization. 9. Ando, R. K., Lee L. 2001. Iterative Residual Rescaling: An Analysis and Generalization of LSI. To appear in the proceedings of SIGIR 2001.

Sampling-Based Relative Landmarks: Systematically Test-Driving Algorithms before Choosing Carlos Soares1 , Johann Petrak2 , and Pavel Brazdil1 2

1 LIACC/FEP, University of Porto {csoares,pbrazdil}@liacc.up.pt Austrian Research Institute for Artificial Intelligence [email protected]

Abstract. When facing the need to select the most appropriate algorithm to apply on a new data set, data analysts often follow an approach which can be related to test-driving cars to decide which one to buy: apply the algorithms on a sample of the data to quickly obtain rough estimates of their performance. These estimates are used to select one or a few of those algorithms to be tried out on the full data set. We describe sampling-based landmarks (SL), a systematization of this approach, building on earlier work on landmarking and sampling. SL are estimates of the performance of algorithms on a small sample of the data that are used as predictors of the performance of those algorithms on the full set. We also describe relative landmarks (RL), that address the inability of earlier landmarks to assess relative performance of algorithms. RL aggregate landmarks to obtain predictors of relative performance. Our experiments indicate that the combination of these two improvements, which we call Sampling-based Relative Landmarks, are better for ranking than traditional data characterization measures.

1

Introduction

With the growing number of algorithms available for data mining, the selection of the one that will obtain the most useful model from a given set of data is an increasingly important task. Cross-validation with adequate statistical comparisons is currently the most reliable method for algorithm selection. However, with the increasing size of the data to be analyzed, it is impractical to try all available alternatives. The most common approach to this problem is probably the choice of the algorithm based on the experience of the user on previous problems with similar characteristics. One drawback with this approach is that it is difficult for the user to be knowledgeable about all algorithms. Furthermore, two sets of data may look similar to the user but they can be sufficiently different to cause significant changes in algorithm performance. In meta-learning, the idea of using knowledge about the performance of algorithms on previously processed data sets is systematized [1,5]. A database of meta-data, i.e., information about the performance of algorithms on data sets P. Brazdil and A. Jorge (Eds.): EPIA 2001, LNAI 2258, pp. 88–95, 2001. c Springer-Verlag Berlin Heidelberg 2001 

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and characteristics of those data sets, is used to provide advice for algorithm selection, given a new problem. Most approaches to meta-learning have concentrated on selecting one or a set of algorithms whose performance is expected to be the best [1,12]. However, taking into account that no prediction model is perfect and that in most meta-learning settings the amount of meta-data is not very large, there is a growing interest in methods that provide a ranking of the algorithms according to their expected performance [3,9,14]. The ranking approach is more flexible, enabling the user to try out more than one algorithm depending on the available resources as well as to accommodate his/her personal preferences. Probably the most important issue in meta-learning is how to obtain good data characteristics, i.e. measures that provide information about the performance of algorithms and that can be computed fast. The earlier approaches used three types of measures, general (e.g. number of examples), statistical (e.g. number of outliers) and information-theoretic (e.g. class entropy) [10, sec. 7.3]. Landmarks were recently suggested as data characterization measures [2,12]. A landmark is a simple and efficient algorithm that provides information about the performance of more complex algorithms. For example, the top node in a decision tree can be an indicator of the performance of the full tree. Another common approach to the problem of algorithm selection is sampling, which consists of drawing a (random) sample from the data and trying at least a few of the available algorithms on it. The algorithm performing best on this sample is then applied to the full data set. Petrak [11] performed a systematic study of this approach in the supervised classification setting. Even with simple sampling strategies, positive results were obtained on the task of single algorithm selection. However, the learning curves presented in that work indicate that large samples are required to obtain a clear picture of the relative performance between the algorithms. In this paper we combine both ideas, landmarks and sampling, in a framework for data characterization, called sampling-based landmarks (SL). In SL the results of algorithms on small samples are not used directly as estimators of algorithm performance, as it is done in sampling. They serve as predictors in the same spirit of landmarking, i.e. as data characteristics used in the metalearning process. Although landmarking has also shown positive results for single algorithm selection [2,12], it does not provide much information about the relative performance of algorithms, as recent results show [3]. To address this problem, we use relative landmarks (RL). RL aggregate landmarks to obtain measures that are predictors of relative, rather than individual, performance. We believe they will be more appropriate for ranking and algorithm selection in general than traditional (non-relative) landmarks. The experiments performed in this paper combine these two improvements to obtain Sampling-based Relative Landmarks. When providing support to data mining users, one must take into account that the evaluation of the model is not only based on its accuracy. Here we will work in the setting defined in [14], where the accuracy and total execution time of supervised classification algorithms are combined.

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In the next section we present sampling-based landmarks. In Section 3 we then describe relative landmarks and how to implement them using the Adjusted Ratio of Ratios, which is a multicriteria evaluation measure for classification algorithms. In Section 4 we combine both concepts into sampling-based relative landmarks and compare them empirically with traditional data characterization measures for ranking. Related work is discussed in Section 5 and in the final section we present some conclusions and describe future work.

2

Sampling-Based Landmarks

Landmarks were introduced in [2,12] as fast and simple learning algorithms whose performance characteristics can be used to predict the performance of complex algorithms. The simplicity of the chosen algorithms was necessary in order to achieve acceptable speed: meta-learning will only be an interesting alternative to cross-validation if data set characterization is significantly faster than running the algorithms. As an alternative to simplifying algorithms, we can achieve speed by reducing the size of the data. A Sampling-based landmark is an estimate of the performance of an algorithm obtained by testing a model that was obtained with that algorithm on a small sample of a data set on another small sample of the same data. Different sampling strategies have been described in the literature to get good performance estimates by using only a small amount of data. Simple strategies include sampling a fixed number or a fixed fraction of cases. Other strategies try to estimate the number of cases needed by analyzing certain statistical properties of the sample [7,8]. Still more elaborate strategies try to find an optimum sample size by repeated evaluation of increasing samples [13]. Here, we use the simple approach of randomly selecting a constant size sample of 100 cases, and a fixed fraction of 10% for testing. Thus, the (usually critical) training effort is reduced to constant time complexity, while testing time is reduced by a constant factor (sampling itself is comparably fast with linear time complexity for sequential access files). Furthermore, the results presented in [11] indicate that the quality of the estimates depend more on the size of the test sample than on the size of the training sample. The use of Sampling-based Landmarks is not restricted to predicting accuracy. For instance, the time to obtain the landmark can also be used to predict the time to run the algorithm on the full set of data and the same applies to the complexity of the model. As explained below, here we concentrate on accuracy and time.

3

Relative Landmarks

Landmarks can be generally useful as indicators of algorithm performance. However, they do not provide information about the relative performance of algorithms, as is required for algorithm selection and, in particular, for ranking [3]. To provide relative performance information, landmarks should be aggregated

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in some way, leading to the notion of relative landmarks (RL). Here RL are based on the Adjusted Ratio of Ratios (ARR), a multicriteria evaluation measure combining accuracy and time to assess relative performance [14]. In ARR the compromise between the two criteria involved is given by the user in the form “the amount of accuracy I’m willing to trade for a 10 times speed-up is X%”. The ARR of algorithm i when compared to algorithm j on data set d is defined as follows: d = ARRi,j

Ad i Ad j

 1 + log

Tid Tjd



∗X

where Adi and Tid are the accuracy and time of i on d, respectively. Assuming, without loss of generality, that algorithm i is more accurate but slower than d will be 1 if i is X% more accurate algorithm j on data set d, the value of ARRi,j d than j for each order of magnitude that it is slower than j. ARRi,j will be larger than one if the advantage in accuracy of i is X% for each additional order of magnitude in execution time and vice-versa. When more than two algorithms are involved, we can generate a relative landmark for each of the n landmarks, l, based on ARR in the following way:  d j =i ARRi,j (1) rlid = n−1 Each relative landmark, rlid , represents the relative performance of landmark i when compared to all other landmarks on data set d1 . Therefore, a set of relative landmarks, rlid , can be used directly as meta-features, i.e. characteristics of the data set, for ranking. Given that the main purpose of relative landmarks is characterizing the relative performance of the algorithms, we can alternatively order the values of the relative landmarks, and use the corresponding ranks, rrld (i), as meta-features.

4

Experiments with Sampling-Based Relative Landmarks

The aim of our experiments was to compare data set characterization by traditional measures (general, statistical and information-theoretic) and by samplingbased relative landmarks (SRL), i.e. a combination of both improvements introduced above. We will refer to the SRL as SRL-scores, their ranks as SRL-ranks and the traditional data characterization as DC-GSI. Next we will describe the experimental setting used to obtain the meta-data. Then, we describe the meta-learning methods used and, finally, the results. Meta-Data: SRL are obtained very simply by creating relative landmarks (Section 3) using the performance of the candidate algorithms on a sample of 1

Since the relative landmarks, rlid , depend on the X parameter and on the set of algorithms used, we store raw performance information, Adi and Tid and calculate the relative landmarks on-the-fly.

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the data (Section 2). Assuming that s(d) is the sampling method used, n is the s(d) number of algorithms, we calculate one SRL, rli , for each algorithm i using Eq. 1, thus obtaining a set of n SRL measures. Here we have used a simple sampling strategy: train on a stratified random sample with 100 cases and test on 10% of the rest of the data set. We have used 45 data sets with more than 1000 cases, mostly from the UCI repository [4] but also a few others that are being used on the METAL project2 (SwissLife’s Sisyphus data and a few applications provided by DaimlerChrysler). Ten algorithms were executed on these data sets3 : two decision tree classifiers, C5.0 and Ltree, which is a decision tree that can introduce oblique decision surfaces; the IB1 instance-based and the naive Bayes classifiers from the MLC++ library; a local implementation of the multivariate linear discriminant; two neural networks from the SPSS Clementine package (Multilayer Perceptron and Radial Basis Function Network); two rule-based systems, C5.0 rules and RIPPER; and an ensemble method, boosted C5.0. The algorithms were all executed with default parameters. Since we have ten algorithms, we generated a set of ten SRL measures and another with the corresponding ranks for each data set. In the DC-GSI setting we have used the 25 meta-features that have performed well before [14]. Meta-learning Methods: Two ranking methods were used. The first is the Nearest-Neighbor ranking using ARR as multicriteria performance measure [14]. Three scenarios for the compromise between accuracy and time were considered, X ∈ {0.1%, 1%, 10%}, for increasing importance of time. To obtain an overall picture of the performance of the ranking method with the three different sets of data characterization measures, we varied the number of neighbors (k) from 1 to 25. The second meta-learning method consists of building the ranking directly from the sampling-based relative landmarks. In other words, the recommended ranking for data set d is defined by the corresponding SL-ranks, rrls(d) (i). This method can be regarded as a baseline that measures the improvement obtained by using sampling-based relative landmarks as predictors, i.e. as meta-features used by the NN ranking method, rather than directly as estimators for ranking. This method is referred to as SL-ranking. The evaluation methodology consists of comparing the ranking predicted by each of the methods with the estimated true ranking, i.e. the ranking based on the estimates of the performance of the algorithms on the full set of data [14]. The distance measure used is average Spearman’s rank correlation that yields results between 1 (for perfect match) and -1 (inverted rankings). The experimental methodology is leave-one-out. Results: The results are presented in Figure 1. The first observation is that in all scenarios of the accuracy/time compromise, SL-ranking always achieves worse results than the alternatives. This is consistent with an observation that can be made from previous work on sampling [11], namely that relatively large sample 2 3

Esprit Long-Term Research Project (#26357) A Meta-Learning Assistant for Providing User Support in Data Mining and Machine Learning (www.metal-kdd.org). References for these algorithms can be found in [11].

Sampling-Based Relative Landmarks

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sizes are required to correctly rank the algorithms directly from the performance on the sample.

Fig. 1. Average Spearman rank correlation coefficient (rS ) obtained by NN/ARR ranking using two types of sampling-based relative landmarks (SRL-scores and SRL-ranks) and traditional data characterization (DC-GSI) for varying number of neighbors (k) in three different scenarios of the compromise accuracy/time. Also included is the performance of the ranking obtained directly from the sampling-based relative landmarks (SL-ranking).

These results also indicate that SRL-scores represent the best overall method especially for reasonable number of neighbors (k < 10, which represents roughly 20% or less of the number of data sets), except when time is the dominant criterion. In the latter case and for k < 4, DC-GSI performs better. This is expected because for such a small sample size, the precision (number of decimal places) used to measure time is not sufficient to be discriminative. However, it is interesting to note that in the same scenario, SRL-scores is again comparable or better than DC-GSI for 4 ≤ k ≤ 10. Focussing the comparison on both types of SRL, SRL-scores and SRL-ranks, we observe that the former seem to be much more stable with smaller number of neighbors. We believe that this makes this approach more appealing, although in the scenario where accuracy is the dominant criterion, the performance obtained with SRL-ranks is better for K ∈ {4, 5, 6}. There is also a tendency for SRLranks to be better than SRL-scores for larger, less common, number of neighbors (10 ≤ k ≤ 25). These results are somewhat surprising, given that SRL-scores are expected to be more sensitive to outliers. We would expect to mitigate this problem by using the information about the performance of algorithms at a more coarse level, i.e. SL-ranks. However, we seem to lose too much information with the latter.

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Carlos Soares, Johann Petrak, and Pavel Brazdil

Related Work

The concepts of relative landmarks and subsampling landmarks, which are essentially the same as the ones described here, have been presented by F¨ urnkranz et al [6]. The authors also present an interesting taxonomy of relative landmarks, that includes both types used here, i.e. using scores or their ranks. However, there are two main differences between the two approaches, the most important being that we combine both concepts, obtaining sampling-based relative landmarks. Also, in [6] the aim is to select a single algorithm while we are concerned with ranking the candidate algorithms.

6

Conclusions

Landmarks have been introduced in [2,12] as simple and efficient algorithms that are useful in predicting the performance of more complex algorithms. We observe that efficiency can be obtained not only by simplifying algorithms but also by sampling the data. Sampling-based landmarks are obtained by running the candidate algorithms on small samples of the data and are used as data set characterization measures rather than as estimators of algorithm performance [11]. As landmarks have little ability to predict relative performance, this makes them less suitable for ranking, as it was shown empirically [3]. Relative landmarks, obtained by adequately aggregating landmarks, can be used to address this issue. In this paper we have used the Adjusted Ratio of Ratios [14], a multicriteria relative performance measure that takes accuracy and time into account, for that purpose. We have empirically evaluated the combination of these two improvements to landmarking, referred to as sampling-based relative landmarks. Here, they were based on very small samples. We compared them to a set of traditional data characterization measures and also to rankings generated directly from the sampling-based landmarks. In our experiments with a Nearest-Neighbor ranking system that also used the ARR multicriteria measure, the best results in general were obtained with sampling-based relative landmarks when the number of neighbors ranged from 10% to 20% of the total number of data sets. Although the results are good, there is still plenty of work to do. Concerning sampling-based landmarks, we intend to study the effect of increasing sample size and other sampling methods. We will also try to reduce the variance of the estimates and to generate simple estimators of the learning curves of each algorithms. We plan to combine sampling-based landmarks with a selection of traditional characterization measures. We also intend to improve relative landmarks, namely by analyzing other ways of aggregating performance and to apply relative landmarks to traditional landmarks, i.e. obtained by simplifying algorithms. Finally, we note that both frameworks, sampling-based and relative landmarks, can be applied in settings where multicriteria performance measures other than ARR are used [9] as well as settings where accuracy is the only important performance criterion.

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References 1. D.W. Aha. Generalizing from case studies: A case study. In D. Sleeman and P. Edwards, editors, Proceedings of the Ninth International Workshop on Machine Learning (ML92), pages 1–10. Morgan Kaufmann, 1992. 2. H. Bensusan and C. Giraud-Carrier. Casa batl´ o is in passeig de gr´ acia or landmarking the expertise space. In J. Keller and C. Giraud-Carrier, editors, Meta-Learning: Building Automatic Advice Strategies for Model Selection and Method Combination, pages 29–46, 2000. 3. H. Bensusan and A. Kalousis. Estimating the predictive accuracy of a classifier. In P. Flach and L. de Raedt, editors, Proceedings of the 12th European Conference on Machine Learning, pages 25–36. Springer, 2001. 4. C. Blake, E. Keogh, and C.J. Merz. Repository of machine learning databases, 1998. http:/www.ics.uci.edu/∼mlearn/MLRepository.html. 5. P. Brazdil, J. Gama, and B. Henery. Characterizing the applicability of classification algorithms using meta-level learning. In F. Bergadano and L. de Raedt, editors, Proceedings of the European Conference on Machine Learning (ECML-94), pages 83–102. Springer-Verlag, 1994. 6. J. F¨ urnkranz and J. Petrak. An evaluation of landmarking variants. In C. GiraudCarrier, N. Lavrac, and S. Moyle, editors, Working Notes of the ECML/PKDD 2000 Workshop on Integrating Aspects of Data Mining, Decision Support and MetaLearning, pages 57–68, 2001. 7. B. Gu, B. Liu, F. Hu, and H. Liu. Efficiently determine the starting sample size for progressive sampling. In P. Flach and L. de Raedt, editors, Proceedings of the 12th European Conference on Machine Learning. Springer, 2001. 8. G.H. John and P. Langley. Static versus dynamic sampling for data mining. In E. Simoudis, J. Han, and U. Fayyad, editors, Proceedings of Second International Conference on Knowledge Discovery and Data Mining (KDD-96). AAAI-Press, 1996. 9. J. Keller, I. Paterson, and H. Berrer. An integrated concept for multi-criteria ranking of data-mining algorithms. In J. Keller and C. Giraud-Carrier, editors, MetaLearning: Building Automatic Advice Strategies for Model Selection and Method Combination, 2000. 10. D. Michie, D.J. Spiegelhalter, and C.C. Taylor. Machine Learning, Neural and Statistical Classification. Ellis Horwood, 1994. 11. J. Petrak. Fast subsampling performance estimates for classification algorithm selection. In J. Keller and C. Giraud-Carrier, editors, Meta-Learning: Building Automatic Advice Strategies for Model Selection and Method Combination, pages 3–14, 2000. 12. B. Pfahringer, H. Bensusan, and C. Giraud-Carrier. Tell me who can learn you and i can tell you who you are: Landmarking various learning algorithms. In P. Langley, editor, Proceedings of the Seventeenth International Conference on Machine Learning (ICML2000), pages 743–750. Morgan Kaufmann, 2000. 13. F. Provost, D. Jensen, and T. Oates. Efficient progressive sampling. In S. Chaudhuri and D. Madigan, editors, Proceedings of the Fifth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. ACM, 1999. 14. C. Soares and P. Brazdil. Zoomed ranking: Selection of classification algorithms based on relevant performance information. In D.A. Zighed, J. Komorowski, and J. Zytkow, editors, Proceedings of the Fourth European Conference on Principles and Practice of Knowledge Discovery in Databases (PKDD2000), pages 126–135. Springer, 2000.

R ecu r s i v e Ad a p ti v e E COC m od els E liz a b e th T a p ia 1, J o s é C a rlo s G o n z á le z1, J a v ie r G a rc ía -V illa lb a 2, J u lio V ille n a 1

1

D e p a rtm e n t o f T e le m a tic s E n g in e e rin g - T e c h n ic a l U n iv e rs ity o f M a d rid , S p a in {etapia, jgonzalez, jvillena}@gsi.dit.upm.es 2 D e p a r t m e n t o f I n f o r m a t i c S y s t e m s , C o m p l u t e n s e U n i v e r s i t y o f M a d r i d , S p a i n [email protected]

Abs tr a ct. a lg o rith m s re c u rs iv e e p ro p o se d . a lg o rith m s

A in rro A b a

g e n e ra m u ltip r o u tp u p a rtic u s e d o n

l fr le o t c o la r L o w

a m u tp rre c la D

e w o rk u t d o c tin g ss o f e n s ity

fo r th e m a in s b a s c o d e s a n d th e s e R e P a rity C h

d e s ig n e d o n D ite ra tiv c u rs iv e e c k is p

o f e ie tte e A P E C O re s e n

rro r a d a p tiv e r i c h 's E C O C P d e c o d in g m C (R E C O C ) te d .

le a rn a p p ro e th o d le a rn

in g a c h , s is in g

1 In tr od u cti on A s th e E C O C [1 ] d e c o d in g s tra te g y is ro u g h ly o f a h a rd d e c is io n ty p e , th e fin a l h y p o th e s is c a n n o t e x p lo it th e k n o w le d g e a ris in g fro m th e o b s e rv e d b in a ry le a rn e rs ’ p e rfo rm a n c e s . In th is w a y , th e E C O C a p p ro a c h c a n n o t le a d to a n y e rro r a d a p tiv e le a rn in g a lg o rith m e x c e p t w h e n u s e d in th e c o re o f A d a B o o s t v a ria n ts [2 ] . T h is is a s trik in g q u e s t c o n s id e rin g th a t o rig in a l A d a B o o s t fo rm u la tio n is e s s e n tia lly b in a ry o rie n te d . F u rth e rm o re , b o th A d a B o o s t a n d E C O C s e e m to b e d iffe re n t fo r M a c h in e L e a rn in g lite ra tu re [3 ], e v e n w h e n E C O C s h o u ld b e n a tu ra l e x te n s io n o f A d a B o o s t. T h i s w o r k f o l l o w s t h e a p p r o a c h i n t r o d u c e d i n [4 ] [ 5 ] . I n t h i s p a p e r , a p a r t i c u l a r i n s t a n c e o f R E C O C l e a r n i n g b a s e d L o w - D e n s i t y P a r i t y C h e c k ( L D P C ) c o d e s [6 ] is p re s e n te d . T h e re m a in d e r o f th is p a p e r is o rg a n iz e d a s fo llo w s . In s e c tio n 2 , w e re v ie w th e R E C O C a p p ro a c h . In s e c tio n 3 , w e p re s e n t th e R E C O C _ L D P C le a rn in g a lg o rith m . In s e c tio n 4 , w e p re s e n t e x p e rim e n ta l re s u lts . F in a lly , in S e c tio n 5 c o n c lu s io n s a n d fu rth e r w o rk a re p re s e n te d .

2 L ow Com p lex i ty E r r or Ad a p ti v e L ea r n i n g Alg or i thm s In p re v io u s w o rk [4 ], w e d e m o n s tra te d th a t A d a B o o s t d e c is io n c o u ld b e in te rp re te d a s a n in s ta n c e o f th re s h o ld d e c o d in g [7 ] fo r a T -re p e titio n 1 c o d e u n d e r th e a s s u m p tio n o f a b in a ry d is c re te m e m o ry le s s c h a n n e l c o n s tru c te d b y th e e n s e m b le o f b in a ry w e a k 1

E a c h c o d e w o rd o f le n g th T c a rrie s a u n iq u e in fo rm a tio n b it a n d T -1 re p lic a s . T h e u n iq u e in fo r m a tiv e c o d e w o r d b it c a n b e re c o v e re d b y s im p le m a jo rity o r th re s h o ld d e c o d in g .

P. Brazdil and A. Jorge (Eds.): EPIA 2001, LNAI 2258, pp. 96–103, 2001. c Springer-Verlag Berlin Heidelberg 2001 

Recursive Adaptive ECOC models

le a rn c la s s firs t lin e a

e rs . L e t o f e rro r e x a m p le r c o d e s .

u s a d , w E a

c o a p e c h

n s id tiv e c a n M -v

e r th e E C O C th in k a lu e d

a p p lic a tio a lg o rith m a b o u t th e o u tp u t la b

n o f th is s b a s e d o c la s s o f E e l c a n b e

re s n b C O b ro

u lt in a C k e n

b in a ry la b e ls b y m e a n s o f a s u ita b le q u a n tiz a tio n

Q

to th e d e ry e rro r c a lg o rith m d o w n in M

s ig n o rre s in to k

o f c tin d u c , k

97

a g e n e ra liz e d g c o d e s . A s a e d b y b in a ry

≥ ⎡l o g

2

M

⎤

p ro c e s s . A fte rw a rd s , e a c h

k −b i t s t r e a m c a n b e c h a n n e l e n c o d e d u s i n g c o d e w o r d s o f l e n g t h n f k . F o l l o w th e E C O C a p p ro a c h , a n o is y c o d e w o rd h c a n b e c o m p u te d a t th e le a rn e r’s s id e th a t th e le a rn in g p ro b le m c a n b e e x p re s s e d a s a g e n e ra l d e c o d in g in s ta n c e . D e c o d is in e s s e n c e a d e c is io n m a k in g p ro c e s s . G iv e n a re c e iv e d n o is y c o d e w o rd , a d e c o tr ie s to f ig u r e o u t a tr a n s m itte d in f o r m a tio n b it o r a tr a n s m itte d c o d e w o r d . M a x im L ik e lih o o d d e c o d in g w h ile m in im iz in g th e p ro b a b ility o f c o d e w o rd e rro r d o n e c e s s a ry m in im iz e s th e p ro b a b ility o f s y m b o l (b it) e rro r. S y m b o l M a x im u m P o s te r io r i (M A P ) d e c o d in g m e th o d s e ffe c tiv e ly m in im iz e s b it e rro r p ro b a b ility c o m p u tin g th e m a x im u m o n th e s e t o f a p o s te r io r i p r o b a b ilitie s (A P P ) [7 ]. L e t c i

in g s o in g d e r u m n o t A b y b e

a c o d e w o rd b it in a c o d e w o rd c o f le n g th n a n d k in fo rm a tiv e c o d e w o rd b its a t th e firs t k p o s itio n s . T h e A P P p ro b a b ilitie s a re a s fo llo w s

p (c T h e e v e n d e c o d in g tim m a th e m a tic a is d e fin e d b y D efi n i ti on

t

c o n te x t r e in c lu d in g l d e s c rip tio n th e p a rity c h

e fe c h o f e c

i

rs in g e n e ra a n n e l s ta tis tic th e c o d in g s c k m a trix H o

( li n ea r block cod e) A

g e n e ra to r m a trix G c o d e w o r d c = u ⋅G

1 ≤i ≤k

|c o n te x t )

(n

lin e a r

l to s , th h e m r th e ,k

)

a ll a v a ila b e re c e iv e d n e . F o r lin e a r g e n e ra to r m

re la tio n H

⋅c

=0

le in fo rm a tio n a t s y m b o l o is y c o d e w o rd h a n d th e b lo c k c o d e s s u c h s tru c tu re T a trix G .

b lo c k c o d e is d e fin e d b y a

n ×k

b in a ry

s o th a t a k -b it b in a ry s o u rc e m e s s a g e u is e n c o d e d a s a n −b it v e c to r o r m o d 2 . I n a d d i t i o n f o r a s y s t e m a t i c c o d e G = [I k P ]. A l t e r n a t i v e l y , a

lin e a r b lo c k c o d e c a n b e d e fin e d th ro u g h p a rity c h e c k m a trix *

(1 )

m o d 2 h o ld s , b e in g c

*

H (n

− k )× n

fo r w h ic h

H (n

− k )× n

th e

th e tra n s p o s e c o d e w o rd .

In o u r le a rn in g -d e c o d in g fra m e w o rk , c h a n n e l s ta tis tic s a re d e fin e d b y s ta tis tic a l b e h a v io r o f b in a ry le a rn e rs ' e rro rs . In th is w a y , w e c a n th in k a b o u t a d is c re te m e m o ry le s s c h a n n e l c o n s tru c te d in a tra in in g p h a s e a n d e x p lic itly u s e d in fu tu re p r e d ic t i o n s b y m e a n s o f s u it a b l e A P P d e c o d i n g a l g o r i t h m s . T h e u s e o f A P P d e c o d i n g te c h n iq u e s fo r E C O C e x p a n s io n s b a s e d o n b in a ry lin e a r c o d e s a llo w s th e d e s ig n o f e rro r a d a p tiv e le a rn in g a lg o rith m s in a rb itra ry o u tp u t d o m a in s . It s h o u ld b e n o te d , h o w e v e r, th a t e rro r a d a p ta tio n is o n ly o n e o f th e le a rn in g c o n s tra in ts . It is w e ll k n o w n th a t E C O C s c h e m e s s h o u ld re s e m b le ra n d o m c o d in g in o rd e r to a c h ie v e s u c c e s s fu l le a rn in g . E C O C c o d e s fo u n d b y e x h a u s tiv e s e a rc h c a n n o t b e d e c o d e d b y A P P m e th o d s a s n o u n d e rly in g m a th e m a tic a l s tru c tu re c a n b e d e fin e d o n th e m . It is fo rm u la tio n th o u g h re q u irin g a lm o s t w o rth w h ile to n o te th a t th e E C O C p s e u d o ra n d o m c o d e s d o e s n o t ta k e a d v a n ta g e o f th e ra n d o m c o d in g c h a ra c te ris tic in th e d e c o d in g s te p . T o b e fa ir, o n e s h o u ld re m e m b e r th a t p ra c tic a l c o d in g th e o ry d id th e s a m e fo r a lm o s t 5 0 y e a rs u n til th e d e v e lo p m e n t o f ite ra tiv e d e c o d in g te c h n iq u e s [8 ] fo r re c u rs iv e e rro r c o rre c tin g c o d e s [9 ] lik e T u rb o C o d e s [1 0 ] [ 1 1 ] o r L D P C c o d e s .

98

Elizabeth Tapia et al.

T h e s e b in a ry lin e a r c o d e s a re fo r c o n s tru c tio n in h e re n tly p s e u d o ra n d o m . D e c o d in g is p e rfo rm e d in a re c u rs iv e w a y e a c h u s in g tim e A P P d e c o d in g m e th o d s . R e g a rd in g th e s e c o n s id e ra tio n s , w e w ill fo c u s o u r a tte n tio n o n E C O C a lik e a lg o rith m s b a s e d b in a r y lin e a r r e c u r s iv e e r r o r c o r r e c tin g c o d e s a n d ite r a tiv e A P P d e c o d in g te c h n iq u e s i.e . th e s o c a lle d o n R E C O C m o d e ls [ 5 ]. B y m e a n s o f a s im p le e x a m p le , le t u s e x p la in h o w th e a b o v e c o n s id e ra tio n s fit in th e d e s ig n o f lo w c o m p le x ity e rro r a d a p tiv e le a rn in g a lg o rith m s in n o n -b in a ry o u tp u t d o m a i n s . L e t u s a s s u m e M =1 6 s o t h a t k = 4 c a n b e a s s u m e d . E a c h o u t p u t l a b e l i s f i r s t e x p r e s s e d i n b i t s t r e a m s u = (u 0 , u 1 , u 2 , u 3 ) a n d t h e n c h a n n e l e n c o d e d b y

(8

m e a n s o f a s im p le

,4 ,4

)2

e x te n d e d Θ H a m m in g c o d e . T h e c o d e is s y s te m a tic w ith

s ix te e n d iffe re n t c o d e w o rd s . A

c = (u 0 ,

tra n s m itte d

u 1,

u 2,

u 3,

z4,

z5,

z 6,

z 7

)

Θ- c o d e w o r d h a s p a r i t y b i t s z i , 4 ≤i ≤ 7 d e f in e d a s f o llo w s

z z

5

+u 5

+u

z

0

4

+u

z

5

+u

+u 1

+u 2

=0

0

+u 1

+u 3

=0

0

+u

1

+u

+u 2

+u

3

2

(2 )

=0 =0

3

E a c h e q u a tio n in (3 ) c a n b e c o n s id e re d tra n s m is s io n o f th r e e in fo rm a tio n b its . In le a r a ls o d e fin e d in te rm s o f fo u r p a rity c h e c k s u le a rn in g o f s o m e ta rg e t c o n c e p t in a n M ’= 8 o u m o d e le d b y m e a n s o f th e s o -c a lle d T a n n e r g r c o n s t r a i n t s S t , 0 ≤t ≤ 3 , a n d c o d e w o r d b i t s e d g e s a re p u t c o n n e c tin g p a rity c o n s tra in ts to c R e d u n d a n t c o n c e p ts a re in tro d u c e d in o rd e n o i s e . A r e c e i v e d n o i s y c o d e w o r d h = (h 0 , h 1 ,

a s im p le p a rity c h e c k c o d e n i n g t e r m s , o u r (8 , 4 , 4 ) c o d e b c o d e s , e a c h o f th e m in v o lv e tp u t s p a c e . T h is re c u rs iv e v ie w a p h s [9 ] [ 1 2 ] . T h e s e t o f p a r i t y d e fin e th e n o d e s in th e g ra p o d e w o r d b i t s ( s e e F i g .1 ) . r to c o p e w ith th e u n d e rly in g h 2 , h 3, h 4, h 5, h 6, h 7 ) is th

fo r c a n d in c a n c o d h w h

th e b e th e b e in g ile

le a rn in g e re s u lt

o f a r a n d o m t o g g l i n g p r o c e s s o n c o d e w o r d b i t s ( b i n a r y c o n c e p t s ) i n c = [c i ], 0 ≤ i ≤ 7 . A s im p le m o d e l fo r th is to g g lin g p ro c e s s is a b in a ry d is c re te a d d itiv e o n e .

f i (c i

) = P (h

.I n th is w a y , th e g ra p h . h i v a ria b le s le a rn e rs ’ p re d ic tio n M -v a lu e d o n e ) c a n

a b a re s . I b e

i

|c i

⎧ p i ⎩1 − p

)= ⎨

o v e s e t o f in s ta n tia te n a d d itio n , c o n s tra in e

c o d a in f d b

i

n s tra t c o d o rm a y a p

h i

h i

in ts e w o tio n rio r

≠c =c i

(3 )

0 ≤i ≤7 i

c a n b e rd re c e b its (b d is trib

d ire c tly p tio n tim in a ry ta rg u tio n g i e

in tro d u c e a s th e y e t c o n c e p = p (u i ) ,

d a r ts 0

in a T e th e b d e fin in ≤i ≤ 3

a n n e r in a ry g th e . T h e

r e s u l t i n g e x t e n d e d T a n n e r g r a p h i s k n o w n a s t h e c o d e F a c t o r g r a p h [8 ] ( F i g . 1 ) . A R E C O C r u l e r e q u i r e s t h e c o m p u t a t i o n o f p r o b a b i l i t i e s p (c i | Θ, f o , . . , f n −1 , g o , . . . g k −1 ) ,

2

s o th a t w e c a n g iv e a n e s tim a te c i

* o f e a c h b in a ry in fo rm a tiv e ta rg e t c o n c e p t

U s i n g s t a n d a r d c o d i n g n o t a t i o n , i t d e n o t e s a (n , k , d c o d e w o rd le n g th , k th e n u m b e r o f in fo rm a tio n b its a n d d

)

lin e a r b lo c k c o d e , b e in g n t h e m i n i m u m c o d e d is t a n c e

th e

Recursive Adaptive ECOC models *

c

i

=a rg M a x

[ p (c

p e d rv h e

s c a n f P e a r in th e ire m e

u i

T h e s e g e n e ra liz T h e o b s e c y c le s . T

ro b v e e d o n

a b ilitie rs io n o re s u lts ly re q u

| Θ, f 0 , . . , f i

b e l 's B c o d n t w

c o m p u e lie f p in g fie o u ld b

n −1

te ro ld e

, g

d b p a g a re k n o

0

,...g

y a a tio a lm w le

)]

m e n [1 o s t d g e

k −1

s s a 3 ] o p o f

i = 0 , . . . . ,k −1

g e -p a s s in g a lg o a lg o rith m in g ra tim a l, d e s p ite o f p ro b a b ilitie s p

99

(4 )

rith m n a m e ly p h w ith c y c le s th e p re s e n c e o i , 0 ≤ i ≤ n −1

g o v e rn in g th e le a rn in g n o is e . H o w e v e r, th e s e p ro b a b ilitie s c a n b e e s tim a te d fro m th e tra in in g e rro r re s p o n s e s a c h ie v e d b y th e s e t o f b in a ry le a rn e rs u n d e r th e tra in in g s e ts T S i in d u c e d in e n c o d in g E C O C tra in in g p h a s e fro m th e o rig in a l tra in in g s a m p le T S .

p

h

=P i

h 0

f

c

S 4

f

h

f

h 4

5

5

z 7

f

6

G r a p h

3

6

h

3

T a n n e r

S

6

f

3

c

2

z 5

4

f 2

S 1

(5 )

3

2

c

z

z

0 ≤ i ≤ n −1

h

f 1

1

S 0

[h i (x ) ≠ y ] h 2

f

0

i

1

0

c

T S

h

7

7

F ig .1 .F a c to r G r a p h f o r th e ( 8 ,4 ,4 ) e x te n d e d H a m m in g c o d e

3 R E COC_ L D P C In o rd e r to o b ta in g o o d re s u lts w ith ite ra tiv e d e c o d in g te c h n iq u e s a p p lie d to re c u rs iv e c o d e s b a s e d o n s im p le p a rity c h e c k c o d e s , s o m e a d d itio n a l c o n s tra in ts o n th e T a n n e r g ra p h s tru c tu re a re re q u ire d . T h e s e c o n s tra in ts a re m e t b y th e s o -c a lle d L D P C c o d e s . D efi n i ti on L D P C cod es [ 6 ] . A L o w - D e n s i t y P a r i t y C h e c k ( L D P C ) c o d e i s s p e c i f i e d b y a c o n ta in in g m o s tly 0 ´s a n d a s m a ll n u m b e r o f 1 ´s . A p s e u d o ra n d o m p a rity c h e c k m a trix H b i n a r y (n , j , k ) L D P C c o d e h a s b l o c k l e n g t h n a n d a p a r i t y - c h e c k m a t r i x H w i t h e x a c t j 1 ´s in e a c h ro w , a s s u m in g j ≥3 a n d k ≥ j . T h u s e v e ry c o d e b it is j p a rity c h e c k s a n d e v e ry p a rity c h e c k in v o lv e s k c o d e w o rd b its . T h e t y p i c a l m i n i m u m d i s t a n c e o f t h e s e c o d e s in c r e a s e s l i n e a r l y w i t h n f o r a f i x e d k a n d j . o n e s p e r c o lu m n a n d k c h e c k e d b y e x a c tly

a . f ,

100

Elizabeth Tapia et al.

L e t u s c o n s id e r th e L D P C c o d e s h o w n in F ig . 2 th ro u g h its fa c to r g ra p h re p re s e n ta tio n . S u c h a c o d e is c o n s tru c te d fro m fiv e p a rity c h e c k s u b c o d e s th u s g iv in g p a r ity c o d in g c o n s tr a in ts S j ,0 ≤ j ≤ 4 . L D P C c o d e s c a n b e d e c o d e d a g e n e ra liz a tio n o f P e a rl’s B e lie f P ro p a g a tio n a lg o rith m [ 1 4 ][ 1 5 ]. C o m p o n e n t s u b c o d e s i.e . p a r ity c o n s tr a in ts b e h a v e lik e c o m m u n ic a tio n s o c k e ts f o r th e s e t o f in v o lv e d b in a ry le a rn e rs W L i is s u in g th e o b s e rv e d b in a ry p re d ic tio n s h i o n b in a ry ta rg e t c o n c e p ts c c o m p u ta tio m o d e ls a re o n T a n n e r T h e re fo re ,

, 0 o fa r g ra th e y i

n

≤ i ≤9 . I t s h o u l d b e n o t e d t h a t t h e B P a l g o r i t h f c o n d itio n a l p ro b a b ilitie s o v e r c y c le -fre e g ra p a w a y fro m b e in g c y c le -fre e . H o w e v e r, ite ra tiv e p h s w ith c y c le s b a s e d o n th e B P a lg o rith m w o m a y a ls o p e rfo rm w e ll fo r o u r R E C O C _ L D P C le S

p

(c i

m h s d e rk a rn

is c o a n d c o d in a lm o in g a

n c e rn e d w fa c to r g r g a lg o rith s t o p tim a lg o rith m .

ith a p h m s lly .

j

) c

(h

i

p

c

h

i

i

)

i

F ig .2 .A ( n = 1 0 , j= 3 , k = 5 ) L D P C c o d e m a p p e d in to a R E C O C _ L D P C s c h e m e

RECOC_LDPC Algorithm Input (n, j, k) LDPC by the parity check matrix H Quantizer Q

bits per input in { 1 , . . . , M

with k M

Training Sample T S

and G

with

=m

T S

T S

} on T S

, Distribution D

Binary Weak Learner W L , Iterations I for BP Processing RECOC ( T S , Q M

,G

,W L 0

,.., W L

n −1

,p o

,..., p

n −1

))

Output h f

(x ) = Q M

−1

( B P ( H

, x ,

I, W L 0

,..., W L

n −1

,p 0

,..., p

n −1

))

T h e R E C O C p ro c e d u re p e rfo rm s th e E C O C e n c o d in g s ta g e b u t w ith a d d itio n a l c o m p u t a t i o n o f t r a i n i n g e r r o r r e s p o n s e s p i , 0 ≤ i ≤ n −1 . I n t h e p r e d i c t i o n s t a g e , t h i s

Recursive Adaptive ECOC models

101

s e t w i l l b e u s e d i n t h e B P d e c o d i n g w i t h Io f i t e r a t i v e d e c o d i n g s t e p s . T h e n , a s e t o f k in fo rm a tiv e b in a ry ta rg e t c o n c e p ts w ill b e e s tim a te d . F in a lly , a fin a l h y p o th e s is w ill b e o b ta in e d b y a p p lic a tio n o f in v e rs e q u a n tiz a tio n p ro c e s s Q

−1

.

M

4 E x p er i m en ta l R es u lts for R E COC_ L D P C lea r n i n g W e h a v e te s te d th e R E C O C _ L D C P L e a rn in g a lg o rith m s w e re de v e lo p e T h e r e f o r e , A d a B o o s t ( A B ) , D e c is io n m u ltic la s s c a s e ) im p le m e n ta tio n s d d o c u m e n ta tio n . F o r L D P C c o d e c r d e v e l o p e d a li b r a r y e x t e n s i o n o f W M a c K a y s o ftw a re [1 5 ]. W e a d o p te d lo n =⎡ g 2

R

M

⎤, b e in g

R =1 − k j

th e

a lg o rith m u s in g p S tu m p 3 (D e ta ils c a n e a tio n a n d E K A [1 6 ] d

o n v a rio u s U C I le a r u b lic d o m a in J a v a W S ) a n d C 4 .5 4 ( d e n o te d b e fu lly d e te rm in e d th e B P p ro p a g a tio n s o ftw a re u s in g p u b lic ( n ,4 , k ) L D P C o u tp u t e n c o d in g

c h a n n e l ra te

(in fo rm a tiv e b in a ry

ta rg e t c o n c e p ts ) p e r c o d R E C O C _ L D C P (R ) + D S , th e te s t e rro r ra te fo r R R u s in g D S le a rn e rs . A ls o , le t u s d e n o te b y R e rro r fo r R E C O C _ L D P C le a rn in g a t c h a n n e l ra b o o s tin g s te p s o n D S le a rn e rs . T e s t e rro r re s P rim a ry T u m o r, L y m p h a n d A u d io lo g y a g a in u s e d in th e B P a lg o rith m a re s h o w n fro m F ig .3 c h a n n e l e n c o d in g i.e . a b a r e tr a n s m is s io n o f th

in

o f

d o m a lib r 4 fo r W E ith m , a in D m e s w

in fo rm a tio n

le n g th

e w o rd E C O C E C O C

te R p o n s s t a to F e q u

n u m b e r

n in g E K A b y C fro m a lg o r d o m s c h e

e s m ig

a n

R E C O C _ L D P C (R )+ A d a B o o s t(T )+ D S T e s t E r r o r - 6 6 % s p lit - P r im . T u m o r - M = 2 2

0 ,2 5 0 ,9 0 ,2

0 ,8 5 0 ,8 0 ,7 5 E rro r

E rro r

0 ,1 5 0 ,1

0 ,7 0 ,6 5

0 ,0 5

0 ,6

0 0

2

4

6

8

1 0

3 0

5 0 1 5 0 Ite r a tio n s

0 ,5 5 0 ,5 0

2

4

6

8

1 0

3 0

5 0 I t e r a t io n s

R e c o c (0 .0 8 )

R e c o c (0 .0 8 )+ A B (3 )

R e c o c (0 .0 8 )+ A B (5 )

C 4

4

3

F ig . 3 . A n n e a l. R E C O C _ L D P C te s t e rro r b e lo w C 4 .

D e c is io n tre e w ith o n ly o n e n o d e R . Q u in la n ’s d e c is io n tre e a lg o rith m

a llo w s

b its

n . L e t u s d e n o te b y _ L D P C le a rn in g a t c h a n n e l ra te _ L D C P (R ) + A B (T ) + D S th e te s t w ith T in n e r b in a ry A d a B o o s t fo r le a rn in g d o m a in s , A n n e a l, a x im u m n u m b e r o f ite ra tio n s I .6 . T e s t e r r o r r e s p o n s e s w ith o u t tiz a tio n s c h e m e Q M o n th e M

v a lu e d o u tp u t d o m a in a r e s h o w n f o r I= 0 . R E C O C _ L D P C T (R )+ A d a B o o s t(T )+ D S T e s t E r r o r - 6 6 % s p lit - A n n e a l - M = 6

in s . a ry . th e K A w e . J . ith

R e c o c (0 .0 4 )

R e c o c (0 .0 4 )+ A B (3 )

R e c o c (0 .0 4 )+ A B (1 0 )

C 4

F ig . 4 . P rim a ry T u m o r. R E C O C _ L D P C a llo w s te s t e rro r b e lo w C 4

in its C 4 .5 R e v is io n 8 p u b lic v e r s io n

102

Elizabeth Tapia et al. R E C O C _ L D P C ( R ) + A d a B o o s t( T ) + D S T e s t E r r o r - 6 6 % s p lit - L y m p h - M = 4

R E C O C _ L D P C (R )+ A B (T )+ D S T e s t E r r o r - 6 6 % s p lit - A u d io lo g y - M = 2 4

0 ,3

0 ,6

0 ,2 5

0 ,5 E rro r

E rro r

0 ,2 0 ,1 5

0 ,4

0 ,1

0 ,3

0 ,0 5

0 ,2 0 ,1

0 0

2

4

6

8

1 0

3 0

5 0

110

0

130 150 I t e r a t io n s

R e c o c ( 0 .0 8 )

R e c o c ( 0 .0 8 ) + A B ( 3 )

R e c o c ( 0 .0 8 ) + A B ( 5 )

C 4

rv e d re s u lts s h o w th a t a s id s ire d b o o s tin g e ffe c t is a c h s ). T h e o b s e rv e d re s u lts a rfo rm a n c e fo r L D P C c o d e s , s te p s a n d d e c re a s in g c h a n n e s t th a t fo r c a s e s w h e re R E m ig h t b e o n th e u n d e rly in g u c h u n d e s ira b le b e h a v io r.

2

3

4

5

R e c o c (0 .0 8 ) R e c o c (0 .0 8 )+ A B (5 )

F ig . 5 . L y m p h . R E C O C _ L D P C w ith in n e r b o o s tin g a llo w s te s t e rro r b e lo w C 4

T h e o b s e c a s e s th e d e (D S le a rn e r d e c o d in g p e o f ite ra tio n s re s u lts s u g g th e p ro b le m b e c a u s in g s

1

6

7

8

9

1 0

2 0

3 0

4 0 5 0 I t e r a t io n s

1 0 0

R e c o c (0 .0 8 )+ A B (3 ) C 4

F i g . 6 .A u d i o l o g y . R E C O C _ L D P C c a n n o t le a rn b e lo w C 4 .

e f r o m C 4 .5 b e n c h m a r k c o m p a r is o n s , in a ll ie v e d w ith re s p e c t to th e b a s e le a rn in g m o d e l re c o n s is te n t w ith th e ty p ic a l B P re c u rs iv e i.e . b e tte r p e r f o r m a n c e f o r in c r e a s in g n u m b e r e l ra te s (n o t s h o w n ). In a d d itio n , p e rfo rm a n c e C O C _ L D P C h a s a n e rro r flo o r (A u d io lo g y ), c o d e its e lf i.e . a r e p r e s e n ta tio n p r o b le m m ig h t

5 Con clu s i on s a n d F u r ther W or k T h e m a in c o n trib u tio n o f th is w o rk h a s b e e n th e d e v e lo p m e n t a g e n e ra l d e c o d in g fra m e w o rk fo r th e d e s ig n o f lo w -c o m p le x ity e rro r a d a p tiv e le a rn in g a lg o rith m s . F ro m th is d e c o d in g v ie w o f th e le a rn in g fro m e x a m p le s p ro b le m , a c h a n n e l is c o n s tru c te d in th e tra in in g p h a s e a n d it is la te r u s e d in a p re d ic tio n s ta g e . L e a rn in g a lg o rith m s in th is m o d e l p la y a d e c o d in g fu n c tio n b y m e a n s o f A P P d e c o d in g m e th o d s u n d e r th e a s s u m p tio n th a t a R e c u rs iv e E rro r C o rre c tin g O u tp u t e n C o d in g (R E C O C ) e x p a n s io n h a s ta k e n p la c e a t a tra n s m itte r o r te a c h e r s id e . T h is fra m e w o rk e m b o d ie s th e s ta n d a rd A d a B o o s t a lg o r ith m a s a n in s ta n c e o f th r e s h o ld d e c o d in g f o r s im p le r e p e tit i o n c o d e s . R E C O C le a rn in g m o d e ls c a n b e d e s c rib e d b y c o d in g re la te d g ra p h ic a l m o d e ls . In a d d itio n , R E C O C p re d ic tio n s c a n b e e x p la in e d b y g e n e ra l m e s s a g e -p a s s a g e s c h e m e s o n th e ir u n d e rly in g g ra p h ic a l m o d e ls . T h is is a n a p p e a lin g d e s c rip tio n o f le a rn in g a lg o rith m s , w h ic h a llo w s a n in tu itiv e b u t p o w e rfu l d e s ig n a p p ro a c h . A n u m b e r o f d i r e c t i o n s f o r f u r t h e r w o r k a n d r e s e a r c h s t a n d o u t . B e s i d e s i t s v a lid a t i o n w i t h r e a l d a ta , it re m a in s to s tu d y c o n v e rg e n c e c h a ra c te ris tic s , th e e ffe c t o f c h a n n e l m o d e l a s s u m p tio n s a n d a lte rn a tiv e b in a ry le a rn in g s c h e m e s . G o o d a lte rn a tiv e s fo r fu rth e r r e s e a r c h a r e G a l l a g e r 's a l g o r i t h m s A a n d B [ 6 ] a n d a s i m p l i f i e d i m p l e m e n t a t i o n [ 1 7 ] o f th e B P a lg o rith m .

Recursive Adaptive ECOC models

103

Ackn ow led g em en ts E liz a n d b y T e c 0 2 . A lm

a b e th T a p ia ’s th e N a tio n a l U th e A m o C o m h n o lo g y (M C Y D u rin g th is w a d e n R e s e a rc h

w o rk is s u n iv e rs ity o p lu te n s e P T , S p a in ) o rk , h e w C e n te r, S a

p p o rte d b y a n A rg e n tin e a n G o v e rn m e n t F f R o s a rio , A rg e n tin a . J a v ie r G a rc ía ’s w o rk ro g ra m a n d b y th e S p a n is h M in is try o f u n d e r p ro je c ts T IC 2 0 0 0 -0 7 3 5 a n d T IC 2 0 0 a s w ith th e IB M R e s e a rc h D iv is io n K 6 5 n J o s e , C a lifo rn ia , U S A (ja v ie rv i@ a lm a d e n

O M E C g is s u p p o S c ie n c e 0 -0 7 3 7 -C /C 2 a t I .ib m .c o m

ra n t rte d a n d 0 3 B M ).

R efer en ces 1 . D ie tte r ic h , T ., B a k ir i, G .: E r r o r - c o r r e c tin g o u tp u t c o d e s : A g e n e r a l m e th o d f o r im p r o v in g m u ltic la s s in d u c tiv e le a rn in g p ro g ra m s . P ro c e e d in g s o f th e N in th N a tio n a l C o n fe re n c e o n A rtific ia l In te llig e n c e (A A A I-9 1 ), p p . 5 7 2 -5 7 7 , A n a h e im , C A : A A A I P re s s (1 9 9 1 ) 2 . S c h a p ir e , R . E ., S in g e r , Y .: I m p r o v e d B o o s tin g A lg o r ith m s U s in g C o n f id e n c e - r a te d P re d ic tio n s . M a c h in e L e a rn in g , V o l. 3 7 , N o . 3 , p p . 2 7 7 -2 9 6 (1 9 9 9 ) 3 . D ie tte r ic h , T .: E n s e m b le M e th o d s in M a c h in e L e a r n in g . I n J . K ittle r a n d F . R o li ( E d s .) . M u ltip le C la s s ifie r S y s te m s , M C S 0 1 . S p rin g e r L e c tu re N o te s in C o m p u te r S c ie n c e , p p . 1 1 5 , (2 0 0 0 ) 4 . T a p ia , E ., G o n z á le z , J .C ., V ille n a , J .: A G e n e r a liz e d C la s s o f B o o s tin g A lg o r ith m s B a s e d o n R e c u r s iv e D e c o d in g M o d e ls . I n J . K ittle r a n d F . R o li ( E d s .) . M u ltip le C la s s if ie r S y s te m s , M C S 0 2 . S p rin g e r L e c tu re N o te s in C o m p u te r S c ie n c e , p p . 2 2 -3 1 , C a m b rid g e , U K , (2 0 0 1 ) 5 . T a p ia , E , G o n z á le z , J .C ., V illa lb a , L : O n th e d e s ig n o f E r r o r A d a p tiv e E C O C a lg o r ith m s . I n P r o c . I D D M 2 0 0 1 W o r k s h o p , 1 2 th E C M L , p p . 1 3 9 - 1 5 0 , F r e i b u r g ( 2 0 0 1 ) 6 . G a lla g e r , R . G .: L o w D e n s ity P a r ity - C h e c k C o d e s . C a m b r id g e , M a s s a c h u s e tts , M .I .T . P r e s s (1 9 6 3 ) 7 . M a s s e y , J .: T h r e s h o ld D e c o d in g . C a m b r id g e , M A : M .I .T . P r e s s ( 1 9 6 3 ) 8 . K s c h is c h a n g F ., F r e y , B .: I te r a tiv e d e c o d in g o f c o m p o u n d c o d e s b y p r o b a b ility p r o p a g a tio n in g ra p h ic a l m o d e ls . IE E E J . S e l. A re a s in C o m m . V o l. 1 6 , N o . 2 , p p . 2 1 9 -2 3 0 (1 9 9 8 ) 9 . T a n n e r , M .: A r e c u r s iv e a p p r o a c h to L o w C o m p le x ity E r r o r C o r r e c tin g C o d e s . I E E E T r a n s . In f. T h e o ry , V o l. 2 7 , p p . 5 3 3 -5 4 7 (1 9 8 1 ) 1 0 .B e r r o u , C ., G la v ie u x , A .: N e a r O p tim u m E r r o r C o r r e c tin g C o d in g a n d D e c o d in g : T u r b o C o d e s . IE E E T ra n s . o n C o m m u n ic a tio n s , V o l. 4 4 , N o . 1 0 , p p . 1 2 6 1 -1 2 7 1 (1 9 9 6 ) 1 1 .B e n e d e tto S ., M o n to r s i G .: U n v e ilin g T u r b o C o d e s : S o m e R e s u lts o n P a r a lle l C o n c a t e n a te d C o d in g S c h e m e s . IE E E T ra n s . In f. T h e o ry , V o l. 4 2 , N o . 2 , p p . 4 0 9 -4 2 8 , (1 9 9 6 ) 1 2 .W ib e r g , N .: C o d e s a n d D e c o d in g o n G e n e r a l G r a p h s . D o c to r a l D is s e r ta tio n , D e p a r tm e n t o f E le c tric a l E n g in e e rin g , L in k ö p in g U n iv e rs ity , S w e d e n (1 9 9 6 ) 1 3 .P e a r l, J .; " F u s io n , P r o p a g a tio n a n d S tr u c tu r in g in B e lie f N e tw o r k s " , A r tif ic ia l I n te llig e n c e , N o . 2 9 , p p . 2 4 1 -2 6 8 (1 9 8 6 ) 1 4 .R ic h a r d s o n , T ., U r b a n k e , R .: T h e C a p a c ity o f L o w D e n s ity P a r ity C h e c k C o d e s u n d e r M e s s a g e P a s s in g D e c o d in g . IE E E T ra n s . In f. T h e o ry , V o l. 4 7 , N o . 2 , p p . 5 9 9 -6 1 8 (2 0 0 1 ) 1 5 .M a c K a y , D . J .: G o o d E r r o r C o r r e c tin g C o d e s b a s e d o n V e r y S p a r s e M a tr ic e s . I E E E T r a n s . In f. T h e o ry , V o l. 4 5 , p p . 3 9 9 - 4 3 1 (1 9 9 9 ) 1 6 .W itte n , I ., F r a n k E .: D a ta M in in g , P r a c tic a l M a c h in e L e a r n in g T o o ls a n d T e c h n iq u e s w ith J A V A Im p le m e n ta tio n s . M o rg a n K a u fm a n n P u b lis h e rs , S a n F ra n c is c o , C a lifo rn ia (2 0 0 0 ) 1 7 .F o s s o r ie r , M . P .C ., M ih a lje v ic , M ., H id e k i, I .: R e d u c e d C o m p le x ity I te r a tiv e D e c o d in g o f L o w D e n s ity P a r ity C h e c k C o d e s B a s e d o n B e lie f P r o p a g a tio n . I E E E T r a n s . o n C o m m ., V o l. 4 7 , p p . 6 7 3 -6 8 0 (1 9 9 9 )

A Study on End-Cut Preference in Least Squares Regression Trees Luis Torgo LIACC-FEP, University of Porto R.Campo Alegre, 823 4150 PORTO, PORTUGAL email: [email protected], URL: http://www.liacc.up.pt/∼ltorgo

Abstract. Regression trees are models developed to deal with multiple regression data analysis problems. These models fit constants to a set of axes-parallel partitions of the input space defined by the predictor variables. These partitions are described by a hierarchy of logical tests on the input variables of the problem. Several authors have remarked that the preference criteria used to select these tests have a clear preference for what is known as end-cut splits. These splits lead to branches with a few training cases, which is usually considered as counter-intuitive by the domain experts. In this paper we describe an empirical study of the effect of this end-cut preference on a large set of regression domains. The results of this study, carried out for the particular case of least squares regression trees, contradict the prior belief that these type of tests should be avoided. As a consequence of these results, we present a new method to handle these tests that we have empirically shown to have better predictive accuracy than the alternatives that are usually considered in tree-based models.

1

Introduction

Regression trees [6] handle multivariate regression methods obtaining models that have proven to be quite interpretable and with competitive predictive accuracy. Moreover, these models can be obtained with a computational efficiency that hardly has parallel in competitive approaches, turning these models into a good choice for a large variety of data mining problems where these features play a major role. Regression trees are usually obtained using a least squares error criterion that guarantees certain mathematical simplifications [8, Sec. 3.2] that further enhance the computational efficiency of these models. This growth criterion assumes the use of averages in tree leaves, and can be seen as trying to find partitions that have minimal variance (i.e. squared error with respect to the average target value). The main drawback of this type of trees is the fact that the presence of a few outliers may distort both the average as well as having a strong influence in the choice of the best splits for the tree nodes. In effect, as we will see in this P. Brazdil and A. Jorge (Eds.): EPIA 2001, LNAI 2258, pp. 104–115, 2001. c Springer-Verlag Berlin Heidelberg 2001 

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paper, the presence of outliers1 may lead to the choice of split tests that have a very small sub-set of cases in one of the branches. Although these splits are the best according to the least squares error criterion they are counter-intuitive to the user and as we will see may even degrade predictive performance on unseen data. Users find it hard to understand that trees have top level nodes with branches that are very specific. Most users expect that top level nodes “discriminate” among the most relevant groups of observations (e.g. the observations with very high value of the target variable and the others). The work presented in this paper addresses the problem of allowing this type of splits in regression trees, which is known as the end-cut preference problem [2, p.313-317]. We study this type of splits and their effect on both predictive accuracy and interpretability of the models. We compare this to the alternative of avoiding this type of splits in the line of what was proposed by Breiman and colleagues [2]. Our extensive experimental comparison over 63 different regression problems shows that the differences in terms of predictive accuracy of both alternatives are quite often statistically significant. However, the overall number of significant differences does not show a clear winner, which contradicts prior belief on the effect of end-cut preference in tree-based regression models. In this paper we propose an alternative method that allows end-cut preference only in lower levels of the trees. The motivation behind this method is to avoid these splits in top level nodes, which is counter-intuitive for the users, but at the same time use them in lower levels as a means to avoid their negative impact in the accuracy of trees using least squares error criteria. Our experimental comparisons show a clear advantage of this method in terms of predictive accuracy when compared to the two alternatives mentioned before. In the next section we present a brief description of least squares regression trees methodology and of the end-cut preference problem. Section 3 presents an experimental comparison between the alternatives of allowing and not allowing end-cut splits. In Section 4 we describe our proposed approach to handle the end-cut preference problem, and present the results of comparing it to the other alternatives. Finally, in Section 5 we provide a deeper discussion of the study carried out in this paper.

2

Least Squares Regression Trees

A regression tree can be seen as a kind of additive regression model [4] of the form, l ki × I (x ∈ Di ) (1) rt (x) = i=1

ki s

where are constants; I (.) is an indicator function returning 1 if its argument is true and 0 otherwise; and Di s are disjoint partitions of the training data D l l   Di = D and = φ. such that i=1 1

i=1

These may be “real” outliers or noisy observations.

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These models are sometimes called piecewise constant regression models. Regression trees are constructed using a recursive partitioning (RP) algorithm. This algorithm builds a tree by recursively splitting the training sample into smaller subsets. The algorithm has three key issues: – A way to select a split test (the splitting rule). – A rule to determine when a tree node is terminal. – A rule for assigning a model to each terminal node (leaf nodes). Assuming the minimization of the least squares error it can be easily proven (e.g. [8]) that if one wants to use constant models in the leaves of the trees, the constant to use in each terminal node should be the average target variable of the cases falling in each leaf. Thus the error in a tree node can be defined as, Err (t) =

1 2 (yi − y t ) nt

(2)

Dt

where Dt is the set of nt training samples falling in node t; and y t is the average target variable (Y ) value of these cases. The error of a regression tree can be defined as,

nl

1 1 2 2 (yi − y l ) = (yi − y l ) n nl n Dl    Dl l∈T l∈T l∈T (3)  where T is the set of leaves of tree T ; and P (l) is the probability of a case falling in leaf l (which is estimated with the proportion of training cases falling in the leaf). During tree growth, a split test s, divides the cases in node t into a set of partitions. The decrease in error of the tree resulting from this split can be measured by, ni × Err (ti ) (4) ΔErr (s, t) = Err (t) − n i Err (T ) =

P (l) × Err (l) =

×

where Err (ti ) is the error on the subset of cases of branch i of the split test s. The use of this formula to evaluate each candidate split would involve several passes through the training data with the consequent computational costs when handling problems with a large number of variables and training cases. This would be particularly serious, in the case of continuous variables that are known to be the major computational bottleneck of growing tree-based models [3]. Fortunately, the use of the least squares error criterion, and the use of averages in the leaves, allow for further simplifications of the formulas described above. In effect, as proven in [8], for the usual setup of binary trees where each node has only two sub-branches, tL and tR , the best split test for a node is the test s that maximizes the expression,

A Study on End-Cut Preference in Least Squares Regression Trees

where SL =

 DtL

yi and SR =



S2 SL2 + R ntL ntR

107

(5)

yi .

DtR

This expression means that one can find the best split for a continuous variable with just a single pass through the data, not being necessary to calculate averages and sums of squared differences to these averages. One should stress that this expression could only be derived due to the use of the least squares error criterion and of the use of averages in the leaves of the trees2 . Breiman and colleagues [2] mention that since the work by Morgan and Messenger [5] it is known that the use of the least squares criteria tends to favor end-cut splits, i.e. splits in which one of the branches has a proportion of cases near to zero3 . To better illustrate this problem we describe an example of this end-cut preference occurring in one of the data sets we will use our experiments, the Machine 4 domain. In this data set the best split test according to the error criterion of Equation 5 for the root node of the tree, is the test M M AX ≤ 48000. This split divides the 209 training cases in two sub-branches, one having only 4 observations. This is a clear example of a end-cut split. Figure 1 helps to understand why this is the best split according to the criterion of Equation 5. As it can be seen in Figure 1, there are 4 observations (upper right part of the figure) that have end-cut values in the variable MMAX, and at the same time outlier values in the target variable. These are the two characteristics that when appearing together lead to end-cut splits. Within this context, a candidate split that “isolates” these cases in a single branch is extremely valuable in terms of the least squares error criterion of Equation 5. Allowing splits like M M AX ≤ 48000 in the example above, may lead to trees that seem quite ad-hoc to users that have a minimal understanding of the domain, because they tend to expect that top level nodes show highly general relations and not very specific features of the domain. This is reinforced by the fact that on most large data sets, trees do tend to be too deep for a user to grasp all details, meaning that most users will only be able to capture top-level splits. As such, although no extensive experimental comparisons have been carried out till now5 , it has been taken for granted that end-cut splits are undesirable, and most existing tree-based systems (e.g. CART [2], THAID [5] or C4.5 [7]) have some mechanism for avoiding them. However, if the drawbacks in terms of user expectations are irrefutable, as we will see in Section 3 the drawbacks of end-cut splits in terms of predictive accuracy are not so clear at all in the case of least squares regression trees.

2 3 4 5

In [8] a similar expression was developed for the least absolute deviation criterion with medians on the leaves of the trees. For a formal proof of end-cut preference see [2, p.313-317]. Available for instance in http://www.liacc.up.pt/∼ltorgo/Regression/DataSets.html. To the best of our knowledge.

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1 0 0 0

T a rg e t

8 0 0

6 0 0

4 0 0

2 0 0

0 0

1 0 0 0 0

2 0 0 0 0

3 0 0 0 0

4 0 0 0 0

5 0 0 0 0

6 0 0 0 0

7 0 0 0 0

M M A X

Fig. 1. An example of a end-cut preference problem.

3

An Experimental Analysis of the End-Cut Preference

In this section we carry out an experimental study of the consequences of end-cut splits. Namely, we compare the hypothesis of allowing this type of splits, and the alternative of using some form of control to avoid them. In this experimental comparison we have used 63 different regression data sets. Their main characteristics (number of training cases, number of continuous variables, and number of nominal variables) are shown in Table 1. Regarding the experimental methodology we have carried out 10 repetitions of 10-fold cross validation experiments, in the light of the recent findings by Bradford and Brodley [1] on the effect of instance-space partitions. Significance of observed differences were asserted through paired t-tests with 95 and 99 confidence levels. The first set of experiments we report compares the following two types of least squares regression trees6 . The first tree has no control over end-cut splits, thus allowing them at any stage of the tree growth procedure as long as they are better according to the criterion of Equation 5. The second type of trees does not allow splits7 that lead to branches that have less cases then a minimum value 6

7

Both are implemented in system RT (http://www.liacc.up.pt/∼ltorgo/RT/), and they only differ in the way they handle end-cut splits. All other features are the same. Both on continuous as well as nominal variables.

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Table 1. The Used Data Sets. Data Set Abalone (Ab) Delta Elevators (DE) Kinematics (Ki) ComputerA (CA) Algal1 (A1) Algal3 (A3) Algal5 (A5) Algal7 (A7) Auto-Mpg (AM) Bank8FM (B8) CloseNikkei (CN) Chlorophyll (Chl) House 16H (H16) Pyrimidines (Py) FacultyD5001 (Fa) ArtificialD2 (D2) Friedman Example (Fr) Machine CPU (Ma) Artificial MV (MV) Puma32NM (P32) WiscoinBreastCancer (WBC) Additive (Ad) Acceleration (Ac) CW Drag (CW) Driving Noise (DN) Fuel Total (FTo) Maximal Torque (MT) Maintenance Interval (MI) Steering Acceleration (SAc) Steering Velocity (SV) Fluid Swirl (FS) Delta Ailerons (DA)

Characteristics 4177; 7; 1 9517; 6; 0 8192; 8; 0 8192; 22; 0 200; 8; 3 200; 8; 3 200; 8; 3 200; 8; 3 398; 4; 3 4500; 8; 0 2000; 49; 1 72;4;1 22784; 16; 0 74; 24; 0 197; 33; 0 40768; 2; 0 40768; 10; 0 209; 6; 0 25000; 7; 3 4500; 32; 0 194; 32; 0 30000; 10; 0 1732; 11; 3 1449; 12; 2 795; 22; 12 1766; 25; 12 1802; 19; 13 1724; 6; 7 63500; 22; 1 63500; 22; 1 530; 26; 6 7129; 5; 0

Data Set Elevators (El) Ailerons(Ai) Telecomm (Te) ComputerS (CS) Algal2 (A2) Algal4 (A4) Algal6 (A6) Anastesia (An) Auto-Price (AP) Bank32NH (B32) CloseDow (CD) House8L (H8) Diabetes (Di) Triazines Employment (Em) Industry (In) Housing (Ho) Marketing (Mkt) Puma8NH (P8) Servo CaliforniaHousing (CH) 1KM (1KM) CO2-emission (CO2) Available Power (AP) Fuel Town (FTw) Fuel Country (FC) Top Speed (TS) Heat (He) Steering Angle (SAn) Fluid Discharge (FD) China (Ch)

Characteristics 8752; 40; 0 7154; 40; 0 15000; 26; 0 8192; 12; 0 200; 8; 3 200; 8; 3 200; 8; 3 80; 6; 0 159; 14; 1 4500; 32; 0 2399; 49; 1 22784; 8; 0 43; 2; 0 186; 60; 0 368; 18; 0 1555; 15; 0 506; 13; 0 944; 1; 3 4500; 8; 0 167; 0; 4 20460; 8; 0 710; 14; 3 1558; 19; 8 1802; 7; 8 1764; 25; 12 1764; 25; 12 1799; 17; 7 7400; 8; 4 63500; 22; 1 530; 26; 6 217; 9; 0

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established by the user. In our experiments we have set this minimum value to 10 cases. Table 2 shows the results of the comparison between the two alternatives in terms of Normalized Mean Squared Error (NMSE). Columns two and three show the data sets where we observed a statistically significant win of some method at different confidence levels, and the fourth column shows the cases where the observed differences were not statistically significant. Table 2. End-Cut versus No End-Cut in terms of NMSE. 99% 95% Not significant 20 2 15 End-Cut Ad,AP,B32,Chl,CO2,CW,D2, Ac,A1,A2,A3,A5,A6,A7, Wins FS,FTo,FTw,He,Ma,MI,MT, FC,FD Ch,CN,Fa,DN,Ho,Te,AP,WBC An,Se,SAc,SAn,SV,TS 17 2 7 No End-Cut 1KM,Ab,Ai,B8,CH,CD,CA, Wins CS,DA,DE,El,Fr,H16,H8,Ki In,Py A4,AP,Di,Mkt,MV,Em,Tr P32,P8

The first thing to remark is that there is a statistically significant difference between the two approaches on 41 of the 63 data sets. This reinforces the importance of the question of how to handle end-cut splits. However, contrary to our prior expectations based on previous works (e.g [2]), we didn’t observe a clear advantage of not using end-cut splits8 . On the contrary, there is a slight advantage of the alternative allowing the use of end-cut splits at any stage of tree growth (the average NMSE over all data sets of this alternative is 0.4080, while not allowing end-cut splits leads to an average NMSE of 0.4140). The main conclusion to draw from these results is that they provide strong empirical evidence towards the need of a re-evaluation of the position regarding end-cut splits in the context of least squares regression trees. Why should end-cut splits be beneficial in terms of predictive error? We believe the best answer to this question is related to the statistic used to measure the error. Least squares regression trees revolve around the use of averages and squared differences to these averages (c.f. Section 2). The use of averages as a statistic of centrality for a set of cases is known to suffer from the presence of outliers. By not allowing the use of end-cut splits that tend to isolate these outliers in a separate branch (c.f. Figure 1), every node will “suffer” the influence of these extreme values (if they exist). This will distort the averages, which may easily lead to larger errors as the predictions of the trees are obtained using the averages in the leaves. Going back to the example described in Section 2 with the Machine data set, if one does not allow the use of end-cut splits, instead of 8

Still, we must say that the method proposed in [2] for controlling these splits is slightly different from the one use d in our experiments.

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immediately isolating the four outlier cases shown in Figure 1, they will end-up falling in a leaf that includes 10 other observations. This leaf has an average target variable value of 553.64, which will be the prediction of the tree for every test case falling in this leaf. However, 10 out of the 14 observations in this leaf, have a target value in the range [208..510]. Thus the distribution in this leaf is clearly being skewed by the outliers and this provides an idea of the risk of using this leaf to make predictions. The same conclusion can be reached by looking at the Mean Squared Errors9 at the leaves of both trees. While the tree using endcut splits has an average MSE over all leaves of 5132.2, the tree without end-cut splits has and average of 15206.4, again highlighting the effect of these outliers, that clearly increase the variance in the nodes. One should remark that this does not mean that the tree using end-cut splits is overfitting the data, as both trees went through the same post-pruning process that is supposed to eliminate this risk (moreover the experimental comparisons that were carried out show that this is not occurring, at least in a consistent way). In resume, although clearly going against the intuition of users towards the generality of the tests in the trees, end-cut splits provide some accuracy gains in several data sets. This means that simply eliminating them can be dangerous if one is using least squares error criteria. We should stress that the same conclusions may not be valid if other error criteria were to be used such as least absolute deviations, or even the criteria used in classification trees, as these criteria do not suffer such effects of outliers. As a consequence of the experimental results reported in Table 2 we propose a new form of dealing with end-cut splits that tries to fulfill the interpretability expectations of users that go against the use of end-cut splits, while not ignoring the advantages of these splits in terms of predictive accuracy. This new method is described in the next section.

4

A Compromising Proposal for Handling End-Cut Preference

The main idea behind the method we propose to deal with end-cut preference is the following. End-cut splits should not be allowed in top level nodes of the trees as they handle very specific (poorly represented in the training sample) areas of the regression input space, thus going against the interpretability requirements of most users. As such, our method will use mechanisms to avoid these splits in top level nodes of the trees, while allowing them in bottom nodes as a means to avoid the distorting effects that outliers have in the averages in the leaves. In order to achieve these goals we propose a simple method consisting of not allowing end-cut splits unless the number of cases in the node drops below a certain user-definable threshold10 . Moreover, as in the experiments of Section 3, a test is considered an end-cut split if one of its resulting branches has less than 9 10

Larger values of MSE indicate that the values are more spread around the average. In the experiments we will report we have set this threshold to 100 cases.

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a certain number of cases11 . This means that nodes with a number of training cases between the first and second of these thresholds are allowed to consider end-cut splits. These are the bottom nodes of the trees12 . Our hypothesis is that with this simple method we will obtain trees that are acceptable in terms of interpretability from the user perspective, but at the same time will outperform both alternatives considered in Section 3 in terms of predictive accuracy. With the purpose of testing this hypothesis we have carried out an experiment similar to the one reported in Section 3, but now comparing our proposed method with the two alternatives of allowing end-cut splits everywhere, and not allowing them at all. The results of comparing our method to the former alternative are shown in Table 3. Table 3. Our method compared to allowing end-cut splits in terms of NMSE. 99% 95% Not significant 16 0 22 Our Method Ab,Ad,Ai,CH,CD,CA,D2,DA, 1KM,A2,A3,A5,AP,B8,CS Wins DE,El,H16,H8,In,Ki,Pu8,SV DN,FD,FTo,FTw,FC,He,MI Mkt,Em,Pu32,SAc,SAn,TS,Tr 2 0 23 End-Cut Ac,A6,A7,AM,B32,Chl,Ch, Wins A1,Fa CN,CO2,CW,Di,FS,Fr,Ho,Ma, MT,MV,Te,AP,Py,An,WBC,Se

This comparison clearly shows that there is no particular advantage in allowing end-cut splits everywhere, when compared to our proposal (with two single exceptions). Moreover, our proposal ensures that this type of splits will not appear in top level nodes of the trees13 , which fulfills the user’s expectations in terms of interpretability of the models. In effect, going back to the Machine example, with our proposal we would not have a root node isolating the four outliers (as with the alternative of allowing end-cut splits), but they would still be isolated in lower levels of the tree14 . What this comparison also shows is that our proposal can outperform the method of allowing end-cut splits in several data sets. It is interesting to observe that most of these 16 cases are included in the set of 17 significant losses of the alternative allowing end-cut splits shown in Table 2. 11 12 13 14

We have used the value of 10 for this threshold. Unless the training sample is less than 100 cases, which is not the case in all but four of our 63 benchmark data sets (c.f. Table 1). Unless the data set is very small. Namely, the root node would consist of the split M M AX ≤ 28000, which divides the 209 training cases in 182 and 27, respectively, and then the 27 cases (that include the 4 outliers) would be split with the end-cut test M M AX ≤ 48000 ( c.f. Figure 1 to understand what is being done with these splits).

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The results of comparing our method to the alternative of not allowing endcut splits are shown in Table 4. Table 4. Our method compared to not allowing end-cut splits in terms of NMSE. 99% 95% Not significant 22 2 13 Our Method Ad,AP,B32,Chl,CD,CO2,CW,D2, Ac,A2,A3,A5,A6,A7, Wins FD,FS,FTo,FTw,He,Ma,MI,MT, FC,H8 DE,DN,H16,In,Mkt,AP,Tr An,Se,SAc,SAn,SV,TS 10 4 12 No End-Cut 1KM,Ai,B8,CH,CA, Ab,A4,AM,Ch,CN,DA, Wins CS,El,Fr,Ki,Pu32 A1,Fa,Pu8,Py Di,Ho,MV,Em,Te,WBC

Once again we observe a clear advantage of our proposal (24 significant wins), although there are still 14 data sets where not allowing end-cut splits seems to be preferable. However, comparing to the alternative of always allowing end-cut splits, which has clear disadvantages from the user interpretability perspective, our method clearly recovers some of the significant losses (c.f. Table 2). It is also interesting to remark that with the single exception of the H8 data set, all 22 wins of the strategy using end-cut splits over the no-end-cuts approach, are included in the 24 wins of our proposal. This means that our method fulfills our objective of being able to take advantage of the gains in accuracy entailed by the use of end-cut splits, in spite of not using them in top levels of the trees. In spite of the advantages of our proposal, there are also some drawbacks that should be considered. Namely, there is a tendency for producing larger trees (in terms of number of leaves) than with the other two alternatives that were considered in this study. This is reflected in the results shown in Table 5, that presents the comparison in terms of number of leaves of our proposal with the other two alternatives. Table 5. Tree size comparison of our method with the other two alternatives. No End-Cut Splits All End-Cut Splits 99% 95% Not significant 99% 95% Not significant Our Wins 23 2 3 1 0 15 Our Losses 31 0 5 20 2 25

These results seem to contradict our goal of a method that produces trees more interpretable to the user than the trees obtained when allowing end-cut splits. Interpretability is known to be a quite subjective issue. Still, we claim that in spite of having a larger number of leaves (c.f. Table 5), the trees obtained with

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Luis Torgo

our method are more comprehensible. As we have mentioned before, in most realworld large data sets, the trees obtained by this type of systems are too large for any user to be able to grasp all details. As such, we argue that only top-level nodes are in effect “understood” by the user. As our method does not allow end-cut splits in these top level nodes, we claim that this leads to trees that are more comprehensible to the user.

5

Discussion

The results of our empirical study on the effects of end-cut preference within least squares regression trees, lead us to the conclusion that there is no clear winner among the two standard alternatives of allowing or not allowing the use of end-cut splits. These results are somehow surprising given the usual position regarding the use of these splits. However, our study confirms the impact of the method used to handle these splits on the predictive accuracy of least squares regression trees. Our analysis of the reasons for the observed results indicates that this study should not be generalized over other types of trees (namely classification trees). The method we have proposed to handle end-cut splits is based on the analysis of the requirements of users in terms of interpretability, and also on the results of our empirical study. By allowing end-cut splits only in lower levels of the trees, we have shown that it is possible to outperform the other two alternatives considered in the study in terms of predictive accuracy. Moreover, this method avoids end-cut splits in top level nodes which goes in favor of user expectations in terms of comprehensibility of the trees. However, our results also show that there is still some space for improvements in terms of predictive accuracy when compared to the alternative of not allowing end-cut splits. Future work, should be concentrated in trying to find not so ad-hoc methods of controlling these splits so as to avoid some of the still existing significant losses in terms of predictive accuracy. Moreover, the bad results in terms of tree size should also be considered for future improvements of our proposal.

6

Conclusions

We have described an empirical study of the effect of end-cut preference in the context of least squares regression trees. End-cut splits have always been seen as something to avoid in tree-based models. The main conclusion of our experimental study is that this assumption should be reconsidered if one wants to maximize the predictive accuracy of least squares regression trees. Our results show that allowing end-cut splits leads to statistically significant gains in predictive accuracy on 22 out of our 63 benchmark data sets. In spite of the disadvantages of end-cut splits in terms of the interpretability of the trees from the user perspective, these experimental results should not be disregarded. We have described a new form of dealing with end-cut splits that tries to take into account our empirical observations. The simple method we have described

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shows clear and statistically significant improvements in terms of predictive accuracy. Still, we have also observed that there is space for further improvements. Future work should try to improve the method we have described, and also to carry out similar studies for tree-based models using different error criteria.

References 1. J. Bradford and C. Broadley. The effect of instance-space partition on significance. Machine Learning, 42(3):269–286, 2001. 2. L. Breiman, J. Friedman, R. Olshen, and C. Stone. Classification and Regression Trees. Statistics/Probability Series. Wadsworth & Brooks/Cole Advanced Books & Software, 1984. 3. J. Catlett. Megainduction: machine learning on very large databases. PhD thesis, Basser Department of Computer Science, University of Sidney, 1991. 4. T. Hastie and R. Tibshirani. Generalized Additive Models. Chapman & Hall, 1990. 5. J. Morgan and R. Messenger. Thaid: a sequential search program forthe analysis of nominal scale dependent variables. Technical report, Ann Arbor: Institute for Social Research, University of Michigan, 1973. 6. J. Morgan and J. Sonquist. Problems in the analysis of survey data, and a proposal. Journal of American Statistics Society, 58:415–434, 1963. 7. J. Quinlan. C4.5: programs for machine learning. Kluwer Academic Publishers, 1993. 8. L. Torgo. Inductive Learning of Tree-based Regression Models. PhD thesis, Faculty of Sciences, University of Porto, 1999.

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Abs tr a ct. M o s t o f t h e e x i s t i n g d a t a m i n i n g a p p r o a c h e s t o t i m e s e r i e s p r e d i c t i o n u s e a s tra in in g d a ta a n e m b e d o f th e m o s t re c e n t v a lu e s o f th e tim e s e rie s , fo llo w in g th e tra d itio n a l lin e a r a u to -re g re s s iv e m e th o d o lo g ie s . H o w e v e r, in m a n y tim e s e rie s p re d ic tio n ta s k s th e a lte rn a tiv e a p p ro a c h th a t u s e s d e riv a tiv e fe a tu re s c o n s tru c te d fro m th e ra w d a ta w ith th e h e lp o f d o m a in th e o rie s c a n p ro d u c e s ig n ific a n t p re d ic tio n a c c u ra c y im p ro v e m e n ts . T h is is p a rtic u la rly n o tic e a b le w h e n th e a v a ila b le d a ta in c lu d e s m u ltiv a ria te in fo rm a tio n a lth o u g h th e a im is s till th e p re d ic tio n o f o n e p a rtic u la r tim e s e rie s . T h is la tte r s itu a tio n o c c u rs fre q u e n tly in fin a n c ia l tim e s e rie s p re d ic tio n . T h is p a p e r p re s e n ts a m e th o d o f fe a tu re c o n s tru c tio n b a s e d o n d o m a in k n o w le d g e th a t u s e s m u ltiv a ria te tim e s e rie s in fo rm a tio n . W e s h o w th a t th is m e th o d im p ro v e s th e a c c u ra c y o f n e x t-d a y s to c k q u o te s p re d ic tio n w h e n c o m p a re d w ith th e tra d itio n a l e m b e d o f h is to ric a l v a lu e s e x tra c te d fro m th e o rig in a l d a ta .

1

In tr od u cti on

R e c e n tly , s e v e ra l d a ta m in in g te c h n iq u e s h a v e b e e n a p p lie d w ith s u c c e s s to tim e s e r ie s p r e d ic tio n b a s e d o n s a m p le s o f h is to r ic a l d a ta ( e .g . [ 1 ] , [ 5 ] , [ 2 0 ] ) . M o s t o f th e s e a p p ro a c h e s u s e s u p e rv is e d m a c h in e le a rn in g te c h n iq u e s a n d a d a ta p re p a ra tio n s ta g e th a t p ro d u c e s a s e t o f e x a m p le s in a tw o -d im e n s io n , ta b u la r, “ s ta n d a rd fo rm ” [2 8 ]. S e v e ra l a p p ro a c h e s c a n b e u s e d to p re p a re th is k in d o f ta b u la r re p re s e n ta tio n fro m th e tim e s e rie s ra w d a ta . C h o o s in g th e m o s t a p p ro p ria te s e t o f fe a tu re s fo r th e tim e s e rie s p ro b le m in h a n d c a n h a v e a s ig n ific a n t im p a c t o n th e o v e ra ll a c c u ra c y o f th e p re d ic tio n m o d e ls . T h is is th e m a in p ro b le m a d d re s s e d in th is p a p e r, fo r th e p a rtic u la r c a s e o f fin a n c ia l tim e s e rie s p re d ic tio n .

1 .1

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T h e d a ta tim e s e rie

s im p le s t to p ro d u c s e rie s a s s a s th e

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T h e U s e o f D o m a in K n o w le d g e in F e a tu re C o n s tru c tio n

1 1 7

p re p a ra tio n te c h n iq u e is u s u a lly c a lle d “ tim e -d e la y e m b e d d in g ” [2 2 ], “ ta p p e d d e la y lin e ” o r “ d e la y s p a c e e m b e d d in g ” [1 7 ]. T o illu s tra te th e b a s ic te m p o ra l e m b e d d in g , le t u s c o n s id e r a n u n iv a ria te tim e s e rie s

X (t) = … , x

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k n o w n . L e t u s fu rth e r ic t th e n e x t v a lu e o f th e c e s s . A s s u m in g th a t th is e m b e d a p p ro a c h e s w ill n e o f th e k p re v io u s c o m p le te e x a m p le w ill

t+ 1

w h e r e x t+ 1 i s t h e v a l u e o f t h e t a r g e t ( d e p e n d e n T h is k in d o f d a ta p re p a ra tio n fo rm s th e b s e rie s p re d ic tio n m e th o d s lik e A R [2 9 ] o r A R th e T a k e n s th e o re m [2 4 ]. T h is th e o re m s ta te s ( 2 ⋅N ) + 1 p a s t v a l u e s i s e n o u g h t o r e c o n s t r u c t d im e n s io n s . In th e c a s e o f th e d e s c rib e d X (t) a n d c o n s id e rin g th e s e rie s to b e g e n e ra te d b y x t-1 , x t-2 , … , x t-(2 N ) w o u l d b e e n o u g h f o r t h e e p re d ic tin g fu tu re v a lu e s o f th e tim e s e rie s . 1 .2

t+ 2

t) v a ria b le . a s is o f th e c la s s ic a l a u to re g re s s iv e tim e M A [6 ], a n d is th e o re tic a lly ju s tifie d b y th a t, w ith s o m e re s tric tio n s , a n u m b e r o f th e m o d e l o f a n o is e le s s s y s te m w ith N tim e s e rie s , a s s u m in g a b s e n c e o f n o is e , a N - d i m e n s i o n a l s y s t e m , t h e f e a t u r e s x t, x tra c tio n o f th e s y s te m m o d e l a n d fo r

L i m i ta ti on s of the T em p or a l E m bed

It s h o u ld b e re m a rk e d th a t m a n y re a l-life s y s te m s s u ffe r c o m p le x in te ra c tio n s w ith o th e r s y s te m s a n d , e v e n if th e y h a v e a n in trin s ic lin e a r b e h a v io r, th e y te n d to g e n e ra te tim e s e rie s th a t p re s e n t s e v e re p ro b le m s to c o m p ly w ith th e T a k e n s th e o re m re s tric tio n s . In p a rtic u la r, th is th e o re m d o e s n o t s e e m to a p p ly to m o s t fin a n c ia l tim e s e rie s , n a m e ly , to s to c k e x c h a n g e tim e s e rie s . In e ffe c t, s to c k e x c h a n g e tim e s e rie s a re g e n e ra te d b y e x tre m e ly c o m p le x s y s te m s th a t in v o lv e th e in te ra c tio n o f th o u s a n d s o r m illio n s o f in d e p e n d e n t a g e n ts (th e in v e s to rs ) e a c h c a p a b le o f c h a n g in g its b e h a v io r o v e r s h o rt tim e fra m e s a c c o rd in g to a v irtu a lly lim itle s s n u m b e r o f p o s s ib le in d iv id u a l “ s ta te s ” , re s u ltin g in a s y s te m w ith a n u m b e r o f d im e n s io n s th a t, in p ra c tic a l te rm s , m u s t b e c o n s id e re d in fin ite [1 4 ]. T h is fa c t im p lie s th a t th e n u m b e r o f h is to ric a l v a lu e s n e e d e d to c o n s tru c t e a c h e x a m p le in a w a y c o n fo rm in g to th e T a k e n s th e o re m c o n d itio n s w o u ld b e u n re a lis tic (th e n e c e s s a ry d a ta w o u ld n o t b e a v a ila b le a n d w o u ld b e u n m a n a g e a b le b y th e m a c h in e le a rn in g a lg o rith m s ). M o re o v e r, th e s y s te m g lo b a l b e h a v io r is n o t s ta tic o v e r tim e (fo r in s ta n c e , th e n u m b e r a n d in d iv id u a l c h a ra c te ris tic s o f th e in te rv e n in g a g e n ts a re n o t c o n s ta n t). T h is n o n -s ta tio n a ry b e h a v io r o f th e s y s te m m e a n s th a t “ o ld ” tim e s e rie s d a ta m a y n o t b e tru ly re p re s e n ta tiv e o f th e c u rre n t s y s te m (in fa c t, it w a s g e n e ra te d b y a re la te d b u t d iffe re n t s y s te m th a t n o lo n g e r e x is ts ) a n d u s in g th e m b lin d ly to g e n e ra te p re d ic tio n s fo r th e c u rre n t s y s te m c a n b e m is le a d in g .

1 1 8

P e d ro d e A lm e id a a n d L u ís T o rg o

T h e s e c h a ra c te ris tic s o f s to c k e x c h a n g e tim e s e rie s re s u lt in th e a lm o s t u n a n im o u s a d m itta n c e th a t b a s e d a ta c o n s is tin g s o le ly o f h is to ric a l v a lu e s o f th e tim e s e rie s b e in g p re d ic te d d o n o t c o n ta in e n o u g h in fo rm a tio n to e x p la in m o re th a n a fra c tio n o f th e v a ria n c e in th e tim e s e rie s . In fa c t, th e E ffic ie n t M a rk e ts T h e o ry [8 ], n o w s o m e w h a t d is c re d ite d ([1 ], [1 1 ], [1 5 ]) b u t s till a c c e p te d a s b a s ic a lly c o rre c t b y m a n y e c o n o m is ts , s ta te s th a t th o s e d a ta d o n o t c o n ta in a n y in fo rm a tio n u s e fu l fo r th e p re d ic tio n o f th e fu tu re b e h a v io r o f th e s y s te m . T h e p ro b le m s th a t im p a ir th e a p p lic a b ility o f T a k e n s T h e o re m to v e ry c o m p le x d y n a m ic s y s te m s d o n o t s e e m to b e re d u c e d b y th e u s e o f m u ltiv a ria te in fo rm a tio n a s b a s is d a ta fo r tim e s e rie s m o d e lin g . A s a n e x a m p le , th e o rig in a l d a ta w e u s e in o u r e x p e rim e n ts in c lu d e s 7 v a lu e s fo r e a c h d a y a n d e a c h s to c k . T h is c o rre s p o n d s to 7 tim e s e rie s th a t a re a v a ila b le to b e u s e d a s b a s ic d a ta fo r m o d e l c o n s tru c tio n . In th is c o n te x t, u s in g a ll th e 7 tim e s e rie s w ith a n e m b e d d im e n s io n o f, s a y , 2 5 (o b v io u s ly in s u ffic ie n t to in c lu d e e n o u g h in fo rm a tio n to d e s c rib e th e s y s te m ), w o u ld re s u lt in 1 7 5 fe a tu re s d e s c rib in g e a c h e x a m p le . E v e n if th o s e fe a tu re s w e re d is c re tiz e d to a d o p t a m a x im u m o f 5 d iffe re n t v a lu e s , th a t w o u ld c re a te a “ re p re s e n ta tio n s p a c e ” w ith th e 5 c a p a c ity o f d is tin g u is h in g 1 7 5 d iffe re n t c a s e s . T h is k in d o f in p u t d im e n s io n is o b v io u s ly to o la rg e c o n s id e rin g th e n u m b e r o f tra in in g a n d te s tin g e x a m p le s a v a ila b le (w e h a v e 1 0 y e a rs o f d a ily d a ta c o rre s p o n d in g to a ro u n d 2 4 0 0 re c o rd s ), a n d w o u ld re s u lt in a v e ry s p a rs e ly p o p u la te d s p a c e th a t w o u ld s e v e re ly lim it th e e ffic ie n c y o f m o s t m a c h in e le a rn in g a lg o rith m s [3 ], [2 3 ]. T h is p ro b le m is re in fo rc e d b y th e fa c t th a t, d u e to th e s y s te m c o m p le x ity a n d th e la c k o f s u ffic ie n t in fo rm a tio n o n th e b a s e d a ta , th e s y s te m b e h a v e s a s if e a c h v a ria b le (d e p e n d e n t a n d in d e p e n d e n t) in c lu d e s a s tro n g n o is e c o m p o n e n t. T h u s , s in c e a ll th e in fo rm a tio n p re s e n t in th e b a s e d a ta o n ly e x p la in s a s m a ll p ro p o rtio n o f th e s y s te m v a ria n c e a n d th e in fo rm a tio n p re s e n t in o u r 1 7 5 v a ria b le s w ill e x p la in a n e v e n s m a lle r p ro p o rtio n o f th a t v a ria n c e , w e c a n e x p e c t e a c h o f th o s e v a ria b le s to h a v e a v e ry s m a ll in d iv id u a l re le v a n c e to th e d e s ire d p re d ic tio n .

1 .3

Alter n a ti v es to the T em p or a l E m bed

In s itu a tio n s w h e re h e a v y o v e rfittin g p ro b le m s c a n b e e x p e c te d d u e to th e s p a rs e ly p o p u la te d re p re s e n ta tio n s p a c e a n d w h e n n o is y d a ta a re a s s o c ia te d w ith a p o s s ib ly la rg e n u m b e r o f in p u t v a ria b le s w ith lo w in d iv id u a l v a lu e to k n o w le d g e e x tra c tio n , it is fre q u e n tly p o s s ib le to o b ta in b e tte r re s u lts b y c o m b in in g s e v e ra l o f th e o rig in a l v a ria b le s [1 6 ], [1 9 ]. T h e a im o f d e v e lo p in g s u c h fe a tu re c o m b in a tio n s is th e c re a tio n o f a re d u c e d s e t o f “ d e riv a tiv e ” v a ria b le s h a v in g a g re a te r d is c rim in a tiv e p o w e r fo r th e m o d e lin g ta s k b e in g c o n s id e re d . O n e o f th e p o s s ib le a p p ro a c h e s to th e d e v e lo p m e n t o f a re d u c e d s e t o f d e riv a tiv e v a ria b le s th a t c o n ta in m o s t o f th e u s e fu l in fo rm a tio n p re s e n t in th e o rig in a l d a ta is th e u s e o f a n a u to m a te d m e th o d th a t s e a rc h e s fo r s o m e c o m b in a tio n o f th e o rig in a l v a ria b le s . T h e m o s t u s e d o f s u c h m e th o d s is “ P rin c ip a l C o m p o n e n t A n a ly s is ” [4 ]. T h is m e th o d d e v e lo p s o rth o g o n a l lin e a r c o m b in a tio n s o f th e o rig in a l v a ria b le s a n d ra n k s th e m o n th e b a s is o f th e ir a b ility to “ e x p la in ” th e ta rg e t v a ria b le v a ria n c e . T h e m a in p ro b le m w ith th is a p p ro a c h is th a t th e o rig in a l v a ria b le s a re re p la c e d b y th e m o s t s ig n ific a n t lin e a r c o m b in a tio n s a n d s o , th e d a ta m in in g a lg o rith m s w ill n o lo n g e r b e a b le to s e a rc h fo r n o n -lin e a r c o m b in a tio n s o f th e o rig in a l v a ria b le s . T h is a p p ro a c h

T h e U s e o f D o m a in K n o w le d g e in F e a tu re C o n s tru c tio n

1 1 9

is th e re fo re p a rtic u la rly a p p ro p ria te fo r “ d a ta re d u c tio n ” w h e n o n ly lin e a r p re d ic tio n m e th o d s w ill b e u s e d , a n d o n p ro b le m s re la te d to s y s te m s k n o w n a t s ta rt to b e b a s ic a lly lin e a r (c le a rly n o t th e c a s e o f s to c k e x c h a n g e tim e s e rie s [1 4 ], [3 1 ]). A n o th e r a p p ro a c h to fe a tu re c o n s tru c tio n c o n s is ts in th e “ m a n u a l” d e v e lo p m e n t o f a re d u c e d s e t o f d e riv a tiv e v a ria b le s u s in g d o m a in k n o w le d g e . T h is a p p ro a c h is p a rtic u la rly e ffic ie n t in d o m a in s w h e re th e re is a n a v a ila b le (b u t in c o m p le te , th u s n o t a llo w in g a d e te rm in is tic p re d ic tio n ) b o d y o f d o m a in th e o ry re la tin g th e d a ta to th e s y s te m m e c h a n ic s a n d b e h a v io r. In s to c k e x c h a n g e p re d ic tio n th e re is n o s u re d o m a in k n o w le d g e a n d , c o n s id e rin g o n ly h is to ric a l s to c k e x c h a n g e in fo rm a tio n a s b a s e d a ta , th e a v a ila b le d o m a in th e o rie s (re la te d to “ te c h n ic a l a n a ly s is ” o f s to c k s [7 ], [1 8 ]) a re p a rtic u la rly u n c e rta in [1 0 ]. H o w e v e r, th e la rg e n u m b e r o f k n o w n te c h n ic a l a n a ly s is in d ic a to rs 1 s e e m s a g o o d s ta rtin g p o in t to b u ild d e riv a tiv e fe a tu re s . In e ffe c t, th e h ig h ly u n c e rta in a p p lic a b ility o f th e s e in d ic a to rs to in d iv id u a l s to c k s , m a rk e ts , a n d tim e fra m e s , lim its th e m a s fin a l g lo b a l th e o rie s , b u t d o e s n o t p re v e n t th e ir u s e fu ln e s s to c o n s tru c t in p u t fe a tu re s fo r m a c h in e le a rn in g a lg o rith m s , s in c e m o s t o f th e s e a lg o rith m s c a n filte r o u t th e fe a tu re s th a t p ro v e to b e le a s t u s e fu l.

D a ta P r e-p r oces s i n g i n F i n a n ci a l T i m e S er i es P r ed i cti on A

2

re v ie w o f th e p u b lis h e d w o rk s o n fin a n c ia l tim e s e rie s p re d ic tio n s h o w s th a t, in s p ite o f th e lim ita tio n s m e n tio n e d in S e c tio n 1 .2 , m o s t w o r k s u s e e ith e r th e b a s ic v e rs io n o f te m p o ra l e m b e d o r v e ry lim ite d tra n s fo rm a tio n s o f th is te c h n iq u e . A s e x a m p le s o f th e u s e o f d ire c t te m p o ra l e m b e d , w e c a n m e n tio n th e u s e o f a d ire c t u n iv a ria te e m b e d o f d im e n s io n tw o to p re d ic t p a rtic u la rly s tro n g d a ily s to c k e x c h a n g e q u o te s v a ria tio n s [2 0 ], o r th e u s e o f a m u ltiv a ria te b a s ic e m b e d o f d a ily s to c k q u o te s in fo rm a tio n a s in p u t d a ta to a g e n e tic a lg o rith m u s e d to c o n d u c t a d ire c t s e a rc h fo r tra d in g c rite ria in [3 0 ]. R e g a rd in g th e u s e o f b a s ic tra n s fo rm a tio n s o f te m p o ra l e m b e d w e c a n re fe r th e a p p ro a c h fo llo w e d b y [1 3 ], w h o e m p lo y s th e d iffe re n c e o f th e lo g a rith m s o f th e la s t v a lu e s o f s e v e ra l tim e s e rie s to p re d ic t th e s to c k q u o te s o f s e v e ra l J a p a n e s e c o m p a n ie s , o r th e w o rk o f [1 5 ] w h e re lo g a rith m ic tra n s fo rm a tio n s o f th e d iffe re n c e s o f th e la s t tw o a n d th re e k n o w n v a lu e s o f e x c h a n g e ra te tim e s s e rie s a re u s e d to p re d ic t th e v a ria tio n d ire c tio n o f th o s e tim e s e rie s . In te re s tin g e x a m p le s o f m o re a m b itio u s a d a p ta tio n s o f th e b a s ic te m p o ra l e m b e d c a n b e fo u n d in tw o e n trie s o f th e im p o rta n t tim e s e rie s p re d ic tio n c o m p e titio n c a rrie d o u t in S a n ta F e in 1 9 9 2 [2 5 ]: M o z e r te s ts s e v e ra l tra n s fo rm a tio n s in v o lv in g d iffe re n t w e ig h ts fo r th e e m b e d d e d v a lu e s , in a n u n iv a ria te c o n te x t re la te d to th e p re d ic tio n o f e x c h a n g e ra te s b e tw e e n th e U S d o lla r a n d th e S w is s fra n c [1 7 ] a n d , fo r th e p re d ic tio n o f th e s a m e tim e s e rie s , Z a n g a n d H u tc h in s o n try a u n iv a ria te e m b e d u s in g n o n c o n s e c u tiv e p a s t v a lu e s fo r d iffe re n t p re d ic tio n tim e fra m e s [3 1 ]. A lth o u g h n o t s o fre q u e n t, it is a ls o p o s s ib le to fin d th e u s e o f m o re s o p h is tic a te d v a ria b le s d e riv e d fro m th e b a s e d a ta . A n e a rly e ffo rt is th e w o rk d e s c rib e d in [2 6 ],

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D e s c r ip tio n s c a n b e f o u n d in a v a r ie ty o f s o u r c e s , lik e , f o r in s ta n c e , h ttp ://tr a d e r s .c o m , o r h ttp ://w w w .tr a d e r s w o r ld .c o m )

1 2 0

P e d ro d e A lm e id a a n d L u ís T o rg o

w h e re a n e u ra l n e tw o rk w ith 6 1 in p u ts is u s e d fo r th e p re d ic tio n o f th e n e x t d a y v a lu e o f th e U S d o lla r / G e rm a n m a rk e x c h a n g e ra te . F o rty fiv e o f th e 6 1 v a ria b le s u s e d in th is w o rk c o rre s p o n d to a n e m b e d o f th e tim e s s e rie s b e in g m o d e le d , w h ile th e o th e r 1 6 v a ria b le s a re d e v e lo p e d fro m m u ltiv a ria te d a ta th a t th e a u th o rs b e lie v e to b e re le v a n t fo r th e p re d ic tio n o f th e tim e s e rie s . T h e w o rk p re s e n te d in [2 7 ] is a n o th e r e x a m p le in v o lv in g m o re s o p h is tic a te d d e riv a tiv e v a ria b le s a n d m o re c o m p le te m u ltiv a ria te b a s e d a ta . In th is la tte r s tu d y , th e o b je c tiv e is a ls o th e p re d ic tio n o f th e U S d o lla r / G e rm a n m a rk e x c h a n g e ra te . T h e a u th o rs u s e 6 9 in p u t v a ria b le s fo r th e n e u ra l n e tw o rk th a t p ro d u c e s th e p re d ic tio n s , b u t n o n e o f th o s e v a ria b le s a re th e re s u lt o f a d ire c t e m b e d o f th e tim e s e rie s b e in g p re d ic te d . In fa c t, 1 2 o f th e 6 9 v a ria b le s a re “ b u ilt” b a s e d o n p a s t v a lu e s o f th e tim e s e rie s , u s in g ty p ic a l “ te c h n ic a l a n a ly s is ” tra n s fo rm a tio n s , a n d th e o th e r 5 7 v a ria b le s re fle c t m u ltiv a ria te fu n d a m e n ta l in fo rm a tio n e x te rio r to th e tim e s e rie s b e in g p re d ic te d (u s in g d a ta a s s o c ia te d to e x c h a n g e r a te s b e tw e e n o th e r c u r r e n c ie s , in te r e s t r a te s , e tc .) . I n th e s e tw o w o r k s , th e la rg e n u m b e r o f v a ria b le s “ fe d ” to th e m a c h in e le a rn in g a lg o rith m s w ill le a d to o v e rfittin g p ro b le m s a n d , in e ffe c t, b o th w o rk s in c lu d e a s m a in o b je c tiv e s th e p re s e n ta tio n o f n e w te c h n iq u e s to re d u c e o v e rfittin g p ro b le m s in n e u ra l n e tw o rk s .

3 A S y s tem

for S tock Q u otes P r ed i cti on

W h e n th e g o a l is th e s h o rt-te rm (u p to a w e e k ) p re d ic tio n o f s to c k q u o te s , th e re le v a n c e o f fu n d a m e n ta l in fo rm a tio n (b o th m ic ro o r m a c ro -e c o n o m ic ) te n d s to b e s m a ll. In e ffe c t, e v e n if th is k in d o f in fo rm a tio n p ro v e s u s e fu l to p re d ic t a p a rt o f th e lo n g -te rm v a ria b ility o f th e s to c k s , th e p ro p o rtio n o f th a t a b ility w ith d ire c t re fle c tio n o n th e v a ria n c e o f th e n e x t fe w d a y s w o u ld b e v e ry s m a ll [1 1 ], [1 8 ]. T h u s , it s e e m s re a s o n a b le to b e lie v e th a t m o s t o f th e s h o rt te rm v a ria b ility o f s to c k v a lu e s is d u e to flu c tu a tio n s re la te d to th e b e h a v io r o f th e in v e s to rs , w h ic h te c h n ic a l a n a ly s is c la im s th a t c a n b e in fe rre d fro m p a s t v a ria tio n s o f th e s to c k q u o te s a n d v o lu m e s . H o w e v e r, th e re a re s till im p o rta n t p ro b le m s to a d d re s s , if a n a p p ro a c h b a s e d o n d e riv e d v a ria b le s b u ilt w ith th e h e lp o f d o m a in k n o w le d g e is to b e trie d . T h e s e p ro b le m s a re re la te d to th e u n c e rta in n a tu re o f th e e x is tin g te c h n ic a l a n a ly s is “ in d ic a to rs ” , a n d to th e v a s t n u m b e r o f e x is tin g in d ic a to rs (th e d ire c t u s e o f a la rg e n u m b e r o f d e riv a tiv e v a ria b le s o f th is k in d c o u ld le a d to o v e rfittin g p ro b le m s s im ila r to th o s e re la te d to th e u s e o f a la rg e d ire c t e m b e d [1 0 ]). A n a p p ro a c h b a s e d o n d e riv e d v a ria b le s w o u ld b e n e fit fro m a p ra c tic a l w a y o f re p re s e n tin g d o m a in k n o w le d g e (in th e fo rm o f te c h n ic a l a n a ly s is in d ic a to rs ) a n d a ls o fro m a n e ffic ie n t w a y o f g e n e ra tin g v a ria b le s fro m th a t re p re s e n ta tio n . A ls o , g iv e n th e la rg e q u a n tity o f p o s s ib le d e riv e d “ te c h n ic a l v a ria b le s ” it m a y b e a d v a n ta g e o u s to p e rfo rm s o m e k in d o f a u to m a tic filte rin g o f th e le s s re le v a n t fe a tu re s . T o try to c irc u m v e n t th e p ro b le m s a s s o c ia te d w ith th is a p p ro a c h , w e h a v e d e v e lo p e d a n in te g ra te d p re d ic tio n s y s te m th a t in c lu d e s a k n o w le d g e re p re s e n ta tio n la n g u a g e th a t a llo w s th e d ire c t d e s c rip tio n o f m o s t te c h n ic a l a n a ly s is in d ic a to rs u s in g p re -d e fin e d la n g u a g e e le m e n ts . B a s e d o n th e s e d e s c rip tio n s th e s y s te m is a b le to a u to m a tic a lly g e n e ra te fro m th e ra w d a ta th e fe a tu re s d e s c rib e d b y th e u s e r. T h is g e n e ra l s e t-u p c o u ld b e u s e d w ith a n y m a c h in e le a rn in g a lg o rith m th a t c o p e s w e ll w ith n o is y d a ta .

T h e U s e o f D o m a in K n o w le d g e in F e a tu re C o n s tru c tio n

1 2 1

W e c h o s e to te s t th is fra m e w o rk w ith a k -n e a re s t n e ig h b o r a lg o rith m [5 ], a n d w ith a re g re s s io n v e rs io n o f th e P A 3 ru le in d u c tio n a lg o rith m [2 ]. T h e k -N N a lg o rith m u s e s a d is ta n c e m e tric th a t in v o lv e s a ra n k in g o f fe a tu re im p o rta n c e , w h ile th e ru le in d u c tio n a lg o rith m d o e s n o t n e e d s u c h ra n k in g . H o w e v e r, d u e to th e d o m a in c h a ra c te ris tic s m e n tio n e d b e fo re , th is s y s te m a ls o g a in s fro m a re d u c tio n o f th e n u m b e r o f fe a tu re s . A s s u c h , o u r p re d ic tio n s y s te m in c lu d e s a fe a tu re ra n k in g a n d s e le c tio n s te p . T h e c o m p le te s y s te m a rc h ite c tu re is s h o w n in F ig u re 1 . T h e d o m a in k n o w le d g e re p re s e n ta tio n la n g u a g e a llo w s a d o m a in e x p e rt to d e fin e te c h n ic a l a n a ly s is in d ic a to rs u s in g a s im p le b u t fle x ib le re p re s e n ta tio n . A s e x a m p le s , c o n s id e r th e fo llo w in g in s tru c tio n s o f th is la n g u a g e : p e r c e n t( c lo ( i) ,c lo ( i+ 1 ) ) ; i= 0 ..3 r a tio ( m o a ( v o l,3 ,0 ) ,m o a ( v o l,1 5 ,0 ) ) T p e rc re sp c o rr v o lu

h e firs t o f th e n t v a ria tio n e c tiv e p re v io u e s p o n d in g to m e s o f th e s to

e s e in s tr b e tw e e n s c lo s in g th e ra tio c k a n d th

u c tio n s d th e la s t v a lu e . T b e tw e e n e m o v in g

e s c rib fo u r h e se th e m a v e ra

e s 4 d a ily c o n d o v in g e o f

fe a tu re s , e a c h c o rre s p c lo s in g v a lu e s o f a in s tru c tio n d e s c rib e s a g a v e ra g e o f th e la s t 3 th e la s t 1 5 d a ily tra d in g

o n d in g s to c k s in g le d a ily v o lu m

to th e a n d th e fe a tu re tra d in g e s 2.

D a ta p re -p ro c e s s in g :

D a ta m in in g :

D o m a in k n o w le d g e re p re s e n ta tio n la n g u a g e

F e a tu re ra n k in g a n d filte rin g

F e a tu re g e n e ra tio n

R a w m u ltiv a ria te tim e s e rie s d a ta

M a c h in e L e a rn in g a lg o rith m

F e a tu re d is c re tiz a tio n

P re d ic tio n

F ig .1 . T h e c o m p le te tim e -s e rie s p re d ic tio n s y s te m

2

T h e fe a tu re s d e fin e d w ith th e la n g u a g e a re a u to m a tic a lly g e n d a ta a n d a p p e n d e d w ith th e re s p e c tiv e ta rg e t v a lu e fo r e a c h g e fo rm a s e t o f e x a m p le s in th e ta b u la r “ n o rm a l fo rm ” . T h e re s u ltin g fe a tu re s c a n h a v e v e ry d iffe re n t d is c re te o r D is c re te fe a tu re s c a n h a v e o rd e re d in te g e r v a lu e s (fo r in s ta n c e , c o c o u n ts th e n u m b e r o f tim e s th e c lo s in g v a lu e is h ig h e r th a n th e o th e la s t 2 0 tra d in g d a y s ), b u t c a n a ls o h a v e n o n -o rd e re d v a lu e s re p re s e n ts th e w e e k d a y o f th e la s t tra d in g s e s s io n ). C o n tin u o u s fe v e ry d iffe re n t ra n g e s o f v a lu e s . G iv e n th e s e d iffe re n t c h a ra ⎯ ⎯ ⎯ ⎯ ⎯ T h v a e x v o

e th ird lu e u s p re s s io lu m e s

p a ra m e te e d in th e n r a tio (m (th e firs t u

r in m o o a (v s in g

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n s tru c to g e a n d ( v o l,3 ,1 a lu e s a n

r s p e c ifie s th e p re s e n )) re la te s d th e s e c o n

th e n u m b e r o f t re fe re n c e e x tw o 3 -d a y m o d u s in g th e firs t

e ra te d fro m th e ra w n e ra te d e x a m p le , to c o n tin u o u s n s id e r a fe a p e n in g v a lu ( e .g . a f e a a tu re s c a n a c te ris tic s a d a y s b e tw a m p le . T h v in g a v e r 3 o f th e la

v a lu e s . tu re th a t e d u rin g tu re th a t ls o h a v e fe a tu re

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la s t th e th e e s).

1 2 2

P e d ro d e A lm e id a a n d L u ís T o rg o

d is c re tiz a tio n m o d u le is ru n b e fo re th e s e t o f e x a m p le s is “ fe d ” to th e d a ta m in in g a lg o rith m s . T h is m o d u le d is c re tiz e s e a c h fe a tu re in to 5 v a lu e s u s in g a tra d itio n a l a p p ro a c h [9 ] th a t is k n o w n to b e h a v e w e ll o v e r n o is y d a ta . T h is d is c re tiz a tio n te c h n iq u e w o rk s in d iv id u a lly o v e r e a c h fe a tu re . It s ta rts b y a n a ly z in g th e e x a m p le s o f th e tra in in g s e t a n d th e n d iv id e s th e ra n g e o f v a lu e s o f e a c h fe a tu re in to fiv e in te rv a ls w ith th e s a m e n u m b e r o f v a lu e s in e a c h in te rv a l. E a c h o f th e s e in te rv a ls is re p re s e n te d b y a n in te g e r v a lu e ra n g in g fro m 1 to 5 , a n d th e e x a m p le s a re d is c re tiz e d in to o n e o f th e s e 5 d is c re te v a lu e s a c c o rd in g ly . T h is s im p le a p p ro a c h to fe a tu re d is c re tiz a tio n p ro d u c e d ro b u s t re s u lts o v e r o u r d a ta . A s s o m e a lg o rith m s a re a b le to w o rk w ith n o n d is c re tiz e d d a ta , w e h a v e c h e c k e d w h e th e r b y u s in g th is d is c re tiz a tio n s te p s o m e in fo rm a tio n w a s b e in g lo s t. W e h a v e n o t n o tic e d a n y s ig n ific a n t a c c u ra c y d iffe re n c e s in th e s e te s ts a n d th u s w e h a v e d e c id e d to w o rk o n ly w ith th e d is c re tiz e d d a ta . A fte r g e n e ra tin g th e tra in in g e x a m p le s , o u r p re d ic tio n s y s te m s ta rts th e c o re d a ta m in in g s te p w ith a fe a tu re ra n k in g a n d s e le c tio n m o d u le . T h e fe a tu re s e le c tio n p ro c e d u re a im s to re d u c e th e o v e rfittin g p ro b le m s re la te d to th e d iffic u lt d o m a in c h a ra c te ris tic s m e n tio n e d in S e c tio n 1 .2 . In e ffe c t, s o m e a lg o rith m s th a t u s e re p re s e n ta tio n la n g u a g e s w ith la rg e r d e s c rip tiv e p o w e r, a re a b le to fit a lm o s t p e rfe c tly th e h y p e rs u rfa c e d e fin e d b y th e tra in in g d a ta . T h is is th e c a s e o f o u r ru le in d u c tio n P A a lg o rith m . T h e s e m e th o d s w o u ld h a v e a te n d e n c y to fin d e x is tin g b u t n o n -m e a n in g fu l s ta tis tic flu c tu a tio n s o n th e tra in in g d a ta if g iv e n e n o u g h irre le v a n t fe a tu re s . T o p re v e n t th is k in d o f o v e rfittin g , w e in c lu d e a fe a tu re ra n k in g a n d filte rin g s te p in o u r s y s te m . T h is s te p u s e s a c o m b in a tio n o f th e fo llo w in g fe a tu re re le v a n c e m e a s u re s : th e in fo rm a tio n g a in ; th e P e a rs o n ’s r c o rre la tio n b e tw e e n e a c h fe a tu re a n d th e ta rg e t v a lu e s ; a n d a p o w e rfu l fe a tu re re le v a n c e m e tric th a t e v a lu a te s th e fe a tu re s in th e c o n te x t o f th e o th e r fe a tu re s [1 2 ]. T h e firs t tw o o f th e s e m e tric s lo o k to e a c h fe a tu re in d iv id u a lly , w h ile th e th ird c o n s id e rs fe a tu re in te ra c tio n s . T h e s e th re e m e a s u re s a re c o m b in e d to fo rm a n o v e ra ll ra n k in g , u s in g a d ire c t a v e ra g in g o f th e th re e in d e p e n d e n t fe a tu re ra n k in g s . R e g a rd in g th e s e le c tio n o f fe a tu re s w e s im p ly re ta in th e h ig h e s t ra n k in g fe a tu re s u p to a c e rta in n u m b e r3. T h e k -N N a lg o rith m w e h a v e u s e d in o u r p re d ic tio n s y s te m is in s p ire d in B o n te m p i’s w o rk [5 ]. It u s e s a n o rth o g o n a l “ M a n h a tta n ” d is ta n c e m e tric th a t w e ig h ts d iffe re n tly th e fe a tu re s a n d a lin e a r k e rn e l fu n c tio n th a t g iv e s g re a te r w e ig h ts to th e tra in in g e x a m p le s fo u n d to b e n e a re s t to th e te s t e x a m p le b e in g p re d ic te d . A fte r s e v e ra l te s ts o v e r s to c k e x c h a n g e tim e s e rie s 4, w e o p te d to u s e a fix e d n e ig h b o rh o o d o f 1 5 0 c a s e s . T h is c o n s id e ra b le n u m b e r o f n e ig h b o rs s e e m s to re s u lt in a g o o d b a la n c e b e tw e e n b ia s a n d v a ria n c e a n d h a s a n im p o rta n t e ffe c t in th e re d u c tio n o f o v e rfittin g p ro b le m s ty p ic a lly a s s o c ia te d to th e v e ry n o is y e x a m p le s s e ts e x p e c te d in s to c k e x c h a n g e tim e s e rie s p re d ic tio n . T h e ru le in d u c tio n a lg o rith m th a t w a s a ls o u s e d in o u r p re d ic tio n s y s te m is a re g re s s io n v a ria n t o f a g e n e ra l-p ro p o s e s e q u e n tia l-c o v e r a lg o rith m c a lle d P A 3 , w h ic h h a n d le s tw o -c la s s p ro b le m s . T h is a lg o rith m w a s d e v e lo p e d to b e e ffic ie n t o v e r n o is y d a ta , a n d p e rfo rm e d w e ll w h e n c o m p a re d w ith o th e r ru le in d u c tio n a lg o rith m s o v e r s e v e ra l n o is y d a ta s e ts (in c lu d in g s to c k e x c h a n g e tim e s e rie s p re d ic tio n ) [2 ]. P A 3

⎯ 4

3

⎯

⎯

⎯

⎯

In th is w o rk w e h a v e u s e d 1 0 fe a tu re s in a ll te s ts . T h is p a ra m e te r tu n in g w a s c a rrie d o u t u s in g o n ly th e s u b -s e t o f s to c k d a ta th a t w a s u s e d fo r tra in in g p u rp o s e s a c c o rd in g to th e p a rtitio n in g th a t w ill b e d e s c rib e d in S e c tio n 4 .

T h e U s e o f D o m a in K n o w le d g e in F e a tu re C o n s tru c tio n

1 2 3

in d u c e s a n o rd e re d lis t o f “ if… th e n … ” ru le s . E a c h ru le h a s th e fo rm “ if < c o m p le x > th e n p re d ic t < c la s s > ” , w h e re < c o m p le x > is a c o n ju n c t o f fe a tu re te s ts , th e “ s e le c to rs ” . In P A 3 , e a c h s e le c to r im p lie s te s tin g a fe a tu re to s e e if its v a lu e is in c lu d e d in a s p e c ifie d ra n g e o f v a lu e s . T h e p o s tc o n d itio n o f a P A 3 ru le is a s in g le B o o le a n v a lu e th a t s p e c ifie s th e c la s s th a t th e ru le p re d ic ts . T o p ro d u c e a re g re s s io n (n u m e ric ) p re d ic tio n in s te a d o f a c la s s p re d ic tio n , w e h a v e u s e d th e v e ry s im p le a p p ro a c h o f a s s ig n in g a s p o s tc o n d itio n o f e a c h ru le th e m e a n v a lu e o f th e tra in in g e x a m p le s c o v e re d b y th e ru le . T h is v a ria n t o f th e o rig in a l P A 3 a lg o rith m w a s a ls o a d a p te d to a c c e p t (a n d to u s e in th e ru le e v a lu a tio n ) n u m e ric v a lu e s in s te a d o f c la s s la b e ls in th e tra in in g e x a m p le s . T h o s e tw o a lg o rith m s w h e re c h o s e n to b e in te g ra te d in o u r p re d ic tio n s y s te m n o t o n ly b e c a u s e th e y te n d to b e e ffic ie n t o v e r n o is y d a ta , b u t a ls o b e c a u s e th e y u s e to ta lly d iffe re n t a lg o rith m ic a p p ro a c h e s . T h is is a n im p o rta n t is s u e s in c e w e w a n te d to te s t th e v a lid ity o f o u r d iffe re n t d a ta p re -p ro c e s s in g m e th o d s . In e ffe c t, it is c o n c e iv a b le th a t s o m e d a ta p re p a ra tio n a p p ro a c h e s le a d to e x a m p le s s e ts b e tte r s u ite d fo r s p e c ific m a c h in e le a rn in g a lg o rith m s , b u t le s s e ffic ie n t w h e n u s e d b y o th e rs .

4

E x p er i m en ta l T es ti n g

T h e m a in g o a l o f th is p a p e r is to s h o w th a t th e u s e o f d o m a in k n o w le d g e to g e n e ra te d e riv a tiv e fe a tu re s fro m th e ra w d a ta le a d s to b e tte r p re d ic tiv e a c c u ra c y re s u lts th a n th e tra d itio n a l e m b e d a p p ro a c h , w ith in fin a n c ia l tim e s e rie s p re d ic tio n p ro b le m s . T o te s t th is h y p o th e s is , w e h a v e c a rrie d o u t a s e t o f c o m p a ra tiv e e x p e rim e n ts . In o u r e x p e rim e n ts w e h a v e u s e d tim e s e rie s d a ta c o n c e rn in g fiv e o f th e m o re a c tiv e ly tra d e d c o m p a n ie s lis te d in th e P o rtu g u e s e B V L P s to c k e x c h a n g e : “ B C P ” , “ B ris a ” , “ C im p o r” , “ E D P ” a n d “ P T ” . T h e b a s e d a ta c o n s is ts o f 8 5 5 d a ily re c o rd s fo r e a c h o f th e fiv e c o m p a n ie s (fro m 2 5 N o v e m b e r 1 9 9 7 to 1 1 M a y 2 0 0 1 ). E a c h o f th o s e d a ily re c o rd s in c lu d e s 7 b a s e v a ria b le s : th e d a te o f th e d a y ; th e c lo s in g v a lu e fo r th e B V L P 3 0 s to c k in d e x ; th e v o lu m e o f tra d e d s to c k s ; a n d th e o p e n in g , m a x im u m , m in im u m a n d c lo s in g v a lu e s o f th e s to c k . R e g a rd in g th e m e th o d o lo g y u s e d to c o m p a re th e d iffe re n t a lte rn a tiv e s c o n s id e re d in th is w o rk w e h a v e u s e d th e fo llo w in g s tra te g y . T h e a v a ila b le d a ta fo r e a c h c o m p a n y w a s s p lit in fo u r s e c tio n s . T h e firs t 5 0 re c o rd s w e re k e p t a s id e fo r th e c o n s tru c tio n o f th e firs t p ro c e s s e d e x a m p le (th u s a llo w in g th e u s e o f e m b e d d im e n s io n s o f u p to 5 0 ). T h e n e x t 4 0 0 re c o rd s w e re u s e d to g e n e ra te 4 0 0 tra in in g e x a m p le s a c c o rd in g to th e th re e s tra te g ie s th a t w ill b e c o m p a re d in th is p a p e r. T h e fo llo w in g 4 0 0 re c o rd s w e re u s e d to c o n s tru c t 4 0 0 te s tin g e x a m p le s . T h e la s t 5 re c o rd s w h e re k e p t a s id e to a llo w th e u s e o f ta rg e t v a lu e s u p to fiv e d a y s a h e a d in th e e x a m p le s . W ith re s p e c t to th e m e th o d u s e d to o b ta in p re d ic tio n s fo r th e 4 0 0 te s t c a s e s w e h a v e u s e d th e fo llo w in g s tra te g y . In itia lly a ll le a rn in g a lg o rith m s w e re g iv e n a c c e s s to th e firs t 4 0 0 e x a m p le s . W ith th is s e t o f e x a m p le s a p re d ic tio n is m a d e fo r th e firs t te s t c a s e . A fte r th is p re d ic tio n is o b ta in e d , th is te s t e x a m p le is a d d e d to th e s e t o f tra in in g c a s e s le a d in g to a n e w tra in in g s e t, n o w w ith 4 0 1 e x a m p le s , w h ic h is u s e d to o b ta in a n e w m o d e l. T h is ite ra tiv e tra in + te s t p ro c e s s (s o m e tim e s k n o w n a s s lid in g w in d o w )

1 2 4

P e d ro d e A lm e id a a n d L u ís T o rg o

c o n tin u e s u n til a p re d ic tio n is o b ta in e d fo r a ll 4 0 0 te s t e x a m p le s . T h is m e a n s th a t fo r in s ta n c e th e p re d ic tio n fo r th e la s t te s t e x a m p le is o b ta in e d w ith a m o d e l th a t w a s le a rn e d u s in g 7 9 9 tra in in g c a s e s (th e o rig in a l 4 0 0 tra in in g e x a m p le s , p lu s th e firs t 3 9 9 te s t e x a m p le s ). G iv e n th e g o a l o f o u r c o m p a ra tiv e e x p e rim e n ts , w e h a v e u s e d a p re d ic tio n h o riz o n o f o n e s in g le d a y . R e g a rd in g th e ta rg e t v a ria b le (th e tim e s s e rie s to p re d ic t) w e h a v e c h o s e n a n a v e ra g e o f th e n e x t d a y q u o te s o f e a c h s to c k . T h is a v e ra g e c o n s is ts o f th e m e a n o f th e o p e n in g , m a x im u m , m in im u m a n d c lo s in g v a lu e s o f th e s to c k d u rin g th e fo llo w in g d a y . W e c a lle d th is a v e ra g e th e “ re fe re n c e v a lu e ” o f th e s to c k . M o re p re c is e ly , w e p re d ic t th e p e rc e n ta g e c h a n g e b e tw e e n th e la s t k n o w n re fe re n c e v a lu e a n d th e n e x t d a y re fe re n c e v a lu e ,

y ( t ) =1 0 0 ×

R e f ( t ) − R e f ( t −1 R e f ( t −1 )

)

(1 )

C l o s e ( t ) +M a x ( t ) +M i n ( t ) +O p e n ( t ) . 4 T h e re a s o n fo r th e u s e o f th is “ re fe re n c e v a lu e ” in s te a d o f u s in g , fo r e x a m p le , th e c lo s in g v a lu e o f e a c h d a y , is re la te d to th e n e a rly s to c h a s tic n a tu re o f th e s e tim e s e rie s . In e ffe c t, th is k in d o f tim e s e rie s b e h a v e s a s if it h a d a n im p o rta n t c o m p o n e n t o f a d d e d w h ite n o is e . T h u s , e v e ry s in g le o b s e rv a tio n o f th e tim e s e rie s is a ffe c te d b y a ra n d o m a m o u n t o f n o is e , w h ic h te n d s to “ d ro w n ” th e re la tiv e ly s m a ll v a ria tio n s o f th e s to c k v a lu e s a ttrib u ta b le to th e s y s te m “ re a l” b e h a v io r ([8 ], [1 0 ]). T h e u s e o f th is re fe re n c e v a lu e re s u lts in tw o m a in a d v a n ta g e s w h e n c o m p a re d w ith th e u s e o f a s in g le d a ily p o in t v a lu e o f th e s to c k q u o te s (fo r in s ta n c e th e c lo s in g v a lu e ). T h e firs t, a n d m o s t im p o rta n t, is th e re d u c tio n in th e p ro p o rtio n o f th e v a ria n c e th a t re s u lts fro m ra n d o m n o is e w ith re la tio n to th e v a ria n c e re s u ltin g fro m th e s u b ja c e n t s y s te m b e h a v io r. T h e s e c o n d a d v a n ta g e is re la te d to th e u s e fu ln e s s o f th e p re d ic te d v a lu e s fo r tra d in g . T o illu s tra te th is la tte r a d v a n ta g e , le t u s s u p p o s e th a t w e p re d ic t a 1 % ris e in th e re fe re n c e v a lu e fo r th e n e x t d a y . B a s e d o n th a t p re d ic tio n , w e c o u ld p la c e a s e ll o rd e r w ith a (m in im u m ) s e ll v a lu e e q u a l to th e p re d ic te d re fe re n c e v a lu e . In th is s itu a tio n , w e c a n a tta in th e s e ll v a lu e d u rin g th e n e x t d a y e v e n if th e p re d ic te d ris e fo r th e re fe re n c e v a lu e fa lls s h o rt, s in c e , in a ty p ic a l d a y (o n e w ith v a ria b ility in th e s to c k v a lu e ) th e m a x im u m v a lu e fo r th e d a y m u s t b e h ig h e r th a n th e re fe re n c e v a lu e . W e h a v e u s e d o u r p re d ic tio n s y s te m to g e n e ra te a n d c o m p a re th re e a lte rn a tiv e w a y s o f g e n e ra tin g s e ts o f e x a m p le s fo r e a c h o f th e 5 s to c k s c o n s id e re d in th is p a p e r. In th e firs t a p p ro a c h , th a t w ill b e la b e le d a s “ D a ta S e t 1 ” in th e ta b le s o f re s u lts , w e h a v e u s e d a d ire c t e m b e d o f th e tim e s e rie s w e a re p re d ic tin g . N a m e ly , w e d e v e lo p e d 2 5 fe a tu re s th a t re p re s e n t th e p e rc e n t v a ria tio n s b e tw e e n th e la s t 2 5 c o n s e c u tiv e p a irs o f v a lu e s o f th e re fe re n c e v a lu e s tim e s e rie s (th is im p lie s u s in g in fo rm a tio n a s s o c ia te d to th e la s t k n o w n 2 6 v a lu e s o f e a c h re fe re n c e v a lu e s tim e s e rie s ). T h e s e c o n d a p p ro a c h c o m p a re d in o u r s tu d y (th a t w e w ill re fe r to a s “ D a ta S e t 2 ” ) u s e s a s im ila r d ire c t e m b e d s tra te g y b u t n o w c o n s id e rin g s e v e ra l o f th e tim e s e rie s a v a ila b le fo r e a c h s to c k . In th is a lte rn a tiv e w e h a v e a ls o u s e d 2 5 fe a tu re s , w h ic h in c lu d e th e 5 la s t k n o w n p e rc e n t c h a n g e s o f th e re fe re n c e v a lu e s tim e s e rie s , a n d th e 4 la s t k n o w n p e rc e n t c h a n g e s o f th e v o lu m e , o p e n in g , m a x im u m , m in im u m a n d c lo s in g v a lu e s tim e w h e re

R e f (t ) =

T h e U s e o f D o m a in K n o w le d g e in F e a tu re C o n s tru c tio n

1 2 5

s e rie s 5. F in a lly , in th e th ird a lte rn a tiv e d a ta p re p ro c e s s in g a p p ro a c h , th a t w e w ill b e la b e le d a s “ D a ta S e t 3 ” , w e d e v e lo p e d 2 5 fe a tu re s b a s e d o n d o m a in k n o w le d g e . T h is k n o w le d g e w a s u s e d b o th to g e n e ra te a n d to s e le c t th e fin a l s e t o f fe a tu re s . S in c e th e re a re lite ra lly h u n d re d s o f te c h n ic a l in d ic a to rs a p p lic a b le to o u r b a s e d a ta 6, th e d e v e lo p m e n t o f th is ty p e o f fe a tu re s re q u ire s s o m e re s tric tin g c h o ic e s . W e h a v e u s e d a p ro c e s s to c h o o s e th e fin a l s e t o f fe a tu re s w h e re s o m e o f th e m w e re fix e d fro m th e s ta rt, w h ile o th e rs w e n t th ro u g h a n a u to m a tic fe a tu re s e le c tio n p ro c e s s . A m o n g th e fo rm e r w e in c lu d e d th e firs t 4 te rm s o f th e s im p le e m b e d u s e d in th e firs t d a ta p re p ro c e s s in g a p p ro a c h . R e g a rd in g th e a u to m a tic s e le c tio n o f th e o th e r fe a tu re s , w e u s e d th e k n o w le d g e re p re s e n ta tio n la n g u a g e to d e s c rib e a n d g e n e ra te a s e t o f fe a tu re s th a t s e e m e d re le v a n t, a n d th e n u s e d a fe a tu re ra n k in g p ro c e s s 7 to d is c a rd th o s e w ith lo w e s t e v a lu a tio n s . In o rd e r to in c re a s e th e s ta tis tic a l s ig n ific a n c e o f th is s e le c tio n p ro c e s s w e h a v e u s e d th e c o m b in e d 2 0 0 0 tra in in g e x a m p le s (4 0 0 tra in in g e x a m p le s × 5 s to c k s ). It is in te re s tin g to a n a ly z e w h ic h w e re th e fe a tu re s th a t re s u lte d fro m th e p ro c e s s d e s c rib e d a b o v e . It w a s ra th e r s u rp ris in g to fin d o u t th a t m o s t o f th e re ta in e d fe a tu re s w h e re n o t th e “ fu ll” te c h n ic a l a n a ly s is in d ic a to rs b u t “ c o n s tru c tiv e e le m e n ts ” o f th o s e in d ic a to rs . A n e x a m p le is th e re te n tio n o f s im p le ra tio s o f m o v in g a v e ra g e s , in s te a d o f m o re c o m p le x v a ria n ts o f th e M o v in g A v e ra g e C o n v e rg e n c e D iv e rg e n c e (M A C D ) in d ic a to r th a t w h e re a ls o c o n s id e re d a s c a n d id a te fe a tu re s . T h e fin a l s e t o f 2 5 c h o s e n fe a tu re s c a n b e g ro u p e d a s fo llo w s :

• O n e fe a tu re b a s e d o n th e d a te tim e s e rie s , s ta tin g th e w e e k d a y o f th e e x a m p le . • S ix fe a tu re s b a s e d o n th e re fe re n c e v a lu e s tim e s e rie s , fo u r o f th e m e m b e d s o f th e d iffe re n c e s , th e o th e r tw o re la tin g m o v in g a v e ra g e s o f d iffe re n t le n g th s . • T h re e fe a tu re s b a s e d o n d ire c t e m b e d s o f d iffe re n c e s o f th e B V L 3 0 tim e s e rie s . • T w o fe a tu re s b a s e d o n th e d iffe re n tia l c h a n g e s o f th e re fe re n c e v a lu e s a n d B V L 3 0 tim e s e rie s , d u rin g tw o d iffe re n t tim e fra m e s . • T h re e fe a tu re s b a s e d o n th e v o lu m e o f tra d e tim e s e rie s , o n e o f th e m a n e m b e d o f th e d iffe re n c e s , th e o th e r tw o re la tin g m o v in g a v e ra g e s o f d iffe re n t le n g th s . • F iv e fe a tu re s b a s e d o n d iffe re n t re la tio n s o f th e o p e n in g , m a x im u m , m in im u m , c lo s in g a n d re fe re n c e v a lu e s o f th e la s t k n o w n d a y . • F iv e fe a tu re s a ls o b a s e d o n re la tio n s o f th e o p e n in g , m a x im u m , m in im u m , c lo s in g a n d re fe re n c e v a lu e s , b u t u s in g m o v in g a v e ra g e s o f d iffe re n t le n g th s . •

7

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e ra ll, a m n c e v a lu e o rd e r to e s s in g th e ⎯ ⎯ ⎯

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fe a tu r tra d e d e rfo rm d tw o

e s , th v o lu a n c e c o m m

W ith th e h e lp o f o u r d o m a in k n o w le d g e re p re s e n ta tio n th e s e tw o firs t s e ts o f fe a tu re s . T h e firs t is r p e r c e n t( r e f( i) ,r e f( i+ 1 ) ) w ith i= 0 ..2 4 . T h e s e c o n d e x p re s s io n s , o n e fo r e a c h o f th e 6 b a s e d a ta tim e s e rie M a n y o f th e m in v o lv in g a c h o ic e o f p a ra m e te rs a n d p o s s ib le v a ria n ts . T h is p ro c e s s is s im ila r to th e o n e u s e d in th e d a ta m in in S e c tio n 3 .

e o ld e s t h m e s u p to o f th e th re o n p re d ic

is to ric a l v a lu e s u s e d a re 1 5 d a y s o ld . e a lte rn a tiv e w a y s o f p re tio n e rro r m e a s u re s [1 0 ],

la n g u a g e e p re s e n te d is re p re s in v o lv e d th u s g re a

it is q u ite s im p le to re p re s e n t b y th e s in g le e x p re s s io n s e n te d b y 6 v e ry s im ila r . tly in c re a s in g th e n u m b e r o f

in g c o m p o n e n t o f o u r s y s te m

d e s c rib e d

1 2 6

P e d ro d e A lm e id a a n d L u ís T o rg o

c h o s e n fo r th e ir re le v a n c e fo r tra d in g c rite ria e v a lu a tio n . T h e firs t is th e p e rc e n t a c c u ra c y o f th e b in a ry (ris e o r fa ll) p re d ic tio n s fo r th e n e x t d a y , d e fin e d a s ,

% A c c =

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t a r g e t v a l u e o f t e s t c a s e i ; yˆ i i s

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e a v e ra g e v a lu e o f th e re tu rn o n n s ig n is c o rre c t a n d a s n e g a tiv e e ra g e R e tu rn o n th e P re d ic te d

N te s t i s t h e n u m b e r o f t e s t c a s e s ; y i i s t h e t r u t h th e p re d ic te d v a lu e fo r th a t te s t c a s e ; a n d ⎧1 i f y ≥ 0 ∧ y ˆ ≥ 0 ⎪ S c o r e ( y , y ˆ ) = ⎨1 i f y < 0 ∧ y ˆ < 0 ⎪ 0 o th e rw is e ⎩ e s e c o n d e v a lu a tio n m e a s u re w e h a v e u s e d is th s t e x a m p le s , ta k e n a s p o s itiv e w h e n th e p re d ic tio it is w ro n g 8. W e c a lle d th is m e a s u re th e A v p le s (A R P E ), w h ic h c a n b e d e fin e d a s ,

A R P E =

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i s t h e n u m b e r o f t e s t c a s e s ; y i i s t h e t r u t h t a r g e t v a l u e o f c a s e i ; yˆ i i s t h e p re d ic te d v a lu e fo r th a t c a s e ; R e fi is th e re fe re n c e v a lu e o f c a s e i.

w h e re ,

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T a b le s 1 a n d 2 s h o w th e a c c u ra c y a n d A R P E re s u lts o b ta in e d in o u r e x p e rim e n ts u s in g th e L a z y 3 a n d P A 6 a lg o rith m s o v e r th e th re e d a ta s e ts g e n e ra te d w ith th e a lte rn a tiv e p re -p ro c e s s in g m e th o d s , w h ic h w e re d e s c rib e d e a rlie r in th is S e c tio n . T h e s e ta b le s a ls o in c lu d e th e re s u lts o b ta in e d w ith tw o tra d itio n a l b e n c h m a rk s : th e N a ïv e P re d ic tio n o f R e tu rn s (N P R ); a n d th e b u y -a n d -h o ld s tra te g y 9. T h e N P R m e re ly p re d ic ts th a t th e n e x t p e rc e n ta g e c h a n g e o f th e re fe re n c e v a lu e (th e re tu rn o f th is v a l u e ) , w i l l b e t h e s a m e a s t h e l a s t k n o w n c h a n g e ( i . e . y ˆ ( t +1 ) = y ( t ) ) . T h e r e s u l t s f o r th is b e n c h m a rk a re p re s e n te d in T a b le 1 a s th e y a re d ire c tly c o m p a ra b le w ith th e o th e r s c o re s s h o w n o n th is ta b le . T h e re s u lts fo r th e b u y -a n d -h o ld b e n c h m a rk a re s h o w in T a b le 2 a s th e a v e ra g e g a in o f th e b u y -a n d -h o ld s tra te g y 10 o v e r th e 4 0 0 tra d in g d a y s in v o lv e d in o u r te s ts , s o th a t th e y a re d ire c tly c o m p a ra b le w ith th e o th e r A R P E m e a s u re v a lu e s p re s e n te d . T h e re s u lts s h o w n o n th e s e ta b le s p ro v id e s tro n g e m p iric a l e v id e n c e to w a rd s o u r h y p o th e s is c o n c e rn in g th e u s e o f d o m a in k n o w le d g e to g e n e ra te th e tra in in g e x a m p le s . In e ffe c t, c o n s id e rin g th e re s u lts o v e r th e 5 s to c k s , w e c a n o b s e rv e th a t th e m o d e ls o b ta in e d w ith d a ta s e t 3 (th a t c o n ta in th e fe a tu re s o b ta in e d w ith d o m a in k n o w le d g e ), c o n s is te n tly a c h ie v e b e tte r a c c u ra c y re s u lts th a n th e o th e rs , in d e p e n d e n tly o f th e a lg o rith m u s e d to o b ta in th e m o d e l. W h e n c o m p a rin g th e re s u lts

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N o tic e th a t th e ta rg e t v a re fe re n c e v a lu e a n d th e A n e x te n d e d d is c u s s io n 0 T h i s s t r a t e g y c o n s i s t s o a t th e p ric e o f th e la s t k

lu e s re fe o f th f b u n o w

o f e a re n c e e se b y in g n re fe

c h e x a v a lu e e n c h m a t th e re n c e

m p le a re th e p e rc e n t c h a n g e s b e tw e e n th e la s t k n o w n o f th e n e x t d a y . a rk s c a n b e fo u n d in [1 0 ] a n d [2 1 ]. p r ic e o f la s t k n o w n tr a in in g c a s e , R e f50+400, a n d s e llin g v a lu e R e f50+400+400.

T h e U s e o f D o m a in K n o w le d g e in F e a tu re C o n s tru c tio n

b e tw e e n d a ta (w ith a s in g le o f m u ltip le tim a re s im ila r. A c o m b in a tio n s re s u lts g re a te r

s e ts 1 a e x c e p tio e s e rie s n in te re s p ro d u c e th a n 0 ).

n d 2 , w n in th e . If w e tin g p o p o s itiv

e a ls o o b s e rv e w o rs e re s B C P s to c k u s in g th e P A 6 c o n s id e r th e A R P E e v a lu a in t to n o tic e is th e fa c t th a e re s u lts (a c c u ra c y re s u lts

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th e s im ), th a n w u re th e lg o rith m a n 5 0 %

1 2 7

p le e m b e d s ith e m b e d s c o n c lu s io n s / d a ta s e ts a n d A R P E

T a ble 1 . P e r c e n t a c c u r a c y o v e r t h e t e s t e x a m p l e s L a z y 3 a lg S e t 1 D a ta S .5 0 6 2 .7 .7 5 6 2 .0 .7 5 6 3 .0 .5 0 6 5 .7 .5 0 6 1 .7 .6 0 6 3 .0

B C P B ris a C im p o r E D P P T A v e ra g e

D a ta 5 7 5 4 5 9 5 8 5 7 5 7

o rith m e t 2 D a ta S 5 6 9 .0 0 6 6 .5 0 6 9 .2 5 7 2 .2 5 6 8 .5 5 6 9 .1

e t 3 0 0 5 5 0 0

D a ta 5 6 5 7 5 6 5 8 5 7 5 7

S e t 1 .5 0 .7 5 .0 0 .0 0 .5 0 .1 5

P A 6 a lg o D a ta S 5 6 .5 6 3 .2 5 7 .0 6 7 .7 6 3 .5 6 1 .6

rith m e t 2 D a ta 6 2 0 6 3 5 6 4 0 7 2 5 6 7 0 6 6 0

S e t 3 .7 5 .7 5 .5 0 .5 0 .7 5 .2 5

N R P 6 5 5 6 5 8 5 9 5 7 5 9

.5 .7 .5 .0 .5 .4

0 5 0 0 0 5

T a ble 2 . A v e r a g e R e t u r n o n t h e P r e d i c t e d E x a m p l e s ( A R P E )

B C P B ris a C im p o r E D P P T A v e ra g e

D a ta 0 .1 0 .1 0 .2 0 .2 0 .4 0 .2

L a z y 3 a lg S e t 1 D a ta S 3 4 0 .2 5 7 6 0 .2 8 6 6 0 .4 0 6 3 0 .5 1 9 4 0 .7 6 6 7 0 .4 4

o rith m e t 2 D a ta 3 0 .2 6 0 .3 4 0 .4 5 0 .5 2 1 .0 4 0 .5

S e t 3 8 6 9 4 9 8 7 8 4 5 6 0

D a ta 0 .1 0 .2 0 .1 0 .3 0 .4 0 .2

S e t 1 9 3 2 8 9 2 0 2 8 2 7 9

P A 6 a lg o D a ta S 0 .2 1 0 .3 1 0 .3 8 0 .5 3 0 .9 2 0 .4 7

rith m e t 2 D a ta 0 .2 5 0 .3 2 0 .4 6 0 .5 1 1 .0 2 0 .5 3

S e t 3 1 5 3 3 4 7 9 1 0 7 1 9

B u y h o 0 .0 0 .0 0 .1 0 .0 0 .1 0 .0

a n d ld 0 2 9 9 4 1 1 0 1 3 7 3

A n a ly z in g th e b e n c h m a rk re s u lts in is o la tio n , w e n o tic e th a t th e N P R a c c u ra c y re s u lts a re c o n s id e ra b ly a b o v e th e 5 0 % a v e ra g e , w h ic h is s o m e h o w u n e x p e c te d . T h is is d u e to th e h ig h a u to -c o rre la tio n (a t la g 1 ) o f th e fiv e tim e s e rie s in a n a ly s is (w h ic h a ls o h e lp s to e x p la in th e p re d ic tio n a b ility o f d a ta s e t 1 , a s u s e d in o u r s y s te m )11. C o m p a rin g o u r re s u lts w ith th o s e a c h ie v e d b y th e b e n c h m a rk s , w e n o tic e th a t a ll th e a lg o rith m / d a ta s e ts c o m b in a tio n s a c h ie v e c o n s id e ra b ly b e tte r A R P E v a lu e s th a n th e b u y -a n d -h o ld b e n c h m a rk . O n th e o th e r h a n d , th e N P R a c c u ra c y re s u lts a re g lo b a lly h ig h e r th a n th e re s u lts o f th e s im p le e m b e d u s e d in d a ta s e t 1 , a lth o u g h th e y a re w o rs e th a n th e re s u lts o f d a ta s e t 2 a n d , p a rtic u la rly , o f d a ta s e t 3 . In o rd e r to a s s e rt th e s ta tis tic a l s ig n ific a n c e o f th e s e re s u lts , w e h a v e c a rrie d o u t o n e -s id e d p a ire d t te s ts o v e r th e 4 0 0 te s t e x a m p le s o f e a c h s to c k , u s in g th e a c c u ra c y s c o re s . T h e a c c u ra c y d iffe re n c e s b e tw e e n m o d e ls o b ta in e d w ith d a ta s e t 1 a n d d a ta s e t 3 w e re o b s e rv e d to b e h ig h ly s ig n ific a n t. In e ffe c t, w ith th e L a z y 3 a lg o rith m a ll th e d if f e r e n c e s a r e s ta tis tic a lly s ig n if ic a n t w ith a 9 9 .5 % c o n f id e n c e le v e l, e x c e p t f o r B C P w h e r e th e le v e l w a s 9 7 .5 % . R e g a r d in g th e P A 6 a lg o r ith m , th e im p r o v e m e n ts o b ta in e d

⎯ 1 1

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A n a n a ly s is o f th o s e tim e s e rie s s h o w e d n o s ig n ific a n t a u to -c o rre la tio n a t o th e r la g s , lim itin g th e p o te n tia l e ffe c tiv e n e s s o f m o re p o w e rfu l p re d ic tio n te c h n iq u e s b a s e d in a u to -c o rre la tio n .

1 2 8

P e d ro d e A lm e id a a n d L u ís T o rg o

w ith d a ta s e t 3 a re s o m e w h a t le s s m a rk e d , b u t s till s ig n ific a n t w ith 9 9 .5 % c o n fid e n c e f o r C im p o r , E D P , a n d P T , w ith 9 7 .5 % c o n f id e n c e f o r B C P , a n d w ith 9 5 % f o r B r is a .

5

Con clu s i on s T h is p a p e r d e s c rib e d a n a p p ro a c h to fin a n c ia l tim e s e rie s p re d ic tio n w h o s e m a in d is tin c tiv e fe a tu re is th e u s e o f d o m a in k n o w le d g e to g e n e ra te th e tra in in g c a s e s th a t fo rm th e b a s is o f m o d e l c o n s tru c tio n . W ith th is p u rp o s e w e h a v e d e v e lo p e d a d o m a in k n o w le d g e re p re s e n ta tio n la n g u a g e th a t a llo w s th e tim e s e rie s e x p e rt to e a s ily e x p re s s h is k n o w le d g e . T h e d e s c rip tio n o b ta in e d w ith th e h e lp o f th is la n g u a g e is th e n u s e d b y o u r p re d ic tio n s y s te m to g e n e ra te a tra in in g s a m p le fro m th e ra w tim e s s e rie s d a ta . W e h a v e c o n tra s te d th is k n o w le d g e in te n s iv e a p p ro a c h w ith th e tra d itio n a l m e th o d o f e m b e d d in g th e la s t tim e s e rie s v a lu e s . W ith th is p u rp o s e w e h a v e c a rrie d o u t a s e rie s o f c o m p a ra tiv e e x p e rim e n ts u s in g tim e s e rie s d a ta fro m fiv e a c tiv e ly tra d e d P o rtu g u e s e c o m p a n ie s . T h e re s u lts o f o u r e x p e rim e n ts w ith th e s e s to c k s p ro v id e s tro n g e m p iric a l e v id e n c e th a t a d a ta p re p ro c e s s in g a p p ro a c h b a s e d o n a d ire c t e m b e d o f th e tim e s e rie s h a s la rg e lim ita tio n s , a n d th a t th e u s e o f fe a tu re s c o n s tru c te d fro m th e a v a ila b le ra w d a ta w ith th e h e lp o f d o m a in k n o w le d g e is a d v a n ta g e o u s . R e g a rd in g fu tu re d e v e lo p m e n ts o f th is re s e a rc h w e in te n d to e x te n d th e e x p e rim e n ta l e v a lu a tio n to p re d ic tio n h o riz o n s la rg e r th a n th e n e x t d a y , a s w e ll a s fu rth e r re fin e th e im p o rta n t fe a tu re s e le c tio n p h a s e .

R efer en ces 1 .

A b u - M o s ta f a , Y ., L e B a r o n , B ., L o , A . a n d W e ig e n d , A . ( e d s .) : P r o c e e d in g s o f th e S ix th In te rn a tio n a l C o n fe re n c e o n C o m p u ta tio n a l F in a n c e , C F 9 9 . M IT P re s s (1 9 9 9 ) 2 . A lm e id a , P . a n d B e n to , C .: S e q u e n tia l C o v e r R u le I n d u c tio n w ith P A 3 . P r o c e e d in g s o f th e 1 0 th In te rn a tio n a l C o n fe re n c e o n C o m p u tin g a n d In fo rm a tio n (IC C I’2 0 0 0 ), K u w a it. S p rin g e r-V e rla g (2 0 0 1 ) 3 . B e llm a n , R .; A d a p ta tiv e C o n tr o l P r o c e s s e s : A G u id e d T o u r . P r in c e to n U n iv e r s ity P r e s s , (1 9 6 1 ) 4 . B is h o p , C .: N e u r a l N e tw o r k s f o r P a tte r n R e c o g n itio n . O x f o r d U n iv e r s ity P r e s s ( 1 9 9 5 ) 5 . B o n te m p i, G .: L o c a l L e a r n in g T e c h n iq u e s f o r M o d e lin g , P r e d ic tio n a n d C o n tr o l. P h .D . D is s e rta tio n , U n iv e rs ité L ib re d e B ru x e lle s , B e lg iu m (1 9 9 9 ) 6 . B o x , G ., a n d J e n k in s , G .: T im e S e rie s A n a ly s is , F o re c a s tin g a n d C o n tro l. H o ld e n -D a y (1 9 7 6 ) 7 . D e m a r k , T .: T h e N e w S c ie n c e o f T e c h n ic a l A n a ly s is . J o h n W ile y & S o n s ( 1 9 9 4 ) 8 . F a m a , E .: E f f ic ie n t C a p ita l M a r k e ts : A r e v ie w o f T h e o r y a n d E m p ir ic a l W o r k . J o u r n a l o f F in a n c e , 2 5 (1 9 7 0 ) 3 8 3 -4 1 7 9 . H a ll, M .: C o r r e la tio n - B a s e d F e a tu r e S e le c tio n f o r M a c h in e L e a r n in g . P h .D . D is s e r ta tio n , D e p a rtm e n t o f C o m p u te r S c ie n c e , U n iv e rs ity o f W a ik a to (1 9 9 9 ) 1 0 . H e lls tr o m , T .: D a ta S n o o p in g in th e S to c k M a r k e t. T h e o r y o f S to c h a s tic P r o c e s s 5 ( 2 1 ) (1 9 9 9 ) 1 1 . H e rb s t, A .: A n a ly z in g a n d F o r e c a s tin g F u tu r e s P r ic e s . J o h n W ile y & S o n s (1 9 9 2 )

T h e U s e o f D o m a in K n o w le d g e in F e a tu re C o n s tru c tio n

1 2 9

1 2 . H o n g , S .: U s e o f C o n te x tu a l I n f o r m a tio n f o r F e a tu r e R a n k in g a n d D is c r e tiz a tio n . I E E E T ra n s a c tio n s o n K n o w le d g e a n d D a ta E n g in e e rin g , 9 (5 ) (1 9 9 7 ) 7 1 8 -7 3 0 1 3 . H u tc h in s o n , J .: A R a d ia l B a s is F u n c tio n A p p r o a c h to F in a n c ia l T im e S e r ie s A n a ly s is . P h .D . D is s e r ta tio n , D e p a r tm e n t o f E le c tr ic a l E n g in e e r in g a n d C o m p u te r S c ie n c e , M a s s a c h u s e tts In s titu te o f T e c h n o lo g y (1 9 9 4 ) 1 4 . K u s tr in , D .: F o r e c a s tin g F in a n c ia l T im e s e r ie s w ith C o r r e la tio n M a tr ix M e m o r ie s f o r T a c tic a l A s s e t A llo c a tio n . P h .D . D is s e r ta tio n , D e p a r tm e n t o f C o m p u te r S c ie n c e , U n iv e r s ity o f Y o rk , U K (1 9 9 8 ) 1 5 . L a w r e n c e , S ., T s o i, A . a n d G ile s C .: N o is y T im e S e r ie s P r e d ic tio n u s in g S y m b o lic R e p re s e n ta tio n a n d R e c u rre n t N e u ra l N e tw o rk G ra m m a tic a l In fe re n c e . T e c h n ic a l R e p o rt U M IA C S -T R -9 6 -2 7 a n d C S -T R -3 6 2 5 , In s titu te fo r A d v a n c e d C o m p u te r S tu d ie s , U n iv e rs ity o f M a ry la n d , M D (1 9 9 6 ) 1 6 . M ic h a ls k i, R .: A T h e o r y a n d M e th o d o lo g y o f I n d u c tiv e L e a r n in g . I n M ic h a ls k i, R ., C a r b o n e ll, J ., a n d M itc h e ll, T ., ( e d s ) : M a c h in e L e a r n in g : A n A r tif ic ia l I n te llig e n c e A p p ro a c h , V o l. 1 . M o rg a n K a u fm a n n (1 9 8 3 ) 1 7 . M o z e r , M .: N e u r a l N e t A r c h ite c tu r e s f o r T e m p o r a l S e q u e n c e P r o c e s s in g . I n : W e ig e n d , A . a n d G e r s h e n f e ld , N . ( e d s .) : T im e S e r ie s P r e d ic tio n : F o r e c a s tin g th e F u tu r e a n d U n d e rs ta n d in g th e P a s t. A d d is o n -W e s le y (1 9 9 4 ) 1 8 . M u r p h y , J .: T e c h n ic a l A n a ly s is o f th e F in a n c ia l M a r k e ts : A C o m p r e h e n s iv e G u id e to T ra d in g M e th o d s a n d A p p lic a tio n s . P re n tic e H a ll (1 9 9 9 ) 1 9 . M u r th y , S ., K a s if , S . a n d S a lz b e r g , S .: A S y s te m f o r I n d u c tio n o f O b liq u e D e c is io n T r e e s . J o u rn a l o f A rtific ia l In te llig e n c e R e s e a rc h , 2 (1 9 9 4 ) 1 -3 2 2 0 . P o v in e lli, R .: T im e S e r ie s D a ta M in in g : I d e n tif y in g T e m p o r a l P a tte r n s f o r C h a r a c te r iz a tio n a n d P r e d ic tio n o f T im e S e r ie s E v e n ts . P h .D . D is s e r ta tio n , M a r q u e tte U n iv e r s ity , M ilw a u k e e , W is c o n s in (1 9 9 9 ) 2 1 . R e f e n e s , A .: T e s tin g S tr a te g ie s a n d M e tr ic s . I n R e f e n e s , A . ( e d .) : N e u r a l N e tw o r k s in th e C a p ita l M a rk e ts . J o h n W ile y & S o n s (1 9 9 5 ) 2 2 . S a u e r , T ., Y o r k e , J . a n d C a s d a g li, M .: E m b e d o lo g y . J o u r n a l o f S ta tis tic a l P h y s ic s 6 5 ( 1 9 9 1 ) 5 7 9 -6 1 6 2 3 . S c o tt, D .; M u ltiv a r ia te D e n s ity E s tim a tio n . J o h n W ile y & S o n s ( 1 9 9 2 ) 2 4 . T a k e n s , F .: D e te c tin g S tr a n g e A ttr a c to r s in T u r b u le n c e . I n R a n d , D . a n d Y o u n g , L . ( e d s .) , L e c tu re N o te s in M a th e m a tic s , V o l. 8 9 8 . S p rin g e r (1 9 8 1 ) 3 6 6 -3 8 1 2 5 . W e ig e n d , A . a n d G e r s h e n f e ld , N . ( e d s .) : T im e S e r ie s P r e d ic tio n : F o r e c a s tin g th e F u tu r e a n d U n d e rs ta n d in g th e P a s t. A d d is o n -W e s le y (1 9 9 4 ) 2 6 . W e ig e n d , A ., H u b e r m a n , B . a n d R u m e lh a r t, D .: P r e d ic tin g S u n s p o ts a n d E x c h a n g e R a te s w ith C o n n e c tio n is t N e tw o r k s . I n C a s d a g li, M . a n d E u b a n k , S . ( e d s .) : N o n lin e a r M o d e lin g a n d F o re c a s tin g , S F I S tu d ie s in th e S c ie n c e s o f C o m p le x ity . A d d is o n -W e s le y (1 9 9 2 ) 2 7 . W e ig e n d , A ., Z im m e r m a n n , H . a n d N e u n e ie r , R .: C le a r n in g . I n R e f e n e s , P ., A b u - M o s ta f a , Y ., M o o d y , J . a n d W e ig e n d , A . ( e d s .) : N e u r a l N e tw o r k s in F in a n c ia l E n g in e e r in g (P ro c e e d in g s o f N N C M ’9 5 ). W o rld S c ie n tific (1 9 9 6 ) 2 8 . W e is s , S . a n d I n d u r k h y a , N .: P r e d ic tiv e D a ta M in in g : A P r a c tic a l G u id e . M o r g a n K a u fm a n n (1 9 9 8 ) 2 9 . Y u le , G .: O n a M e th o d o f I n v e s tig a tin g P e r io d ic itie s in D is tu r b e d S e r ie s w ith S p e c ia l R e f e r e n c e t o W o l f e r 's S u n s p o t N u m b e r s . P h i l . T r a n s . R o y a l S o c i e t y , S e r i e s A , 2 2 6 ( 1 9 2 7 ) 3 0 . Y u r e t, D . a n d M a z a , M .: A G e n e tic A lg o r ith m S y s te m f o r P r e d ic tin g d e O E X . T e c h n ic a l A n a ly s is o f S to c k s a n d C o m m o d itie s , 1 2 (6 ) (1 9 9 4 ) 2 5 5 -2 5 9 3 1 . Z a n g , X . a n d H u tc h in s o n , J .: S im p le A r c h ite c tu r e s o n F a s t M a c h in e s : P r a c tic a l I s s u e s in N o n lin e a r T im e S e r ie s P r e d ic tio n . I n W e ig e n d , A . a n d G e r s h e n f e ld , N . ( e d s .) : T im e S e r ie s P re d ic tio n : F o re c a s tin g th e F u tu re a n d U n d e rs ta n d in g th e P a s t. A d d is o n -W e s le y (1 9 9 4 )

Optimizing the Sharpe Ratio for a Rank Based Trading System Thomas Hellstr¨om Department of Computing Science Ume˚ a University, 901 87 Ume˚ a, Sweden [email protected] http://www.cs.umu.se/˜ thomash

Abstract. Most models for prediction of the stock market focus on individual securities. In this paper we introduce a rank measure that takes into account a large number of securities and grades them according to the relative returns. It turns out that this rank measure, besides being more related to a real trading situation, is more predictable than the individual returns. The ranks are predicted with perceptrons with a step function for generation of trading signals. A learning decision support system for stock picking based on the rank predictions is constructed. An algorithm that maximizes the Sharpe ratio for a simulated trader computes the optimal decision parameters for the trader. The trading simulation is executed in a general purpose trading simulator ASTA. The trading results from the Swedish stock market show significantly higher returns and also Sharpe ratios, relative the benchmark.

1

Introduction

The returns of individual securities are the primary targets in most research that deal with the predictability of financial markets. In this paper we focus on the observation that a real trading situation involves not only attempts to predict the individual returns for a set of interesting securities, but also a comparison and selection among the produced predictions. What an investor really wants to have is not a large number of predictions for individual returns, but rather a grading of the securities in question. Even if this can be achieved by grading the individual predictions of returns, it is not obvious that it will yield an optimal decision based on a limited amount of noisy data. In Section 2 we introduce a rank measure that takes into account a large number of securities and grades them according to the relative returns. The rank concept has in a previous study [5] shown a potential for good predictability. In Section 4, perceptron models for prediction of the rank are defined and historical data is used to estimate the parameters in the models. Results from time series predictions are presented. The predictions are used as a basis for a learning decision support system for stock picking described in Section 5. The surprisingly successful results are discussed. Section 6 contains a summary of the results together with ideas for future research. P. Brazdil and A. Jorge (Eds.): EPIA 2001, LNAI 2258, pp. 130–141, 2001. c Springer-Verlag Berlin Heidelberg 2001 

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2

131

Defining a Rank Measure

The k-day return Rk (t) for a stock m with close prices y m (1), ..., y m (t1 ) is defined for t ∈ [k + 1, ..., t1 ] as Rkm (t) =

y m (t) − y m (t − k) . y m (t − k)

(1)

We introduce a rank concept Am k , based on the k-day return Rk as follows: for a stock s in the set {s1 , ..., sN } is computed by ranking The k-day rank Am m k the N stocks in the order of the k-day returns Rk . The ranking orders are then normalized so the stock with the lowest Rk is ranked −0.5 and the stock with the highest Rk is ranked 0.5. The definition of the k-day rank Am k for a stock m belonging to a set of stocks {s1 , ..., sN }, can thus be written as Am k (t) =

#{Rki (t)|Rkm (t) ≥ Rki (t), 1 ≤ i ≤ N } − 1 − 0.5 N −1

(2)

where the # function returns the number of elements in the argument set. This is as integer between 1 and N . Rkm is the k-day returns computed for stock m. The scaling between −0.5 and +0.5 assigns the stock with the median value on Rk the rank 0. A positive rank Am k means that stock m performs better than this median stock, and a negative rank means that it performs worse. This new measure gives an indication of how each individual stock has developed relatively to the other stocks, viewed on a time scale set by the value of k. The scaling around zero is convenient when defining a prediction task for the rank. It is clear that an ability to identify, at time t, a stock m, for which Am h (t + h) > 0, h > 0 means an opportunity to make profit in the same way as identifying a stock, for which Rh (t + h) > 0. A method that can identify stocks m and times t with a mean value of Am h (t + h) > 0, h > 0, can be used as a trading strategy that can do better than the average stock. The hit rate for the predictions can be defined as the fraction of times, for which the sign of the predicted rank Am h (t + h) is correct. A value greater than 50% means that true predictions have been achieved. The following advantages compared to predicting returns Rh (t + h) can be noticed: 1. The benchmark for predictions of ranks Am h (t + h) performance becomes clearly defined: – A hit rate > 50% , for the predictions of the sign of Am h (t+h) means that we are doing better than chance. When predicting returns Rh (t + h), the general positive drift in the market causes more than 50% of the returns to be > 0, which means that it is hard to define a good benchmark. – A positive mean value for predicted positive ranks Ah (t + h) (and a negative mean value for predicted negative ranks) means that we are doing better than chance. When predicting returns Rh (t+h), the general positive drift in the market causes the returns to have a mean value > 0. Therefore, a mere positive mean return for predicted positive returns does not imply any useful predicting ability.

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2. The rank values A1k (t), ..., AN k (t), for time t and a set of stocks 1, ..., N are uniformly distributed between −0.5 and 0.5 provided no return values are equal. Returns Rkm , on the other hand, are distributed with sparsely populated tails for the extreme low and high values. This makes the statistical analysis of rank predictions safer and easier than predictions of returns. 3. The effect of global events gets automatically incorporated into the predictor variables. The analysis becomes totally focused on identifying deviations from the average stock, instead of trying to model the global economic situation.

3

Serial Correlation in the Ranks

We start by looking at the serial correlation for the rank variables as defined m in (2). In Table 1 mean ranks Am 1 (t + 1) are tabulated as a function of Ak (t) for 207 stocks from the Swedish stock market 1987-1997. Table 2 shows the “U p f raction”, i.e. the number of positive ranks Am 1 (t + 1) divided by the number of non-zero ranks. Table 3 finally shows the number of observations of Am 1 (t + 1) in each table entry. Each row in the tables represents one particular value on k, covering the values 1, 2, 3, 4, 5, 10, 20, 30, 50, 100. The label for each column is the mid-value of a symmetrical interval. For example, the column labeled 0.05 includes points with k-day rank Am k (t) in the interval [ 0.00, ..., 0.10 [. The intervals for the outermost columns are open-ended on one side. Note that the stock price time series normally have 5 samples per week, i.e. k = 5 represents one week of data and k = 20 represents approximately one month. Example: There are 30548 observations where −0.40 ≤ Am 2 (t) < −0.30 in the investigated data. In these observations, the 1-day ranks on the following day, Am 1 (t + 1), have an average value of 0.017, and an ”U p f raction” = 52.8%. Table 1. Mean 1-step ranks for 207 stocks

k-day rank k -0.45 -0.35 -0.25 -0.15 -0.05 0.05 0.15 0.25 0.35 0.45 1 0.067 0.017 -0.005 -0.011 -0.011 -0.004 -0.005 -0.010 -0.014 -0.033 2 0.060 0.017 0.002 -0.004 -0.010 -0.003 -0.007 -0.015 -0.017 -0.032 3 0.057 0.016 0.003 -0.005 -0.003 -0.008 -0.011 -0.011 -0.015 -0.034 4 0.054 0.018 0.003 -0.003 -0.005 -0.008 -0.011 -0.013 -0.012 -0.032 5 0.051 0.015 0.004 -0.002 -0.004 -0.009 -0.010 -0.009 -0.016 -0.032 10 0.040 0.013 0.005 -0.001 -0.003 -0.006 -0.007 -0.009 -0.012 -0.030 20 0.028 0.008 0.003 -0.003 -0.002 -0.002 -0.006 -0.011 -0.009 -0.019 30 0.021 0.007 0.002 0.004 -0.003 -0.003 -0.006 -0.006 -0.011 -0.015 50 0.014 0.005 0.000 -0.000 -0.001 -0.002 -0.005 -0.004 -0.006 -0.010 100 0.007 0.003 0.001 -0.002 -0.003 -0.004 -0.004 -0.004 -0.003 -0.008

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Table 2. Fraction up/(up+down) moves (% )

k-day rank k -0.45 -0.35 -0.25 -0.15 -0.05 0.05 0.15 0.25 0.35 0.45 1 59.4 52.9 49.1 47.3 48.0 49.6 49.5 48.2 47.8 46.4 2 58.4 52.8 49.7 48.9 48.4 49.7 48.9 47.4 47.6 46.2 3 58.1 52.4 50.3 48.9 49.1 49.0 48.1 48.1 47.8 46.1 4 57.5 52.5 50.4 49.2 49.0 48.7 48.0 47.9 48.6 46.3 5 57.1 52.0 50.4 49.4 49.1 48.5 48.2 48.6 47.7 46.3 10 55.6 51.7 50.4 49.8 49.3 48.8 48.7 48.5 48.2 46.3 20 53.8 51.1 50.2 49.6 49.4 49.5 49.0 48.3 48.7 47.8 30 52.7 50.9 50.3 50.8 49.1 49.2 48.8 48.9 48.5 48.4 50 52.0 50.7 49.6 49.9 49.6 49.6 49.0 49.3 49.1 48.9 100 51.4 50.4 49.9 49.5 49.2 49.2 49.0 49.2 49.6 49.1

The only clear patterns that can be seen in the table are a slight negative serial correlation: negative ranks are followed by more positive ranks and vice versa. To investigate whether this observation reflects a fundamental property of the process generating the data, and not only idiosyncrasies in the data, the relation between current and future ranks is also presented in graphs, in which m one curve represents one year. Figure 1 shows Am 1 (t + 1) versus A1 (t). I.e.: 1-day ranks on the following day versus 1-day ranks on the current day. The same relation for 100 simulated random-walk stocks is shown in Figure 2 for comparison. From Figure 1 we can conclude that the rank measure exhibits a mean reverting behavior, where a strong negative rank in mean is followed by a positive rank. Furthermore, a positive rank on average is followed by a negative rank on the following day. Looking at the “U p f raction” in Table 2, the uncertainty in these relations is still very high. A stock m with a rank Am 1 (t) < −0.4 has a pos(t + 1) the next day in no more than 59.4% of all cases. However, itive rank Am 1 the general advantages described in the previous section, coupled with the shown correlation between present and future values, do make the rank variables very interesting for further investigations. In [3] the observed mean reverting behavior is exploited in a simple trading system. The rank measure in the next section is used both as input and output in a model for prediction of future ranks.

4

Predicting the Ranks with Perceptrons

For a stock m, we attempt to predict the h-day-rank h days ahead by fitting a function gm so that Aˆm (3) h (t + h) = gm (It ) where It is the information available at time t. It may, for example, include stock returns Rkm (t), ranks Am k (t), traded volume etc. The prediction problem 3

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k-day rank k -0.45 -0.35 -0.25 -0.15 -0.05 0.05 0.15 0.25 0.35 0.45 1 30878 30866 31685 30837 30434 31009 31258 30539 30951 31550 2 30926 30548 31427 30481 30442 31116 31263 30435 30841 31675 3 30922 30440 31202 30404 30350 31146 31061 30449 30814 31697 4 30887 30315 31052 30320 30371 31097 31097 30328 30777 31776 5 30857 30293 30951 30275 30191 31049 31144 30254 30701 31816 10 30755 30004 30648 29958 30004 30875 30889 30155 30571 31775 20 30521 29635 30306 29591 29679 30560 30580 29836 30377 31692 30 30388 29371 30083 29388 29567 30349 30437 29652 30190 31503 50 30117 29006 29728 28979 29306 29876 30109 29236 29927 31159 100 29166 28050 28790 28011 28238 29015 29049 28254 29012 30460

2 0 7 s to c k s

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0 .1

0 .0 5

0

− 0 .0 5

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0 1 − d a y ra n k

0 .5

m Fig. 1. 1-day ranks Am 1 (t + 1) versus A1 (t). Each curve represents one year between 1987 and 1997.

Optimizing the Sharpe Ratio for a Rank Based Trading System

1 0 0 ra n d o m

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w a lk s to c k s

M e a n 1 − d a y ra n k 1 d a y a h e a d

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m Fig. 2. 1-day ranks Am 1 (t + 1) versus A1 (t). Each curve represents one year with 100 simulated random-walk stocks.

is as general as the corresponding problem for stock returns, and can of course be attacked in a variety of ways. Our choice in this first formulation of the problem assumes a dependence between the future rank Am h (t + h) and current (t) for different values on k. I.e.: a stock’s tendency to be a winner in ranks Am k the future depends on its winner property in the past, computed for different time horizons. This assumption is inspired by the autocorrelation analysis in Hellstr¨ om [5], and also by previous work by De Bondt, Thaler [1] and Hellstr¨ om [3] showing how these dependencies can be exploited for prediction and trading. Confining our analysis to 1, 2, 5 and 20 days horizons, the prediction model 3 is refined to m m m m (4) Aˆm h (t + h) = gm (A1 (t), A2 (t), A5 (t), A20 (t)). The choice of function gm could be a complex neural network or a simpler function. Our first attempt is a perceptron, i.e. the model is Aˆm h (t + h) = m m m m m m m m f (pm 0 + p1 A1 (t) + p2 A2 (t) + p3 A5 (t) + p4 A20 (t))

(5)

where the activation function f for the time being is set to a linear function. m m m m The parameter vector p m = (pm 0 , p1 , p2 , p3 , p4 ) is determined by regression on historical data. For a market with N stocks, N separate perceptrons are built, each one denoted by the index m. The h-day rank Am h for time t + h is predicted from the 1-day, 2-day, 5-day and 20-day ranks, computed at time t. To facilitate

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further comparison of the m produced predictions, they are ranked in a similar way as in the definition of the ranks themselves: Aˆm h (t + h) ← −0.5+ 1 ˆi (#{Aˆih (t)|Aˆm h (t) ≥ Ah (t), 1 ≤ i ≤ N } − 1) N .

(6)

In this way the N predictions Aˆm h (t + h), m = 1, ..., N, get values uniformly distributed between −0.5 and 0.5 with the lowest prediction having the value −0.5 and the highest prediction having the value 0.5. 4.1

Data and Experimental Set-Up

The data that has been used in the study comes from 80 stocks on the Swedish stock market from January 1, 1989 till December 31, 1997. We have used a sliding window technique, where 1000 points are used for training and the following 100 are used for prediction. The window is then moved 100 days ahead and the procedure is repeated until end of data. The sliding window technique is a better alternative than cross validation, since data at time t and at time t + k, k > 0 is often correlated (consider for example the returns R5m (t) and R5m (t + 1)). In such a case, predicting a function value Am 1 (t1 + 1) using a model trained with data from time t > t1 is cheating and should obviously be avoided. The sliding window approach means that a prediction Aˆm h (t + h) is based on close prices y m (t − k), ..., y m (t). Since 1000 points are needed for the modeling, the predictions are produced for the years 1993-1997.

4.2

Evaluation of the Rank Predictions

The computed models gm , m = 1, ..., N at each time step t produce N predictions of the future ranks Am h (t + h) for the N stocks. The N predictions Aˆm , m = 1, ..., N , are evenly distributed by transformation 6 in [−0.5, ..., 0.5]. h As we shall see in the following section, we can construct a successful trading system utilizing only a few of the N predictions. Furthermore, even viewed as N separate predictions, we have the freedom of rejecting predictions if they are not viewed as reliable or profitable1 . By introducing a cut-off value γ, a selection of predictions can be made. For example, γ = 0.49 means that we are only ˆm considering predictions Aˆm h (t + h) such that |Ah (t + h)| > 0.49. The results for 1-day predictions of 1-day ranks Aˆm 1 (t + 1) for a γ = 0.0 and 0.49 are presented in Tables 4 and 5. Each column in the tables represents performance for one trading year with the rightmost column showing the mean values for the entire time period. The rows in the table contain the following performance measures: 1

As opposed to many other applications, where the performance has to be calculated as the average over the entire data set.

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1. Hitrate+ . The fraction of predictions Aˆm h (t + h) > γ, with correct sign. A value significantly higher than 50% means that we are able to identify higher-than-average performing stocks better than chance. 2. Hitrate− . The fraction of predictions Aˆm h (t + h) < −γ, with correct sign. A value significantly higher than 50% means that we are able to identify lower-than-average performing stocks better than chance. 3. Return+ . 100·Mean value of the h-day returns Rhm (t + h) for predictions Aˆm h (t + h) > γ. 4. Return− . 100·Mean value of the h-day returns Rhm (t + h) for predictions Aˆm h (t + h) < −γ. 5. #P red+ . Number of predictions Aˆm h (t + h) > γ. 6. #P red− . Number of predictions Aˆm h (t + h) < −γ. 7. #P red. Total number of predictions Aˆm h (t + h). All presented values are average values over time t and over all involved stocks m. The performance for the one-day predictions are shown in the Tables 4 and 5. In Table 4 with γ = 0.00, the hit rates Hitrate+ and Hitrate− are not significantly different from 50% and indicate low predictability. However, the difference between the mean returns (Return+ and Return− ) for positive and negative rank predictions shows that the sign of the rank prediction really separates the returns significantly. By increasing the value for the cut-off value γ to γ = 0.49, the hit rate goes up to 64.2.0% for predicted positive ranks (Table 5). Furthermore, the difference between the mean returns for positive and negative rank predictions (Return+ and Return− ) is substantial. Positive predictions of ranks are in average followed by a return of 0.895% while a negative rank prediction in average is followed by a return of 0.085%. The rows #P red+ and #P red− show the number of selected predictions, i.e. the ones greater than γ and the ones less than −γ respectively. For γ = 0.49 these numbers add to about 2.7% of the total number of predictions. This is normally considered insufficient when single securities are predicted, both on statistical grounds and for practical reasons (we want decision support more often than a few times per year). But since the ranking approach produces a uniformly distributed set of predictions each day (in the example 80 predictions) there is always at least one selected prediction for each day, provided γ < 0.5. Therefore, we can claim that we have a method by which, every day we can pick a stock that goes up more than the average stock the following day with probability 64%. This is by itself a very strong result compared to most published single-security predictions of stock returns (see for example Burgess and Refenes [2], Steurer [8] or Tsibouris and Zeidenberg [9]).

5

Decision Support

The rank predictions are used as basis for a decision support system for stock picking. The layout of the decision support system is shown in Figure 3. The 1-day predictions Aˆm 1 (t + 1) are fed into a decision maker that generates buy and sell signals that are executed by the ASTA trading simulator. The decision maker

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R a n k p re d ic to rs

D e c is io n m a k e r

n e w x

m = 1 ,… ,N m

A

(t)

1 m

A

(t)

A

2 m

(t) m

A

(t)

5 2 0

å p

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x = (b u y th re s e ll th re s m in c a s h m a x tra d

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s h o ld , h o ld , % , e s iz e % )

B u y ! S e ll !

A S T A tra d in g s im u la to r

Fig. 3. The trading system is based on 1-day rank predictions for N stocks, and a decision maker parameterized by the x-vector. The learning element comprises a numerical optimizer, which finds the x that maximizes the Sharpe ratio for the historical data.

Table 4. 1-day predictions of 1-day ranks |Aˆ1 (t + 1)| > 0.00

Y ear : Hitrate+ Hitrate− Return+ Return− #P red+ #P red− #P red

93 94 95 96 97 93-97 51.1 53.4 53.3 53.0 52.5 52.7 51.8 53.6 53.4 53.2 52.6 52.9 0.389 0.101 0.155 0.238 0.172 0.212 0.253 -0.176 -0.094 0.057 0.008 0.010 7719 8321 8313 8923 8160 41510 7786 8343 8342 8943 8172 41664 15505 16664 16655 17866 16332 83174

Table 5. 1-day predictions of 1-day ranks |Aˆ1 (t + 1)| > 0.49

Y ear : 93 94 95 96 97 93-97 Hitrate+ 59.7 65.1 67.9 66.7 61.2 64.2 Hitrate− 52.7 53.2 56.4 59.4 56.7 55.7 Return+ 1.468 0.583 0.888 0.770 0.745 0.895 Return− 1.138 -0.236 -0.402 -0.040 -0.055 0.085 #P red+ 211 215 218 228 214 1088 #P red− 222 220 220 234 217 1115 #P red 15505 16664 16655 17866 16332 83174

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is controlled by a parameter vector x, comprising the threshold values of the step functions that generate buy and sell signals from the rank predictions. Two other parameters control the amount of money the trader is allowed to invest in one single trade, and how large a fraction of the total wealth should be kept in cash at all times. The learning element comprises an optimizing algorithm, which finds the parameter vector x that maximizes the mean annualized Sharpe ratio for the simulated trader. The learning period is 2 years and the found optimal x is then used to control the trading in the following year. The procedure is repeated yearly, using the last 2 years as learning period. The ASTA system is a general-purpose tool for development of trading and prediction algorithms. A technical overview of the system can be found in Hellstr¨ om [4] and examples of usage in Hellstr¨ om [3] and Hellstr¨ om, Holmstr¨om [6]. More information can also be found at http://www.cs.umu.se/∼thomash. The rank measure and also the prediction algorithm described in Section 4 is implemented in ASTA and therefore the test procedure is very straightforward. A transaction cost of 0.15% (minimum 90 Swedish crowns ∼ USD) is assumed for every buy or sell order. 5.1

Trading Results

The annual trading profit is presented in Table 6. As can be seen, the performance is very good. The trading strategy outperforms the benchmark (the Swedish Generalindex) consistently and significantly every year and the mean annual profit made by the trading is 129.4%. The mean annual index increase during the same period is 27.4%. The Sharpe ratio which gives an estimate of a risk adjusted return shows the same pattern. The average Sharpe ratio for the trading strategy is 3.0 while trading the stock index Generalindex gives 1.6. By studying the annual performance we can conclude that these differences in performance is consistent for every year 1993-1997. Further more, the number of trades every year is consistently high (seven buy and seven sell per week), which increases the statistical credibility of the results. The trading results are also displayed in Figure 4. The upper diagram shows the equity curves for the trading strategy and for the benchmark index. The lower diagram shows the annual profits. Table 6. Trading results for the trading system shown in Figure 3.

Y ear : 93 94 95 96 97 Mean Total P rof it 120.8 116.7 142.9 165.8 100.8 129.4 6102 Index prof it 52.1 4.6 18.3 38.2 23.8 27.4 222 Dif f. 68.7 112.2 124.6 127.7 76.9 102.0 5880 #.trades 640 706 700 770 671 697 3487 Sharpe 1.7 2.4 3.2 4.5 3.1 3.0 Index sharpe 2.8 0.1 1.4 2.4 1.4 1.6

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Thomas Hellstr¨ om E q u ity c u rv e s fo r T ra d in g (6 1 0 2 % ) a n d In d e x (2 2 2 % ) 8 0 T ra d in g In d e x 6 0 4 0 2 0 0 J a n 9 3

J a n 9 4

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2 0 0 1 5 0 1 0 0 5 0 0

9 3

9 4

9 5 B u y : b s 1 (1 )

9 6

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Fig. 4. Performance for the simulated trading with stock picking based on 1-day rank predictions as shown in Figure 3. The top diagram shows the equity curves while the lower diagram displays the annual profits. The trading outperforms the benchmark index consistently every year.

Let us look at possible reasons and mechanisms that may lie behind the good results. In [7], Lo and MacKinley report on positive cross-autocovariances across securities. These cross effects are most often positive in sign and are characterized by a lead-lag structure where returns for large-capitalization stocks tend to lead those of smaller stocks. Initial analysis of the trades that the rank strategy generates, expose a similar pattern, where most trading signals are generated for companies with relatively low traded volume. A positive cross-autocovariances can therefor provide part of an explanation to the successful trading results.

6

Conclusions

We have successfully implemented a model for prediction of a new rank measure for a set of stocks. The shown result is clearly a refutation of the Random Walk Hypothesis (RWH). Statistics for the 1-day predictions of ranks show that we are able to predict the sign of the threshold-selected rank consistently over the investigated 5-year-period of daily predictions. Furthermore, the mean returns that accompany the ranks show a consistent difference for positive and negative

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predicted ranks which, besides refuting the RWH, indicates that the rank concept could be useful for portfolio selection. The shown experiment with an optimizing trading system shows that this is indeed the case. The mean annual profit is 129.4% compared to 27.4% for the benchmark portfolio, over the investigated 5year-period. The risk adjusted return, as measured by the Sharpe ratio, exhibits the same relation. The trading system gives a Sharpe ratio of 3.0 while trading the benchmark portfolio gives only 1.6. Of course, the general idea of predicting ranks instead of returns can be implemented in many other ways than the one presented in this paper. Replacing the perceptrons with multi layer neural networks and also adding other kind of input variables to the prediction model (4) are exciting topics for future research.

References 1. W. D. Bondt and R. Taler. Does the stock market overreact? Journal of Finance, 40(3):793–805, 1985. 2. A. N. Burgess and A. N. Refenes. The use of error feedback terms in neural network modelling of financial time series. In C. Dunis, editor, Forecasting Financial Markets, Financial Economics and Quantitative Analysis, pages 261–274. John Wiley & Sons, Chichester, England, 1996. 3. T. Hellstr¨ om. ASTA - a Tool for Development of Stock Prediction Algorithms. Theory of Stochastic Processes, 5(21)(1-2):22–32, 1999. 4. T. Hellstr¨ om. ASTA - User’s Reference Guide. Technical Report UMINF-00.16 ISSN-0348-0542, Department of Computing Science Ume˚ a University, Ume˚ a Sweden, 2000. 5. T. Hellstr¨ om. Predicting a Rank Measure for Portfolio Selection. Theory of Stochastic Processes, 6(22)(3-4):64–83, 2000. 6. T. Hellstr¨ om and K. Holmstr¨ om. Parameter Tuning in Trading Algorithms using ASTA. In Y. S. Abu-Mostafa, B. LeBaron, A. W. Lo, and A. S. Weigend, editors, Computational Finance 1999, pages 343–357, Cambridge, MA, 1999. MIT Press. 7. A. W. Lo and A. C. MacKinley. A Non-Random Walk Down Wall Street. Princeton University Press, Princeton, 1999. 8. E. Steurer. Nonlinear modelling of the DEM/USD exchange rate. In A.-P. Refenes, editor, Neural Networks in the Capital Markets, chapter 13, pages 199–212. John Wiley & Sons, Chichester, England, 1995. 9. G. Tsibouris and M. Zeidenberg. Testing the efficent markets hypothesis with gradient descent algorithms. In A.-P. Refenes, editor, Neural Networks in the Capital Markets, chapter 8, pages 127–136. John Wiley & Sons, Chichester, England, 1995.

Choice: The Key for Autonomy Luis Antunes, Jo˜ ao Faria, and Helder Coelho Faculdade de Ciˆencias, Universidade de Lisboa Campo Grande, 1749-016 Lisboa, Portugal {xarax@di., faria@, hcoelho@di.}fc.ul.pt

Abstract. Agents must decide, i.e., choose a preferred option from among a large set of alternatives, according to the precise context where they are immersed. Such a capability de¨nes to what extent they are autonomous. But, there is no one way of deciding, and the classical mode of taking utility functions as the sole support is not adequate for situations constrained by qualitative features (such as wine selection, or putting together a football team). The BVG agent architecture relies on the use of values (multiple dimensions against which to evaluate a situation) to perform choice among a set of candidate goals. In this paper, we propose that values can also be used to guide the adoption of new goals from other agents. We argue that agents should base their rationalities on choice rather than search.

1

Introduction

For more than a decade, agent programming was based upon the BDI (BeliefDesire-Intention) model [12], and backed by Bratman’s human practical reasoning theory [6]. However, this framework is not completely clari¨ed and extended for taking motivations and open situations into account. When looking deeply into the autonomy issue, we were faced with decision making at large, within non-deterministic contexts, because the BDI idea was not able to allow the implementation of a sound choice machinery. As a matter of fact, this issue is innovative from a cognitive science point of view, and our proposal based on values allows for a richer alternative to the so-called classical utility functions. From a cognitive modelling standpoint, we bring the issue of choice into the nucleus of the agent architecture, and provide the mechanisms for adaptation of the choice machinery. From a decision theory standpoint, we propose a choice model that expands on the notion of utility to tackle multiple dimensions, and dynamic adaptation. From a philosophy of mind standpoint, we argue that evaluation of the results of choice cannot be made in absolute terms (the perfect choice does not exist), and so rationality is individual, situated and multi-varied. From a social simulation standpoint, we provide mechanisms to regulate (and later observe) interactions, namely, rules for goal adoption based on curiosity and imitation. In [1, 3], we have proposed a new model of rationality that goes beyond utility and encompasses the notion of value as a central component for decision-making P. Brazdil and A. Jorge (Eds.): EPIA 2001, LNAI 2258, pp. 142–154, 2001. c Springer-Verlag Berlin Heidelberg 2001 

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Table 1. Comparison between the utilitarian and the multiple-values approaches. Utility functions Choice functions one dimension several dimensions utility values closed world open world linear orderings quasi-orderings beforehand computation execution-time computation

and computing importance. In this model, an agent has its cognitive machinery roughly included in a BDI framework, and produces its choices from available alternatives by considering, for the given situation, how each relevant value is a¨ected. A calculus performs choices by collapsing all these partial assessments into a sorted list of actions to be performed. This must be made in execution time, since it is not possible to foretell all relevant possibilities beforehand. Evaluative assessments can evolve, as values are dynamic objects in the mind, and so can be added, removed, or changed. This framework does not add up to multi-attribute utility theory [10], anymore than it does to classical utility: the conditions for both these two choice theories are far too demanding, namely all alternatives must be comparable, and transitivity (or coherence) must be observed. All these operations are favoured by the contact of the agent with the environment, including other agents, or some user. If we want to achieve enhanced adaptability to a complex, dynamic environment, we should provide the agent with motivations, rather than plain commands. A degree of autonomy is requested, as well as responsibility and animation. Autonomy is a social notion, and concerns the in¨uence from other agents (including the user). An autonomous agent should be allowed to refuse some order or suggestion from another agent, but it should be allowed to adopt it as well. In [3], the value-based adaptive calculus provided some interesting results when facing decision problems that called for some adaptability, even in the absence of all the relevant information. However, there remains one di¨ culty in assessing the results of those experiments: how do we evaluate our evaluations? We need meta-values with which to assess those results, but this calls for a designer, and amounts to look for emergent phenomena. It can be argued that if these ‘higher’ values exist why not to use them for decision? This dilemma shows clearly the ad hoc character of most solutions, and the di¨ culty in escaping it. We can conceive two ways out. The ¨rst is the development of an ontology of values, to be used in some class of situations. Higher or lower, values have their place in this ontology, and their relations are clearly de¨ned. For a given problem the relevant values can be identi¨ed and used, and appropriate experimental predictions postulated and tested. The second is the object of this paper. By situating the agent in an environment with other agents, autonomy becomes a key ingredient, to be used with care and balance. The duality of value sets becomes a necessity, as agents cannot

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access values at the macro level, made judiciously coincide with the designer values. The answer is the designer, and the problem is methodological. The BVG (Beliefs, Values and Goals) model update mechanism provides a way to put to test this liaison between agent and designer. And, it clari¨es de¨nitely one of the mysteries of the BDI model, usually translated in an ad hoc way when some application is implemented. In the next section we shed some light on the notion of choice, and argue for the introduction of motivational concepts di¨erent from the ones usually considered in BDI (i.e. desires). Decision is about choice and preference, and not about plans and search. Next we introduce the BVG architecture, and its related mechanisms for decision. In the fourth section we sustain that the multiple values decision framework will produce agents with enhanced autonomy, and present some value-based modes for regulating agent interaction. Then, we deal with one of these modes, by presenting concrete mechanisms for goal adoption. Section 6 discusses some forms of orderings we can use for the serialisation of candidate options. In section 7 and 8 we introduce our main case study, and discuss some of the experimental results we obtained. Finally we conclude by arguing that choice is one of the main ingredients for autonomy.

2

Departing from BDI “Practical reasoning is a matter of weighing con¨icting considerations for and against competing options, where the relevant considerations are provided by what the agent desires/values/cares about and what the agent believes.” [6, page 17]

Bratman’s theory of human practical reasoning was the inspiring set of ideas of the most used model of agency till today, the BDI model, where the trade-o¨ is between two distinct processes: deciding what (deliberation) versus deciding how (means-ends reasoning). Yet, the aim of the overall mechanism is directed towards actions, agent autonomy is out of the argumentation. So, the decisionmaking activity is not faced and its choosing stage not fully understood. We are ¨rmly convinced that without discussing how “competing options” are ranged, ordered, and selected, autonomy is no longer possible. Our thesis is the following: any agent uses values to decide and ¨nally execute some action. So, we need a theory of human practical decision to help us design and implement such autonomous agents. Looking back to the ¨rst implementation of the BDI model, IRMA and PRS architectures (cf. respectively [7, 13]), we found a simple control loop between the deliberation and the means-ends reasoning processes. Further enhancements focused the deliberation process, the commitment strategies, the intention reconsideration [15], and the introduction of a belief revision function, a meta-level control component, or a plan generation function. However, if we take a mainstream account of decision making such as [14], we ¨nd four stages involved: information gathering, likelihood estimation, deliberation (pondering of the alternatives) and choosing. If we look at Wooldridge’s [15]

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descriptions of both deliberation (deciding what to do) and means-ends reasoning (deciding how to do it), we will discover that both are decision processes, and so can be encompassed by the above account. Studying the famous Cohen and Levesque’s equation, Intention = Choice + Commitment, we discovered that the choice part was no so much dissected when compared to the commitment one, and no good reasons were found. BDI is a logician’s dream that such processes can be ‘solved’ by theorem proving, or search, but those are not problems to be solved, rather decisions to be made. Or, broadly speaking, the issue at stake is not search, but rather choice. Search would imply the optimisation of a (onedimensional) function, whereas in choice we can have a weighing over several dimensions (n-dimensional valuing). The whole decision process is a mix of quantitative and qualitative modes of reasoning: ¨rst, a list of sub-goals is built by deliberation, and without any order; second, a partial order is imposed by weighing and valuing con¨icting considerations (e.g. feelings); third, the ¨rst sub-goals attached with values are “organised” unconsciously before the mind makes itself up. Recent ¨ndings of neuropsychology have come to the conclusion that many of our actions and perceptions are carried out by the unconscious part of our brains, and this means that emotion is no longer the sole control apparatus of decision-making [5]. The BVG (Beliefs, Values, Goals) model relaxes desires and intentions (gathered together into a general class of goals), puts out consciousness considerations, and only asserts that emotions are part of an overall global control machinery. We prefer, for simpli¨cation reasons, that the agent is in control of its own mind (cf. [8]). Making these choices, we can study what a¨ects the decision-making process (cf. ¨gure 1).

W o r ld B e lie fs

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E x e c u tio n

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Fig. 1. Decision-making with the BVG architecture. Rectangles represent processes, and ovals represent sets with the main mental concepts. Arrows depict the ¨ow of data through the decision process.

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Our work has mostly addressed the deliberation (in the sense of pondering of alternatives, since we regard ‘BDI-deliberation’ as a decision process in itself) part of the decision process. However, there is something to be said about the choosing stage. Once a sorting of the alternatives achieved, choosing can be as simple as to pick the ¨rst of the list, but other heuristics can be used, such as using an adequate probability distribution to pick one of the n ¨rst options, or again using values to inform this new process. The agent’s character is closely associated with his ability to choose the best/most appropriate sub-goal, i.e., each agent (egotistic, laconic, deceiving, etc.) has a speci¨c policy for choosing/preferring some goal. The so-called personality of an agent means heuristics for re-ordering options for arranging con¨gurations (clusters) of preferences, in a n-dimensional space. The agent prefers an action by selecting credibility values (set-of-support) and by computing choice functions (policies), even amalgamating similar options (sub-goals) before a decision comes out.

3

The BVG Architecture

The BVG architecture roughly follows Castelfranchi’s principles for autonomy contained in his “Double Filter Architecture” [8]. The reference schema of the BVG architecture for decision-making includes goals, candidate actions to be chosen from, beliefs about states of the world, and values about several things, including desirability of those states. Values are dimensions along which situations are evaluated, and actions selected. By dimension we mean a non empty set endowed with an order relation. In the model proposed in [1], emotions have a determinant role in the control of the choice process. One main role of emotions is to set the amount of time available for a decision to be made. We proposed a cumulative method, that improves the quality of the decision when time allows it. The idea is based on the di¨erent importance of the other relevant values. Options are evaluated against the most important values ¨rst. The other key issue in the BVG architecture is the update of the choice machinery based on assessments of the consequences of the previous decisions. These assessments can be made in terms of (1) some measure of goodness (the quality of the decision, measured through its consequences on the world); (2) the same dimensions that the agent used for decision; and (3) a di¨erent set of dimensions, usually the dimensions that the designer is interested in observing, what amounts to look for emergent behaviour (cf. [3]). Issues  (1) and (2) were addressed in [3], where a cumulative choice function F = ck Fk was proposed, that, given some goal and alternatives characterised by values Vk , would sort those alternatives out, selecting the best of them for execution. Afterwards, the result of this decision gets evaluated and is fed back into the choice mechanism. An appropriate function performs updates on the features that are deemed relevant for the decision. For case (1), function G takes an assessment in dimension Vn , and distributes credit to every vki , feature of

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winning alternative i. In case (2), a more complex function H takes a multidimensional assessment in V1 ♠ ♠♠♠♠ Vn . In both cases, the choice function F remains unchanged, since we sustain that our perception of alternatives is more likely to change than the way we perform choice. For instance, if based on some price-evaluating function P , we pick some wine for dinner and it turns out to be bad, we will probably prefer to mark that wine as a bad choice than to change P . P can no doubt change, but more slowly, and as a result of other factors, like the perception that we constantly pick bad wines, or a major increase in our income. Case (3) relates the evaluation of the experiments to the behaviours of the agents. We have a keen concern for autonomous behaviours. But autonomy can only be located in the eyes of the observer. To be autonomous, some behaviour need not be expected, but also not extravagant. This hard-to-de¨ne seasoning will be transported into our agents by an update function such as described above, but one that doesn’t depend exclusively on agent-available values. Returning to the wines example, suppose someone invites us over to dinner. A subservient friend would try to discover some wine we know and like to serve us with dinner. An autonomous one would pick some wine of his preference, regardless of the fact we don’t drink any alcohol. In between of these two extreme behaviours is the concept of autonomy we are looking for. Our friend knows what we like, and serves something close but new, knowing we will cherish his care. A similar point was made in [4], where the opinions of a group of experts are to be combined. The opinion of each expert receives an a priori weight, and each expert aims at increasing his weight by being right most times about the outcome of the decision. The proven optimal strategy is to keep honesty and report one’s true opinion, even if locally it might appear as the worst choice.

4

Autonomy in BVG

We propose several steps in this move towards enhanced autonomy. First, let us observe that adaptation and learning should be consequences of the interaction between the agent and the world and its components. If the agent would adapt as a result of any form of orders from its designer, it wouldn’t be adaptation or learning, but design. Of course, if the agent is to respond to a user, this user should be present in its world. Castelfranchi’s [8] postulates emphasise the role of social interactions in the agent’s autonomy. We draw on these postulates to introduce some of the mechanisms involved in agent interaction. For further work on these issues, cf. [2]. Agents can share information, in particular evaluative information. Mechanisms to deal with this information can be ¨t into BVG in two di¨erent ways. (1) An agent receives information from another and treats it as if it was an assessment made by himself (possibly ¨ltered through a credibility assignment function). Choice can be performed as always, since the new information was incorporated into the old one and a coherent picture is available. (2) The receiving agent registers the new information together with the old one, and all

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is considered together by the choice function F when the time comes. A new component of F , say Fn+1 , deals with the ‘imported’ information separately. Agents can also share goals. They can pick goals from each other for several reasons. We try to characterise those reasons by recurring to values. We have addressed the adoption of goals by imitation (see [1]). Other reasons could be: curiosity (the appeal of something new in the absence of foreseen drawbacks); a¨ect (the adoption of some goal just because it pleases (or serves) another agent); etc. In section 5 we provide the mechanisms for some of these cases. Finally, agents can share values. In humans, the acquisition of these takes years, and relies heavily on some ingredients: some ‘higher’ value, or notion of what’s good and what’s bad, that, by the way, we would postulate as a common element to any ontology of values; intricate dedicated mechanisms, that include some of the ones we have been addressing, but also more di¨ cult ones like kid’s playing and repeating (as opposed to usual computer-like ‘one-shot comprehension’ [11]). Our mechanisms for value sharing are necessarily simple, and consist basically of conveying values and respective components of the choice and update functions. Decisions to adopt are arbitrary, as we are at this point more interested in looking at the e¨ects of this operations in the performance of the agents and their system.

5

Goal Adoption

Castelfranchi defends an agent should adopt a goal only if this new goal serves an already existent goal of his [8]. In [1] this idea is embodied into a goal adoption rule and expanded into value-based goal adoption. The general mechanism introduced was that of imitation. A possible goal is perceived and considered for adoption according to the agent’s values. More complex rules were produced, that were based on values as the links between goals of the di¨erent agents. In the case we wanted to maintain Castelfranchi’s rule, our rule of adoption by imitation is to adopt the candidate goal if there would be already a goal that shared some value with the new goal to adopt. In the absence of a goal to be served by the goal candidate for adoption, we propose another rule that would base adoption upon the values concerning the imitated agent: Adopt(agA, Goal((V1 ,ω1 ),...,(Vk ,ωk )) (agB, G0 )) if ∃Bel(agA, Val(agB, ((Vi ,  i ), . . . , (Vj ,  j ))) : ∃Val(agA, ((Vi ,  i ), . . . , (Vj ,  j ))) :  ∀m : i ♠ m ♠ j, sameValue(Vm ,  m ,  m )

(1)

In this paper, we use a slightly di¨erent rule of adoption by imitation, by adapting Castelfranchi’s requirement, while weakening the ¨nal condition linking the two goals, i.e., the values of agB are known through the description of its goal G0 , and it su¨ ces for agA to have one value coincident with the ones of agB

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(we could have used agA’s goals to infer its values, but con¨icts might occur): Adopt(agA, Goal((V1 ,ω1 ),...,(Vk ,ωk )) (agB, G0 )) if ∃Val(agA, (Va ,  a )) : ∃i(= a) ∈ {1, . . . , k} : sameValue(Vi , ωi ,  a )

(2)

Now we introduce another mechanism for value-based adoption: curiosity. An agent will adopt a goal from another agent if all of the values involved in this goal are completely new to him: Adopt(agA, Goal((V1 ,ω1 ),...,(Vk ,ωk )) (agB, G0 )) if ¬∃a : [1 ♠ a ♠ k ∧ Val(agA, (Va ,  a )]

(3)

We end this section by clearing up what the predicate sameValue means in the present framework. Given that most of our value features are numbers in a bounded scale, we set as standards the mean point of that scale (in cases were the scale is unbounded (V4 , see section 7) we postulated a ‘normal’ mean value). Agents de¨ne themselves with respect to each value by stipulating on which side of that standard they are in the respective scale. So, in a scale from 0 to 20, with standard 10, two agents with preference values 12 and 15 will be on the same side (i.e., they share this value).

6

Orderings

In classical decision theory, we ¨lter the set of possible options through a utility function (U ), and into a linear ordering [9]. In particular, options with the same utility become indistinguishable. In the set of options, an equivalence relation  becomes implicitly de¨ned: a b i¨ U (a) = U (b). But we want to distinguish a from b, or rather, give the agent the possibility of choosing one of the two options, based on its motivations. The agent’s motivations cannot be substituted by the sole motivation of maximising (expected) utility. The situations we want to address demand for orderings weaker than the classical linear one, whether our standpoint is a deterministic analysis, or when the states of the world are not fully known, and a uncertainty measure can be associated: a probability, that depends on the agent’s parameters. It is very clear to us that all uncertainty is prone to probabilisation, and this puts us foundationally in a subjectivist perspective of probability. If this were not the case, we would be stuck either with incomplete models or in situations where we cannot quantify the uncertainty. When we aim to serialise alternatives, we have several orderings on the different dimensions that are relevant to choice. These orderings are really quasiorderings (i.e., re¨exive, transitive and non antisymmetrical) and may have dichotomy or not. With these quasi-orderings we can build clusters of alternatives. Inside each cluster we can consider linear orderings, but the ¨nal decision must

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consider the universe of the di¨erent clusters. The global ordering (of all alternatives) we aim to get is typically not total (doesn’t have dichotomy, because di¨erent dimensions are not comparable) and not partial (doesn’t have antisymmetry, to avoid the indistinguishability of equally ‘scoring’ options, as explained above). When we group alternatives in clusters built out of di¨erent dimensions, we are in fact using a common process in decision. (No agent in a market really knows all alternatives, only those that are accessible to him.) Clusterisation allows for the decrease of complexity, by excluding alternatives from the search spaces. Thus, the decision problem can be decomposed in simpler sub-problems. But the problem of integrating the results of those sub-problems remains. This integration or amalgamation of the relevant options must be made in terms of a dihcotomic quasi-ordering, because two di¨erent options must be distinguished, so that a choice can be performed. But the arrival at this ‘total’ mixture of orderings happens only in execution-time, it does not represent an intrinsic (a priori) property of the agent. And this allows for the evolution of the choice machinery in its components.

7

Case-Study: Selecting Wines

Experimentation has been conducted along a case study whose increasing complexity demands for the successive introduction of our ideas. The general theme is selection of wines by some intelligent agent. In [3], the agent would characterise wines through ¨ve dimensions against which to evaluate them: (V1 ) the rating of the producer; (V2 ) the quality of a given region in a given year, (V3 ) the price; (V4 ) the window of preferable consumption; and (V5 ) the quality of the given wine. Choice 5 would then be performed by calculating the result of a choice function F = k=1 ck Fk for each of the alternatives, and then picking up the lowest score. When the wines get tasted, the results of each tasting are fed back into the agent’s choice machinery, and the impressions of the agent on the respective wine are updated. These results can be a simple rating of the quality of the wine, or a more complex qualitative description of the impressions of the wine. The results of performing the update in either of these two ways (cases 2 and 3 in section 3) led to di¨erent results on the agent’s selection procedure.

8

Results

Somewhat unrealistically, once our agent achieved a conclusion about the best decision to be made, it would stick unconditionally to this decision: provided stock availability, it would keep buying the same wine. The reasons for this behaviour are clear, and have to do with the experimental setting not allowing for enough openness in the world, i. e. there is not enough source of change. So the agent does not have enough reason to change its choice. This is not such a bad result in certain contexts, for instance, people tend to stick to the same

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brand of car through large periods of their lives. This issue is linked with that of cognitive consonance, in that the weight of the previous decision overwhelms the desire to experiment new options (and the burden of carrying out a new complete choice process). The solution we adopted was to limit stock availability, and let agents compete for the best wines, the market imposes itself on the agents. Other alternatives (to be eventually addressed) would be to adapt the choice function F to accommodate some novelty factor. This would amount to consider a new value representing the fact that every time we buy some wine we have a little less will to buy it again. In fact this amounts to using the ‘law of diminishing returns,’ classical in decision theory. Another solution would be to consider the choice procedure not to produce a unique winning decision, but a set of winning decisions from which our agent takes a probabilistically informed pick (see ¨gure 1). Each option in this set has a weight that comes from its contribution for the global score of the set. With these weights we can build a random distribution. A series of simulations addressed the issue of goal exchange. To minimise the number of processes to control, we followed the policy of when in lack of reasons to perform some action (taken from a class of similar actions), this selection is arbitrarily done (usually using random numbers with adequate distribution). In our simulation, an agent will drop a randomly selected goal once in every four times he is active. This would allow us to concentrate on the mechanisms of goal exchange, instead of those of goals mental management. We took 26 agents, of which only 2 were endowed with some goals. In some cases all goals were dropped rather quickly, whereas in others all agents had virtually all goals. In the most interesting cases, goals start travelling through the society. An agent who originally had all the goals may end up with just two, although he has spread them around before loosing him. There’s the risk of the society loosing goals, although that did not happen frequently. The bigger danger is of the society loosing sense. What was meant as a means of enhancing bonds (through the share of interests) in the society ended up causing chaos. A typical result after 1000 runs would be: agA, from his original goals {g1 , g2 , g3 , gd4 , gd5 , gd6 } has goals {gd6 , g3 } only, he dropped goals some 14 times, including gd6 (so this goal was later adopted from another agent). Goal gd4 was lost, although this never would happen for goals g1 , g2 , and g3 which were originally also owned by agB. A total of 269 goals were dropped, and the whole society has now 76 goals, spread through the agents. Two agents have no goals, although all agents have had goals at some time. When we cross these simulations with the choice-perform-update ones, we reach the conclusion that what were the reasons for the selected actions may have been lost, with a high probability. Agents are committed to selections but they no longer have access to the rationality that caused those commitments, and so will have trouble deciding whether or not to keep them. Even worse, this hazards the update process and undermines the whole choice model, since this model by and large depends on a feedback circle that is now broken.

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It is apparent that the overlooking of grounded goal management was the cause for this problem. The focus on preference-based choice was too heavy, and a return to a more solidly built mental basis may be in need, before readdressing the choice issues. This basis may as well be provided by BDI models, because of their emphasis in the web of technical, well-founded and well-structured mental states and corresponding relationships, and also because they are the inspiring models of BVG. Nevertheless, this only means that the balance between goal management and goal selection should be more thoroughly addressed. In no way these results undermine the value of explicitly focussing on choice in the agent architecture context.

9

Conclusions

The main driving force behind the BVG architecture has always been to design new rationalities (cognitive agent idealisations) and to inquire into motivation: what makes us do what we do; what allows us to balance what we ought to do, with what we can do, with what we want to do. And even how do we rationalise a bad (for our own judgement) decision in order not to pain over it again and again. The BVG model is another way to surpass the usual di¨ culties associated with the use of normative models from economics and decision theory (maximisation of expected utility). It provides a framework where multiple values are used to compute practical (good enough) decisions (reasoning from beliefs to values, and after, to goals and actions), and then these values are updated according to the outcome of those decisions. In this and other recent papers we have thrived to show how this model produces enhanced autonomy in an environment where the multiplicity of agents causes high complexity and unpredictability, by paying more attention to the choice machinery besides optimisation. But, the topic multiple agents is now in focus and the experiments done so far helped to improve our ideas around a better BVG proposal. Our model departs from BDI (where choice is done by maximisation), by relaxing desires, and stating that agents need reasons for behaviour that surpass the simple technical details of what can be done, how it can be done and when it can be done. These reasons (which we might call ‘dirty,’ as opposed to ‘clean,’ logical ones) are then the basis of the agent’s character, and are founded on values as representatives of the multiple agent’s preferences. With the experimentation herein reported, we concluded that the dropping of those ‘clean’ reasons was perhaps hasty, and even a preference-conscious agent must possess a sound basis of logical mental concepts on which to ground. It is then only natural to return again to BDI as a provider of such a machinery, and to build the multiplevalue schema on top of it. Another conclusion is the necessity of goals on which to base behaviour. Values are not enough, even when they can cause goals to be adopted. A careful weaving is still in order. However, we have found that interesting behaviours can be obtained from our agents: we ¨nd independent behaviours, as well as leaders and followers; we can observe several degrees of adaptation to a choice pattern, depending on the parameters of the model; we

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can follow the spread of goals through a society of value-motivated agents. The agents’ exploration of the space of possibilities is carried out di¨erently from what would happen with a search procedure (even if guided by heuristics) since is driven by the agents’ preferences, and these are heterogeneous. Situated decision making is choosing among several alternatives and preferences in ways that emulate human beings. Alternatives are actions in the world, that are selected according to preference rankings or probability judgements (nspace values) to ¨t agent behaviours to precise dynamic contexts. Such an aim is the key for autonomy.

Acknowledgements The research herein reported was conducted with partial support from FCT, within research unit LabMAC. We would like to thank the anonymous reviewers for the careful reading of the paper.

References 1. Luis Antunes and Helder Coelho. Redesigning the agents’ decision machinery. In Ana Paiva, editor, A¨ ective Interactions, volume 1814 of Lecture Notes in Arti¨cial Intelligence. Springer-Verlag, 2000. Revised and extended version of the paper presented in the Workshop on A¨ect in Interactions (Towards a new generation of interfaces), Siena, October 1999. 2. Luis Antunes, Jo˜ ao Faria, and Helder Coelho. Autonomy through value-driven goal adoption. In Maria Carolina Monard and Jaime Sim˜ ao Sichman, editors, International Joint Conference: 7th Iberoamerican Conference on Arti¨cial Intelligence/15th Brazilian Conference on Arti¨cial Intelligence (open discussion track proceedings). ICMC/USP, S˜ ao Carlos, SP, Brasil, 2000. 3. Luis Antunes, Jo˜ ao Faria, and Helder Coelho. Improving choice mechanisms within the BVG architecture. In Yves L¨esperance and Cristiano Castelfranchi, editors, Intelligent Agents VII, Lecture Notes in Arti¨cial Intelligence. Springer-Verlag, 2000. Proceedings of ICMAS 2000 workshop (ATAL), to appear. 4. M. J. Bayarri and M. H. DeGroot. Gaining weight: A bayesian approach. In J. M. Bernardo, M. H. DeGroot, D. V. D. V. Lindley, and A. F. M. Smith, editors, Bayesian Statistics 3. Oxford University Press, 1988. 5. A. Bechara, H. Damasio, D. Tranel, and A. R. Damasio. Deciding advantageously before knowing the advantageous strategy. Science, 275, 1997. February, 28. 6. Michael E. Bratman. What is intention? In Philip R. Cohen, Jerry L. Morgan, and Martha E. Pollack, editors, Intentions in Communication, pages 15–32. The MIT Press, Cambridge, MA, 1990. 7. Michael E. Bratman, David J. Israel, and Martha E. Pollack. Plans and resourcebounded practical reasoning. Computational Intelligence, 4:349–355, 1988. 8. Cristiano Castelfranchi. Guarantees for autonomy in cognitive agent architecture. In Michael Wooldridge and Nick Jennings, editors, Intelligent Agents: agent theories, architectures, and languages, volume 890 of Lecture Notes in Arti¨cial Intelligence. Springer-Verlag, 1995. Proceedings of ECAI’94 workshop (ATAL).

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9. Simon French. Decision Theory: An Introduction to the Mathematics of Rationality. Ellis Horwood Limited, Chichester, England, 1986. 10. Ralph L. Keeney and Howard Rai¨a. Decisions with Multiple Objectives: Preference and Value Tradeo¨ s. John Wiley and Sons, 1976. 11. A. Monk. Cyclic interaction: a unitary approach to intention, action and the environment. Cognition, 68, 1998. 12. Martha Pollack and Marc Ringuette. Introducing the Tileworld: experimentally evaluating agent architectures. In Thomas Dietterich and William Swartout, editors, Proceedings of AAAI’90. AAAI Press, Menlo Park, CA, 1990. 13. Anand S. Rao and Michael P. George¨. Modeling agents within a BDI-architecture. In R. Fikes and E. Sandewall, editors, Proceedings of the 2nd International Conference on Principles of Knowledge Representation and Reasoning (KR’91), pages 473–484, Cambridge, Mass., 1991. Morgan Kaufmann publishers Inc.: San Mateo, CA, USA. 14. Robert A. Wilson and Frank C. Keil, editors. The MIT Encyclopedia of the Cognitive Sciences. The MIT Press, Cambridge, MA, 1999. second printing. 15. Michael Wooldridge. Reasoning about rational agents. The MIT Press, Cambridge, MA, 2000.

Dynamic Evaluation of Coordination Mechanisms for Autonomous Agents Rachel A. Bourne1 , Karen Shoop1 , and Nicholas R. Jennings2 1

Department of Electronic Engineering Queen Mary, University of London London E1 4NS, UK {r.a.bourne,karen.shoop}@elec.qmul.ac.uk 2

Dept of Electronics and Computer Science University of Southampton, Highfield Southampton SO17 1BJ, UK [email protected]

Abstract. This paper presents a formal framework within which autonomous agents can dynamically select and apply different mechanisms to coordinate their interactions with one another. Agents use the task attributes and environmental conditions to evaluate which mechanism maximises their expected utility. Different agent types can be characterised by their willingness to cooperate and the relative value they place on short- vs long-term rewards. Our results demonstrate the viability of empowering agents in this way and show the quantitative benefits that agents accrue from being given the flexibility to control how they coordinate.

1

Introduction

Autonomous agents are increasingly being deployed in complex applications where they are required to act rationally in response to uncertain and unpredictable events. A key feature of this rationality is the ability of agents to coordinate their interactions in ways that are suitable to their prevailing circumstances [5]. Thus, in certain cases it may be appropriate to develop a detailed plan of coordination in which each of the participant’s actions are rigidly prescribed and numerous synchronisation points are identified. At other times, however, it may be appropriate to adopt much looser coordination policies in which the agents work under the general assumption that their collaborators are progressing satisfactorily and that no explicit synchronisation is needed. What this illustrates is that there is no universally best method of coordinating. Given this fact, we believe agents should be free to adopt, at run-time, the method that they believe is best suited to their current situation. Thus, for example, in relatively stable environments social laws may be adopted as the most appropriate means of coordinating [10], whereas in highly dynamic situations one-off contracting models may be better suited [11], and in-between, mechanisms that involve the high-level interchange of participants’ goals may be best [4]. P. Brazdil and A. Jorge (Eds.): EPIA 2001, LNAI 2258, pp. 155–168, 2001. c Springer-Verlag Berlin Heidelberg 2001 

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To achieve this degree of flexibility, agents need to be equipped with a suite of coordination mechanisms (CMs) (with different properties and characteristics), be provided with a means of assessing the likely benefit of adopting the various mechanisms in the prevailing circumstances, and have the ability to select and then enact the best mechanism. Against this background, this paper develops and empirically evaluates a generic decision making model that agents can employ to coordinate flexibly. Specifically, we identify a number of potentially differentiating features that are common to a wide range of CMs, provide a decision-theoretic model for evaluating and selecting between competing mechanisms, and empirically evaluate the effectiveness of this model, for a number of CMs, in a suitably general agent scenario. This work builds upon the preliminary framework of [2], but makes the following advances to the general state of the art. Firstly, using a range of CMs, we show that agents can effectively evaluate and decide which to use, dependent on their prevailing conditions. Secondly, the evaluation functions associated with these CMs highlight the different types of uncertainty agents need to cope with and the different environmental parameters they need to monitor, in order to coordinate flexibly. Thirdly, we show that individual agent features such as their willingness to cooperate and the degree to which they discount their future rewards affects which CM they adopt. The remainder of the paper is structured in the following manner. Section 2 outlines the key components of the reasoning model and introduces the exemplar coordination models we evaluate in this work. Section 3 describes the grid world scenario we use for our evaluation. Section 4 formalises the reasoning models. Section 5 describes the experimental results and analysis. Section 6 looks at related work in this area. Finally, in section 7 we draw our conclusions.

2

Coordination Mechanisms

Flexible coordination requires the agents to know both how to apply a given CM and how to reason about which mechanism to select. In the former case, an agent must have access to the necessary protocols for coordinating with other agents and/or the environment. In the latter case, an agent must be capable of evaluating and comparing the possible alternatives.

2.1

Protocols for Coordination

Coordination involves the interworking of a number of agents, subject to a set of rules. The specification of exactly what is possible in a particular coordination context is given by the coordination protocol [8]. Thus, such protocols indicate the parties (or roles) that are involved in the coordination activity, what communication flows can occur between these parties, and how the participants can legally respond to such communications. Here we refer to the instigator of the coordination as the manager and to the other agents that assist the manager as the subordinates (or subs).

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For example, in the Contract Net protocol, the manager initiates a two-stage process whereby bids are requested and received, and then selected and subs are appointed. In a simpler mechanism, such as being commanded by a superior officer, a sub simply obeys the commands it receives. In all cases, however, the key point is that for each mechanism an agent supports, it must have the ability and the know-how to enact the protocol. 2.2

Evaluation of Mechanisms

A manager that is faced with a coordination task will have several potential CMs at its disposal. Each such mechanism requires a means of determining the expected value it will provide, which should be comparable with the others available. To this end, an evaluation function is needed. The value of a given CM may depend on many features including: the reward structure, the likely time of completion, and the likely availability of subordinates. Generally speaking, the more complex the coordination protocol and reward structure, the more complex the evaluation function. In particular, the more uncertainty that exists in the agent’s ability to set up and enact a CM, the harder it is to evaluate its use accurately. Moreover, some of the parameters that are needed for evaluation are likely to vary from mechanism to mechanism. A final consideration is that the value of an agent’s current situation may also depend on the state of the mechanism it has adopted. For example, an agent that has successfully recruited other agents may value its state more highly than one still engaged in the recruitment process. For all these reasons, evaluation functions need to be tailored to the specific CM they describe. When subordinates are invited to assist in coordination, they too must assess the value of accepting. These valuations are typically less complex than those for the managers since the reward on offer and the completion time are generally declared, though in some cases a sub may also need to handle uncertainty. Subs also need to take into account whether accepting an offer would incur any additional cost, such as a penalty for dropping a commitment to another agent. 2.3

Sample Mechanisms

This section outlines the protocols and reward structures for the CMs considered in this work (their evaluation functions are left to section 4). Clearly this list is not exhaustive. Rather our aim is to incorporate specific exemplars that are typical of the broad classes of coordination techniques that have been proposed in the literature. Thus, the precise form of each mechanism is of secondary importance to its broad characteristics and performance profile. Moreover, additional mechanisms can be incorporated simply by providing appropriate characterisations and evaluation functions. Nevertheless we believe that the chosen mechanisms are sufficient for our main objective of demonstrating the efficacy of dynamically selecting CMs. In this work, tasks are assumed to have several attributes: a minimum personnel requirement (mpr ), a total requirement of agent effort (effort), and a

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reward that is paid to the managing agent when the task is accomplished. Thus a task that has mpr of 3 and effort of 6 may be realised by 3 agents each contributing 2 units, by 6 agents each contributing 1 unit, but not by 2 agents each contributing 3 units. It follows that tasks with a high mpr are likely to incur a delay before the necessary subs are recruited and all agents can start working on the task together. Here agents can only work on one task at a time. However, each agent has a default task (mpr = 1, effort = 1) that it puts on hold whenever it agrees to participate in a more complex one. The type of task and how many are generated can all be varied experimentally. Asocial CM: This mechanism is used when a manager elects to perform a task alone; therefore there is no need to coordinate with any subs. The manager adopts the task, works on it and, ultimately, receives all the reward. This CM can only be used on tasks for which mpr = 1. Social Law CM: A manager may elect to have the task performed by invoking a social law (SL) that has been agreed in advance by all the agents in the system1 . For a task with mpr = n, the nearest n−1 other agents are commanded to work on the task with the manager. Because the social law extends to all agents, the subordinates cannot refuse to help. They simply assist until they are released from the task. The reward is then divided equally among all the participants. In our experimental setting, the location of subs was performed by a central coordinator allowing minimal set up delay and the prevention of multiple managers attempting to command subs at the same time. A truly distributed version is possible though would require a longer set up time. Pot Luck CM: A manager that elects to use Pot Luck (PL) coordination, sets terms under which it is willing to pay subs on a piecemeal (step-by-step) basis. These terms are then offered to all agents in the direct vicinity (this is called “pot luck” since the manager makes no active effort to recruit subs in the hope that some are already present or wander by shortly). When the task is completed the manager receives the full reward. From the subordinate’s point of view, it is occasionally offered “temporary” work for an indefinite period at a fixed rate; it either accepts and works on the task, or declines and ignores the offer. This CM is likely to be more successful when the environment is densely populated. But because the manager issues a blanket offer, it runs the risk of both over- and under-recruitment of subs. A sub can decommit from a PL task at any time at no penalty, keeping any reward it has already earned. Contract Net CM: A manager that elects to use Contract Net (CN) coordination requests bids from other agents that submit their terms according to their current circumstances. The manager selects from among the bids received and sends out firm offers. An agent receiving an offer either accepts and works on the task, eventually receiving a reward based on its bid, or declines. The manager may thus fail to recruit sufficient subs in which case it repeats the 1

The process of agreeing the social law is not considered in this work. In particular, this means that the associated costs of acheiving consensus are not factored into the cost of this mechanism.

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request-bid-offer cycle. When the task is accomplished, the manager receives the whole reward but must pay off the subs with the agreed amounts. Again, under this CM a manager may under recruit if some agent declines its offer. Once a sub has accepted a task under this CM, it may later decommit though it will have to pay a penalty for doing so. If a manager abandons a task under this CM, it must pay off any subs it has recruited, according to their terms.

3

Grid World Scenario

The scenario involves a number of autonomous agents occupying a grid world (see [2] for more details). Tasks are generated randomly according to the experimental conditions and are found by the agents who must decide whether or not to take them on. Each agent always has a specific (default) task that may be carried out alone. Tasks are located at squares in the grid and each has an associated mpr , effort and reward . One unit of effort is equivalent to one agent working on the task at the square for one time step (provided sufficient agents work on it in total). When accepting a task, an agent must decide how to tackle it; if the mpr is greater than one, it must recruit other agents to assist it, according to the various CMs at its disposal. To simplify the evaluation functions, tasks persist until they have been achieved. A more realistic setting with deadlines on tasks will require that the evaluation functions be extended to take into account the possibility of a task not being completed in time. The agents themselves have various features that can be parameterised to simulate different behavioural types. Each agent has a willingness to cooperate (wtc) factor which it uses when bidding for and evaluating tasks; when this factor is low (wtc < 1) the agents are greedy and when high (wtc > 1) they are selfless; in-between (wtc = 1) agents are neutral. Agents also use a discount factor (see below) which reflects their capacity to value short- vs long-term rewards. The agents move synchronously around the grid world, being capable of five actions: up, down, left, right and work (remain). To simplify the analysis below, the grid is formed into a torus so that an agent moving up from the top of the grid arrives at the bottom in the corresponding column; similarly for the left and right edges. This enables us to use a relatively simple probabilistic model of square occupancy by agents. This scenario offers a broad range of environments in which the effectiveness of reasoning about the various CMs can be assessed. While this scenario is obviously idealised (in the tradition of the tileworld scenario for single agent reasoning), we believe it incorporates the key facets that an agent would face when making coordination decisions in realistic environments. In particular, the ability to systematically control variability in the scenario is needed to evaluate our claims about the efficacy of flexible coordination and the dynamic selection of CMs according to prevailing circumstances.

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Agent Decision-Making

Since the agents always have a specific task to achieve with mpr = 1 and effort = 1 they always have a non-zero expectation of their future reward. However, they can increase this reward by initiating or participating in collaborative tasks (CTs) with other agents. In deciding on its collaborations, each agent aims to maximise its future rewards by adopting the best mechanism under the circumstances. Thus at all instants in time, an agent will have a current goal being undertaken using a particular CM with the agent taking a particular role. Agents may find tasks in the environment or be offered them by other agents. In either case, however, an agent needs a means of evaluating new tasks under each of the CMs. It must also be able to compare these values with its current task so as to determine when to accept a new offer. Thus each CM has an associated evaluation function which it can use to approximate the value of potential new tasks, as well as any current task being undertaken using it. These evaluation functions have some common features, but they also differ between the CMs in that they may use different aspects of the (perceived) environment. An important consideration that needs to be incorporated into the evaluation of new offers is that of liability. If, for example, an agent has agreed to participate under the Contract Net CM, it may incur a penalty for decommitting – any new offer will need to be greater than the current task and the decommitment penalty. Conversely, a manager must manage its liabilities so that, if a task becomes unprofitable, it can “cut its losses” and abandon it (since the situation has already deteriorated from the time it was adopted). Our agents are myopic in that they can only see as far as the next reward, however since tasks may arrive at different times in the future we discount all rewards back to the present using a discount factor, 0 < δ < 1. When δ ≈ 1, the difference between long- and short-term rewards is not great; however, when δ 0} is a set of updating programs U s superscripted by the states s ∈ S. Definition 3. Let s ∈ S be a state. An agent α at state s, written as Ψαs , is a pair (T , U), where T is the multi-dimensional abductive logic program of α, and U = {U 1 , . . . , U s } is a sequence of updating programs. If s = 0, then U = {}. An agent α at state 0 is defined by its initial theory and an empty sequence of updating programs, that is Ψα0 = (T , {}). At state 1, α is defined by (T , {U 1 }), where U 1 is the updating program containing all the updates that α has received at state 1, either from other agents or as self-updates. In general, an agent α at state s is defined by Ψαs = (T , {U 1 , . . . , U s }), where each U i is the updating program containing the updates that α has received at state i. Definition 4. A multi-agent system M = {Ψvs1 , . . . , Ψvsn } at state s is a set of agents v1 , . . . , vn each of which at state s. Note that the definition of multi-agent system characterizes a static society of agents in the sense that it is not possible to add/remove agents from the system, and all the agents are at one common state. To begin with, the system starts at state 0 where each agent is defined by Ψα0 = (Tα , {}). Suppose that at state 0 an agent β wants to propose an update of the knowledge state of agent α with C by triggering the project α : C. Then, at the next common state α will receive the update β ÷ C indicating that an update has been proposed by β. Thus, at state 1, α will be (Tα , {U 1 }), where U 1 = {β ÷ C} if no other updates occur for α. Within logic programs we refer to agents by using the corresponding subscript. For instance, if we want to express the update of the theory of an agent Ψα with C, we write the project α:C. The agent’s semantics is given by a syntactical transformation (defined in Sect. 3.2), producing a generalized logic program for each agent, and apply to queries for it as well. Nevertheless, to increase readability, we will immediately present a case study example that, though simple, allows one to glean some of the capabilities of the framework. To increase readability, we rely on natural language when explaining some details. The agent cycle, mentioned in the example and defined in Sect. 4, operates on the results of the transformation, but the example can be understood, on a first reading, without requiring detailed knowledge of the transformations.

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Fig. 1. DAG of Alfredo at states 0 and 1

3.1

Case Study

This example shows how the DAG of an agent can be modified through updates, and how its knowledge state and reactions are affected by such modifications. With this aim, we hypothesize two alternative scenarios. Alfredo lives together with his parents, and he has a girlfriend. Being a conservative lad, Alfredo never does anything that contradicts those he considers to be higher authorities, in this case his mother, his father, and the judge who will appear later in the story. Furthermore, he considers the judge to be hierarchically superior to each of his parents. As for the relationship with his girlfriend, he hears her opinions but his own always prevail. Therefore Alfredo’s view of the relationships between himself and other agents can be represented by the following DAG D = (V, E), depicted in Fig.1a) (where the inspection point of Alfredo, i.e. the vertex corresponding to Alfredo’s overall semantics, is represented by a bold circle): V = {α, β, γ, μ, ϕ, α } and E = {(γ, α) , (α, μ) , (α, ϕ) , (μ, β) , (ϕ, β) , (β, α )} where α is Alfredo, β is the judge, γ is the girlfriend, μ is the mother, ϕ is the father and α is the inspection point of Alfredo. Initially, Alfredo’s programs Pα0 and Rα0 at state 0 contain the rules: r1 : girlf riend ← r3 : get married ∧ girlf riend ⇒ γ : propose r4 : not happy ⇒ ϕ : (?−happy) r2 : move out ⇒ α : rent apartment r5 : not happy ⇒ μ : (?−happy) r6 : modif y edge(β, u, v, a) ⇒ α : edge(u, v) stating that: Alfredo has a girlfriend (r1); if he decides to move out, he has to rent an apartment (r2); if he decides to get married, provided he has a girlfriend, he has to propose (r3); if he is not happy he will ask his parents how to be happy (r4, r5); Alfredo must create a new edge between two agents (represented by u and v) in his DAG every time he proves the judge told him so (r6). Alfredo’s set of abducibles, corresponding to the actions he can decide to perform to reach his goals, is: A = {move out, get married} . In the first scenario, Alfredo’s goal is to be happy, this being represented at the agent cycle level (cf. Sect. 4) together with

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not false (to preclude the possibility of violation of integrity constraints) and with the conjunction of active rules: G = ?−(happy ∧ not false ∧ r2 ∧ r3 ∧ r4 ∧ r5 ∧ r6) During the first cycle (we will assume that there are always enough computational units to complete the proof procedure), the projects ϕ : (? − happy) and μ : (? − happy) are selected. Note that these correspond to the only two active rules (r4 and r5) whose premises are verified. Both projects are selected to be performed, producing 2 messages to agents ϕ and μ (the reader is referred to [8] for details on how communication can be combined into this framework). In response to Alfredo’s request to his parents, Alfredo’s mother, as most latin mothers, tells him that if he wants to be happy he should move out, and that he should never move out without getting married. This correspond to the observed updates μ ÷ (happy ← move out) and μ ÷ (false ← move out ∧ not get married) which produce the program Pμ1 at state 1 containing the following rules: r7 : happy ← move out

r8 : false ← move out ∧ not get married

Alfredo’s father, on the other hand, not very happy with his own marriage and with the fact that he had never lived alone, tells Alfredo that, to be happy he should move out and live by himself, i.e. he will not be happy if he gets married now. This corresponds to the observed updates ϕ÷(happy ← move out) and ϕ ÷ (not happy ← get married) which produce the program Pϕ1 at state 1 containing the following rules: r9 : happy ← move out

r10 : not happy ← get married

The situation after these updates is represented in Fig.1b). After another cycle, the IFF proof procedure returns no projects because the goal is not reachable without producing a contradiction. From r7 and r8 one could abduce move out to prove happy but, in order to satisfy r8, get married would have to be abduced also, producing a contradiction via r10. This is indeed so because, according to the DAG, the rules of Pϕ1 and Pμ1 cannot reject one another other since there is no path from one to the other. Thus, in this scenario, Alfredo is not reactive at all being not able to take any decision. Consider now this second scenario where the initial theory of Alfredo is the same as in the first, but his parents have decided to get divorced. Suppose that at state 1 Alfredo receives from the judge the update β ÷modif y edge(β, ϕ, μ, a) corresponding to the decision to give Alfredo’s custody to his mother after his parents divorce. This produces the program Pβ1 containing the rule: r11 : modif y edge(β, ϕ, μ, a) ← After this update, the projects ϕ : (? − happy), μ : (? − happy) and α : edge(ϕ, μ) are selected for execution, which correspond to the evaluation of the active rules r4, r5 and r6. In response to Alfredo’s request to his parents, given the precedence of opinion imposed by the judge, suppose that they reply the same rules as in the first scenario, producing the following two programs: Pμ2 containing the rules received from the mother: r12 : happy ← move out

r13 : false ← move out ∧ not get married

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Fig. 2. DAG of Alfredo at state 2

and Pϕ2 containing the rules received from the father: r14 : happy ← move out

r15 : not happy ← get married

The update α÷edge(ϕ, μ) produces a change in the graph, and the current situation is the one depicted in Fig.2. Now, the proof procedure returns the projects α : rent apartment and γ : propose. These projects correspond to the evaluation of rules r2 and r3 after the abduction of {move out, get married} to prove the goal (?−happy). Note that now it is possible to achieve this goal without reaching a contradictory state since henceforth the advice from Alfredo’s mother (r12 and r13) prevails over and rejects that of his father (r14 and r15). To this second scenario, Alfredo gets married, rents an apartment, moves out with his new wife and lives happily ever after. 3.2

Syntactical Transformation

transThe semantics of an agent α at state m, Ψαm , is established by a syntactical  formation (called multi-dimensional dynamic program update ) that, given Ψαm = (T , U), produces an abductive logic program [6] P, A, R, where P is a normal logic program (that is, default atoms can only occur in bodies of rules), A is a set of abducibles and R is a set of active rules. Default negation can then be removed from the bodies of rules in P via the dual transformation defined by Alferes et al [3]. The transformed program P  is a definite logic program. Consequently, a version of the IFF proof procedure proposed by Kowalski et al [10] and simplified by Dell’Acqua et al [6] to take into consideration propositional definite logic programs, can then be applied to P  , A, R. In the following, to keep notation simple we write rules as A ← B ∧ not C, rather than as A ← B1 ∧ . . . ∧ Bm ∧ not C1 ∧ . . . ∧ not Cn. Suppose that D, PD , A, RD , with D = (V, E), is the multi-dimensional abductive logic program of agent α, and S = {1, . . . , m} a set of states. Let the vertex α ∈ V be the inspection point of α. We will extend the DAG D with

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two source vertices: an initial vertex sa for atoms and an initial vertex sp for projects. We will then extend D with a set of directed edges (sa0 , s ) and (sps , s ) connecting sa to all the sources s in D at state 0, and connecting sp to all the sources s in D at every state s ∈ S. Let K be an arbitrary set of propositional variables as described above, and K the propositional language extending K to:   − − A , Avs , A− vs , APvs , APvs , reject(Avs ), K=K∪ reject(A− vs ) | A ∈ K, v ∈ V ∪ {sa, sp}, s ∈ S   rel edge(us , vs ), rel path(us , vs ), rel vertex(us ), ∪ edge(us , vs ), edge(us , vs )− | u, v ∈ V ∪ {sa, sp}, s ∈ S Transformation of Rules and Updates (RPR) Rewritten program rules: Let γ be a function defined as follows: ⎧ A P vs ← B ∧ C − if F is A ← B ∧ not C ⎪ ⎪ ⎪ ⎪ − ⎪ − ⎪ APvs ← B ∧ C if F is not A ← B ∧ not C ⎪ ⎪ ⎪ ⎨ − if F is false ← B ∧ not C∧ γ(v, s, F ) = falsePvs ← B ∧ C ∧ − ⎪ ∧Z1 ∧ not Z2 ∧Z1 ∧ Z2 ⎪ ⎪ ⎪ − ⎪ B ∧ C ⇒ Z if F is B ∧ not C⇒Z ⎪ P v s ⎪ ⎪ ⎪ ⎩ B ∧ C− ⇒ Z− if F is B ∧ not C ⇒ not Z P vs The rewritten rules are obtained from the original ones by replacing their heads A (respectively, the not A) by the atoms APvs (respectively, A− Pvs ) and by replacing negative premises not C by C − . (RU) Rewritten updates: Let σ be a function defined as follows: σ(s, i÷C) = γ(i, s, C) where i÷C is not one of the cases below. Note that updates of the form i÷(?−L1 ∧ . . . ∧ Ln ) are not treated here. They will be treated at the agent cycle level (see Section 4). The following cases characterize the DAG rewritten updates: σ(s, i÷edge(u, v)) = edge(us , vs ) σ(s, i÷not edge(u, v)) = edge(us , vs )− σ(s, i÷modify edge(j, u, v, x)) = modify edge(j, u, v, x) σ(s, i÷not modify edge(j, u, v, x)) = modify edge(j, u, v, x)− (IR) Inheritance rules: Avs ← Aut ∧ not reject(Aut ) ∧ rel edge(ut , vs ) − − A− vs ← Aut ∧ not reject(Aut ) ∧ rel edge(ut , vs )

for all objective atoms A ∈ K, for all u, v ∈ V ∪ {sa} and for all s, t ∈ S. The inheritance rules state that an atom A is true (resp., false) in a vertex v at state s if it is true (resp., false) in any ancestor vertex u at state t and it is not rejected, i.e., forced to be false.

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(RR) Rejection Rules: reject(A− us ) ← APvt ∧ rel path(us , vt )

reject(Aus ) ← A− Pv ∧ rel path(us , vt ) t

for all objective atoms A ∈ K, for all u, v ∈ V ∪ {sa} and for all s, t ∈ S. The rejection rules say that if an atom A is true (respectively, false) in the program Pv at state t, then it rejects inheritance of any false (respectively, true) atoms of any ancestor u at any state s. (UR) Update Rules: Avs ← APvs

− A− vs ← APvs

for all objective atoms A ∈ K, for all v ∈ V ∪ {sa} and for all s ∈ S. The update rules state that an atom A must be true (respectively, false) in the vertex v at state s if it is true (respectively, false) in the program Pv at state s. (DR) Default Rules: A− sa0 for all objective atoms A ∈ K. Default rules describe the initial vertex sa for atoms (at state 0) by making all objective atoms initially false. (CSRvs ) Current State Rules: A ← Av s

A− ← A− vs

for every objective atoms A ∈ K. Current state rules specify the current vertex v and state s in which the program is being evaluated and determine the values of the atoms A and A− . Transformation of projects (PPR) Project Propagation rules: Zus ∧ not rejectP (Zus ) ∧ rel edge(us , vs ) ⇒ Zvs Zu−s ∧ not rejectP (Zu−s ) ∧ rel edge(us , vs ) ⇒ Zv−s for all projects Z ∈ K, for all u, v ∈ V ∪ {sp} and for all s ∈ S. The project propagation rules propagate the validity of a project Z through the DAG at a given state s. In contrast to inheritance rules, the validity of projects is not propagated along states. (PRR) Project Rejection Rules: rejectP (Zu−s ) ← ZPvs ∧ rel path(us , vs ) rejectP (Zus ) ← ZP−vs ∧ rel path(us , vs ) for all projects Z ∈ K, for all u, v ∈ V ∪ {sp} and for all s ∈ S. The project rejection rules state that if a project Z is true (respectively, false) in the program Pv at state s, then it rejects propagation of any false (respectively, true) project of any ancestor u at state s. (PUR) Project Update Rules: ZPvs ⇒ Zvs

ZP−vs ⇒ Zv−s

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for all projects Z ∈ K, for all v ∈ V ∪ {sp} and for all s ∈ S. The project update rules declare that a project Z must be true (respectively, false) in v at state s if it is true (respectively, false) in the program Pv at state s. (PDR) Project Default Rules: − Zsp s

for all projects Z ∈ K and for all s ∈ S. Project default rules describe the initial vertex sp for projects at every state s ∈ S by making all projects initially false. (PARvs ) Project Adoption Rules: Zvs ⇒ Z for every project Z ∈ K. These rules, only applying to positive projects, specify the current vertex v and state s in which the project is being evaluated. Projects evaluated to true are selected at the agent cycle level and executed. Transformation rules for edge (ER) Edge Rules: edge(u0 , v0 ) for all (u, v) ∈ E. Edge rules describe the edges of D at state 0. Plus the following rules that characterize the edges of the initial vertices for atoms (sa) and projects (sp): edge(sa0 , u0 ) and edge(sps , us ) for all sources u ∈ V and for all s ∈ S. (EIR) Edge Inheritance rules: edge(us+1 , vs+1 ) ← edge(us , vs ) ∧ not edge(us+1 , vs+1 )− edge(us+1 , vs+1 )− ← edge(us , vs )− ∧ not edge(us+1 , vs+1 ) edge(us , us+1 ) ← for all u, v ∈ V such that u is not the inspection point of the agent, and for all s ∈ S. Note that EIR do not apply to edges containing the vertices sa and sp. (RERvs ) Current State Relevancy Edge Rules: rel edge(X, vs ) ← edge(X, vs )

rel edge(X, Y ) ← edge(X, Y ) ∧ rel path(Y, vs )

Current state relevancy edge rules define which edges are in the relevancy graph wrt. the vertex v at state s. (RPR) Relevancy Path Rules: rel path(X, Y ) ← rel edge(X, Y ) rel path(X, Z) ← rel edge(X, Y ) ∧ rel path(Y, Z). Relevancy path rules define the notion of relevancy path in a graph. 3.3

Multi-dimensional Updates for Agents

This section introduces the notion of multi-dimensional dynamic program update, a transformation that, given an agent Ψαm = (T , U), produces an abductive

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logic program (as defined in [6]). Note first that an updating program U for an agent α can contain updates of the form α÷(?−L1 ∧ . . . ∧ Ln ). Such updates are intended to add L1 ∧ . . . ∧ Ln to the current query of the agent α. Thus, those updates have to be treated differently. To achieve this, we introduce a function β defined over updating programs. Let U be an updating program and α an agent in M. If U does not contain any update starting with “α÷(?−”, then, β(α, U ) = (true, U ). Otherwise, suppose that U contains n updates starting with “α÷(?−”, say α÷(?−C1 ), . . . , α÷(?−Cn ) for n conjunctions C1 , . . . , Cn of atoms. Then, β(α, U ) = (C1 ∧ . . . ∧ Cn , U − {α÷(?−C1 ), . . . , α÷(?−Cn )}). Given a set Q of rules, integrity constraints and active rules, we write Ω1 and Ω2 to indicate: Ω1 (Q) = {C | for every rule and integrity constraint C in Q} and Ω2 (Q) = {R | for every active rule R in Q}. Follows the notion of multidimensional dynamic program updates for agents. Definition 5. Let m ∈ S be a state and Ψαm = (T , U) an agent α at state m. Let T = D, PD , A, RD  and U = {Us | s ∈ S and s > 0}. The multidimensional dynamic program α at the state m is  m  update for agent  Ψα = P  , A, R  where: P  = v∈V γ(v, 0, Pv ) ∪ s∈S (Ω1 (Qs )) ∪ IR ∪ RR ∪    UR ) ∪ PRR ∪ PDR ∪ ER ∪ EIR ∪ RER(α m ) ∪ RPR and R =  ∪ DR ∪ CSR(αm v∈V γ(v, 0, Rv ) ∪ s∈S (Ω2 (Qs )) ∪ PPR ∪ PUR ∪ PAR(αm ), where β(α, Us ) = ( , Ps ), and σ(s, Ps ) = Qs , for every s ∈ S. Note that P  is a normal logic program, that is, default atoms can only occur in bodies of clauses.

4

The Agent Cycle

In this section we briefly sketch the behaviour of an agent. We omit the details to keep the description general and abstract. Every agent can be thought of as a multi-dimensional abductive logic program equipped with a set of inputs represented as updates. The abducibles are (names of) actions to be executed as well as explanations of observations made. Updates can be used to solve the goals of the agent as well as to trigger new goals. The basic “engine” of the agent is the IFF proof procedure [10,6], executed via the cycle represented in Fig.3. Assume that β(α, Us ) = (L1 ∧ . . . ∧ Ln , Ps ), σ(s, Ps ) = Qs and Ψαs−1 = (T , {U1 , . . . , Us−1 }). The cycle of an agent α starts at state s by observing any inputs (projects from other agents) from the environment (step 1), and by recording them in the form of updates in the updating program Us . Then, the proof procedure is applied for  r sunits of time (steps 2 and 3) with respect to the abductive logic program Ψα obtained by updating the current one with the updating program Us . The new goal is obtained by adding the goals not false ∧ L1 ∧ . . . ∧ Ln and the active rules in Ω2 (Qs ) received from Us to the current goal G. The amount of resources available in steps 2 and 3 is bounded by some amount r. By decreasing r the agent is more reactive, by increasing r the agent is more rational. Afterwards (steps 4 and 5), the selectable projects are selected from G , the last formula of the derivation, and executed under the control of an abductive logic programming proof procedure such as ABDUAL in [3]. If the selected

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Cycle(α,r,s,Ψαs−1 ,G) 1. Observe and record any input in the updating program Us . 2. Resume the IFF by propagating the inputs wrt. the  procedure program Ψαs and the goal G ∧ not false ∧ L1 ∧ . . . ∧ Ln ∧ Ω2 (Qs ). 3. Continue applying the IFF procedure, using for steps 2 and 3 a total of r units of time. Let G be the last formula in this derivation. 4. Select from G the projects that can be executed. 5. Execute the selected projects. 6. Cycle with (α,r,s + 1,Ψαs ,G ). Fig. 3. The agent cycle

project takes the form j : C (meaning that agent α intends to update the theory of agent j with C at state s), then (once executed) the update α ÷ C will be available (at the next cycle) in the updating program of j. Selected projects can be thought of as outputs into the environment, and observations as inputs from the environment. From every agent’s viewpoint, the environment contains all other agents. Every disjunct in the formulae derived from the goal G represents an intention, i.e., a (possibly partial) plan executed in stages. A sensible action selection strategy may select actions from the same disjunct (intention) at different iterations of the cycle. Failure of a selected plan is obtained via logical simplification, after having propagated false into the selected disjunct. Integrity constraints provide a mechanism for constraining explanations and plans, and action rules for allowing a condition-action type of behaviour.

5

Conclusions and Future Work

Throughout this paper we have extended the Multi-dimensional Dynamic Logic Programming framework to include integrity constraints and active rules, as well as to allow the associated acyclic directed graph to be updatable. We have shown how to express, in a multi-agent system, each agent’s viewpoint regarding its place in its perception of others. This is achieved by composing agents’ view of one another in acyclic directed graphs, one for each agent, which can evolve over time by updating its edges. Agents themselves have their knowledge expressed by abductive generalized logic programs with integrity constraints and active rules. They are kept active through an observe-think-act cycle, and communicate and evolve by realizing their projects to do so, in the form of updates acting on other agents or themselves. Projects can be knowledge rules, active rules, integrity constraints, or abductive queries. With respect to future work, we are following two lines of research. At the agent level, we are investigating how to combine logical theories of agents expressed over graph structures [13], and how to express preferences among the beliefs of agents [7]. At the multi-agent system level, we are investigating into the representation and evolution of dynamic societies of agents. A first step towards this goal is to allow the set of vertices of the acyclic directed graph to be also updatable, representing the birth (and death) of the society’s agents. Our ongoing work and future projects is discussed in [2].

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Acknowledgments We would like to thank Jos´e Alferes for all his comments. L. M. Pereira acknowledges the support of POCTI project FLUX. The work of J. A. Leite was also supported by PRAXIS Scholarship no. BD/13514/97.

References 1. J. J. Alferes, J. A. Leite, L. M. Pereira, H. Przymusinski and T. C. Przymusinski. Dynamic Updates of Non-Monotonic Knowledge Bases. Journal of Logic Programming 45(1-3), pages 43-70, 2000. 2. J. J. Alferes, P. Dell’Acqua, E. Lamma, J. A. Leite, L. M. Pereira, and F. Riguzzi. A logic based approach to multi-agent systems. ALP Newsletter, 14(3), August 2001. 3. J. J. Alferes, L. M. Pereira and T. Swift. Well-founded Abduction via Tabled Dual Programs. In Proc. of ICLP’99. MIT Press. 1999 4. M. Bozzano, G. Delzanno, M. Martelli, V. Mascardi and F. Zini, Logic Programming and Multi-Agent System: A Synergic Combination for Applications and Semantics. In The Logic Programming Paradigm - A 25-Year Perspective, pages 5-32, Springer 1999. 5. D. De Schreye, M. Hermenegildo and L. M. Pereira, Paving the Roadmaps: Enabling and Integration Technologies. Available from http://www.compulog.org/net/Forum/ Supportdocs.html 6. P. Dell’Acqua, L. M. Pereira, Updating Agents. In S. Rochefort, F. Sadri and F. Toni (eds.), Procs. of the ICLP’99 Workshop MASL’99, 1999. 7. P. Dell’Acqua, L. M. Pereira, Preferring and Updating with Multi-Agents. In 9th DDLP-WS. on ”Deductive Databases and Knowledge Management”, Tokyo, 2001 8. P. Dell’Acqua, F. Sadri, and F. Toni. Combining introspection and communication with rationality and reactivity in agents. In Logics in Artificial Intelligence, LNCS 1489, pages 17–32, Berlin, 1998. Springer-Verlag. 9. N. Jennings, K. Sycara and M. Wooldridge. A Roadmap of Agent Research and Development. In Autonomous Agents and Multi-Agent Systems, 1, Kluwer, 1998. 10. T. H. Fung and R. Kowalski. The IFF proof procedure for abductive logic programming. J. Logic Programming, 33(2):151–165, 1997. 11. R. Kowalski and F. Sadri. Towards a unified agent architecture that combines rationality with reactivity. In D. Pedreschi and C. Zaniolo (eds), Procs. of LID’96, pages 137-149, Springer-Verlag, LNAI 1154, 1996. 12. J. A. Leite, J. J. Alferes and L. M. Pereira, Multi-dimensional Dynamic Logic Programming, In Procs. of CLIMA’00, pages 17-26, July 2000. 13. J. A. Leite, J. J. Alferes and L. M. Pereira, Multi-dimensional Dynamic Knowledge Representation. In Procs. of LPNMR-01, pp 365-378, Springer, LNAI 2173, 2001. 14. J. A. Leite and L. M. Pereira. Generalizing updates: from models to programs. In Procs. of LPKR’97, pages 224-246, Springer, LNAI 1471, 1998. 15. S. Rochefort, F. Sadri and F. Toni, editors, Proceedings of the International Workshop on Multi-Agent Systems in Logic Programming, Las Cruces, New Mexico, USA,1999. Available from http://www.cs.sfu.ca/conf/MAS99. 16. I. Niemel¨ a and P. Simons. Smodels - an implementation of the stable model and well-founded semantics for normal logic programs. In Procs. of the 4th LPNMR’97, Springer, July 1997. 17. F. Sadri and F. Toni. Computational Logic and Multiagent Systems: a Roadmap, 1999. Available from http://www.compulog.org. 18. The XSB Group. The XSB logic programming system, version 2.0, 1999. Available from http://www.cs.sunysb.edu/˜sbprolog.

Enabling Agents to Update Their Knowledge and to Prefer Pierangelo Dell’Acqua1 and Lu´ıs Moniz Pereira2 1

Department of Science and Technology Campus Norrk¨ oping, Link¨ oping University Norrk¨ oping, Sweden [email protected] 2

1

Centro de Inteligˆencia Artificial - CENTRIA Departamento de Inform´ atica Faculdade de Ciˆencias e Tecnologia Universidade Nova de Lisboa 2829-516 Caparica, Portugal [email protected]

Introduction

In a previous paper [5] we presented a combination of the dynamic logic programming paradigm proposed by J. J. Alferes et al. [1,10] and a version of KS-agents proposed by Kowalski and Sadri [7]. In the resulting framework, rational, reactive agents can dynamically change their own knowledge bases as well as their own goals. In particular, at every iteration of an observe-think-act cycle, the agent can make observations, learn new facts and new rules from the environment, and then it can update its knowledge accordingly. The agent can also receive a piece of information that contrasts with its knowledge. To solve eventual cases of contradiction within the theory of an agent, techniques of contradiction removal and preferences among several sources can be adopted [8]. The actions of an agent are modeled by means of updates, inspired by the approach in [3]. A semantic characterization of updates is given in [1] as a generalization of the stable model semantics of normal logic programs [6]. Such a semantics is generalized to the three-valued case in [3], which enable us to update programs under the well-founded semantics. J. J. Alferes and L. M. Pereira [2] propose a logic programming framework that combines two distinct forms of reasoning: preferring and updating. In particular, they define a language capable of considering sequences of logic programs that result from the consecutive updates of an initial program, where it is possible to define a priority relation among the rules of all successive programs. Updating and preferring complement each other in the sense that updates create new models, while preferences allow us to select among pre-existing models. Moreover, within the framework, the priority relation can itself be updated. In [2] the authors also define a declarative semantics for such a language. In this paper we set forth an extension of the language introduced in [5] to allow agents to update their knowledge and to prefer among alternative choices. P. Brazdil and A. Jorge (Eds.): EPIA 2001, LNAI 2258, pp. 183–190, 2001. c Springer-Verlag Berlin Heidelberg 2001 

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In the resulting framework agents can, not only update their own knowledge, for example on advice from some other agent, but can also express preferences about their own rules. Preferences will allow an agent to select among alternative models of its knowledge base. In our framework, preferences can also be updated, possibly on advice from others. We exhibit examples to show how our approach functions, including how preferring can enhance choice of reactivity in agents. The declarative semantics of this approach to agents can be found in [4]. In the remaining of the paper, we will use the following example (taken from [2]) as a working example. This example, where rules as well as preferences change over time, shows the need to combine preferences and updates in agents, including the updating of preferences themselves. Happy story. (0) In the initial situation Maria is living and working everyday in the city. (1) Next, as Maria have received some money, Maria conjures up other, alternative but more costly, living scenarios, namely traveling, settling up on a mountain, or living by the beach. And, to go with these, also the attending preferences, but still in keeping with the work context, namely that the city is better for that purpose than any of the new scenarios, which are otherwise incomparable amongst themselves. (2) Consequently, Maria decides to quit working and go on vacation, supported by her increased wealth, and hence to define her vacation priorities. To wit, the mountain and the beach are each preferable to travel, which in turn gainsays the city. (3) Next, Maria realizes her preferences keep her all the while undecided between the mountain and the beach, and advised by a friend opts for the former. To keep the notation short, we follow some abbreviations: we let c stand for “living in the city”, mt for “settling on a mountain”, b for “living by the beach”, t for “traveling”, wk for “work”, vac for “vacations”, and mo for “possessing money”.

2

Enabling Agents to Update Their Knowledge

This section introduces the language and concepts that allow agents to update their knowledge. Typically, an agent can hold positive and negative information. An agent, for example, looking at the sky, can observe that it is snowing. Then, after a while, when weather conditions change, the agent observes that it is not snowing anymore. Therefore, he has to update his own knowledge with respect to the new observed information. This implies that the language of an agent should be expressive enough to represent both positive and negative information. Knowledge updating refers not only to facts, as above, but also to rules which can also be overridden by newer rules which negate previous conclusions. In order to represent negative information in logic programs, we need more general logic programs that allow default negation not A not only in premises of their clauses but also in their heads1 . We call such programs generalized logic programs. It is convenient to syntactically represent generalized logic programs 1

For further motivation and intuitive reading of logic programs with default negations in the heads see [1].

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as propositional Horn theories. In particular, we represent default negation not A as a standard propositional variable. Propositional variables whose names do not begin with “not” and do not contain the symbols “:” and “÷” are called objective atoms. Propositional variables of the form not A are called default atoms. Objective atoms and default atoms are generically called atoms. Agents interact by exchanging information: for instance, when an agent β communicates C to an agent α. Then, α may or may not believe C. In case α does believe it, α has to update its knowledge accordingly. This kind of agent interaction is formalized via the concepts of project and update. Propositional variables of the form α:C (where C is defined below) are called projects. α:C denotes the intention (of some agent β) of proposing the updating the theory of agent α with C. We assume that projects cannot be negated. Propositional variables of the form β ÷ C are called updates. β ÷ C denotes an update that has been proposed by β of the current theory (of some agent α) with C. We assume that updates can be negated. A negated update not β÷C in the theory of an agent α indicates that agent β did not have the intention of proposing the updating the theory of agent α with C. Definition 1. A generalized rule is a rule of the form L0 ← L1 ∧ . . . ∧ Ln (n ≥ 0), where L0 (L0 = false) is an atom and every Li (1 ≤ i ≤ n) is an atom, an update or a negated update. Note that, according to the definition above, only objective atoms and default atoms can occur in the head of generalized rules. Definition 2. An integrity constraint is a rule of the form false ← L1 ∧ . . . ∧ Ln ∧ Z1 ∧ . . . ∧ Zm (n ≥ 0, m ≥ 0), where every Li (1 ≤ i ≤ n) is an atom, an update or a negated update, and every Zj (1 ≤ j ≤ m) is a project. Integrity constraints are rules that enforce some condition over the state, and therefore always take the form of denials (without loss of generality) in a 2-valued semantics. Note that generalized rules are distinct from integrity constraints and should not be reduced to them. In fact, in generalized rules it is of crucial importance which atom occurs in the head. Definition 3. A generalized logic program P is a set of generalized rules and integrity constraints. Definition 4. A query Q takes the form ?− L1 ∧ . . . ∧ Ln (n ≥ 1), where every Li (1 ≤ i ≤ n) is an atom, an update or a negated update. Reactivity is a useful ability that agents must exhibit, e.g., if something happens, then the agent needs to perform some action. Agent’s reactive behaviour is formalized via the notion of active rules. As active rules will be evaluated bottom-up, we employ a different notation for them to emphasize this aspect. Definition 5. An active rule is a rule of the form L1 ∧ . . . ∧ Ln ⇒ Z (n ≥ 0), where every Li (1 ≤ i ≤ n) is an atom, an update or a negated update, and Z is a project.

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Active rules are rules that can modify the current state, to produce a new state, when triggered. If the body L1 ∧ . . . ∧ Ln of the active rule is satisfied, then the project (fluent) Z can be selected and executed. The head of an active rule must be a project that is either internal or external. An internal project operates on the state of the agent itself, e.g., if an agent gets an observation, then it updates its knowledge, or if some conditions are met, then it executes some goal. External projects instead operate on the state of other agents, e.g., when an agent α proposes to update the theory of another agent β. Example 1. Suppose that the underlying theory of Maria (represented with m) contains the following active rules: mo ⇒ m:not wk b ⇒ m:goToBeach t ⇒ p:bookTravel The heads of the first two active rules are project internal to Maria. The first states that if Maria has money, then she wants to update her own theory with not wk. The head of the last active rule is an external project: if Maria wants to travel, she proposes to book a travel to Pedro (represented with p). We assume that for every project α:C, C is either a generalized rule, an integrity constraint, an active rule or a query. Thus, a project can only take one of the following forms: α:(L0 ← L1 ∧ . . . ∧ Ln ) α:(false ← L1 ∧ . . . ∧ Ln ∧ Z1 ∧ . . . ∧ Zm ) α:(L1 ∧ . . . ∧ Ln ⇒ Z) α:(?−L1 ∧ . . . ∧ Ln ) Note that projects can only occur in the head of active rules and in the body of integrity constraints. Updates and negated updates can occur in the body of generalized rules and in the body of integrity constraints. For example, the integrity constraint false ← A ∧ β:B in the theory of an agent α enforces the condition that α cannot perform a project β:B when A holds. The active rule A ∧ notβ÷B ⇒ β:C in the theory of α states to perform project β:C if A holds and α has not been proposed (by β) to update its theory with B. When an agent α receives an update β ÷ C, α may or may not believe C depending on whether α trusts β. This behaviour, characterized at the semantic level in [4], can be understood with an axiom schema of the form: C ← β ÷ C ∧ not distrust(β ÷ C) in the theory of α.

3

Enabling Agents to Prefer

Preferring is an important ability that agents must exhibit to select among alternative choices. Consider for instance the following example.

Enabling Agents to Update Their Knowledge and to Prefer

Example 2. Let Q be the underlying theory of Maria. ⎧ c ← not mt ∧ not b ∧ not t ⎪ ⎪ ⎪ ⎪ wk ⎪ ⎪ ⎨ vac ← not wk Q= mt ← not c ∧ not b ∧ not t ∧ mo ⎪ ⎪ ⎪ ⎪ b ← not c ∧ not mt ∧ not t ∧ mo ⎪ ⎪ ⎩ t ← not c ∧ not mt ∧ not b ∧ mo

187

⎫ (1) ⎪ ⎪ ⎪ (2) ⎪ ⎪ ⎪ ⎬ (3) (4) ⎪ ⎪ ⎪ (5) ⎪ ⎪ ⎪ ⎭ (6)

As Q has a unique 2-valued model {c, wk}, Maria decides to live in the city (c). Things change if we add the rule mo (indicating that Maria possesses money) to Q. In this case, Q has four models: {c, mo, wk}, {mt, mo, wk}, {b, mo, wk} and {t, mo, wk}, and thus c is no longer true. Maria is now unable to decide where to live. To incorporate the ability of preferring, we extend the agent language to make it possible to express preferences among the rules of the agent itself. Let < be a binary predicate symbol whose set of constants includes all the generalized rules. Definition 6. A priority rule is a generalized rule defining the predicate symbol .

3

Context Independent Conflicts

The Context Independent Conflicts result from the assignment, by different agents, of contradictory belief statuses to the same belief. Every agent maintains not only its individual beliefs but also participates on the maintenance of the distributed beliefs that include its own views. While the responsibility for individual beliefs relies on each source agent, the responsibility for distributed beliefs is shared by the group of agents involved. Three elementary processing criteria for the accommodation of distributed beliefs were implemented: – The CONsensus (CON) criterion - The distributed belief will be Believed, if all the perspectives of the different agents involved are believed, or Disbelieved, otherwise; – The MAJority (MAJ) criterion - The distributed belief will be Believed, as long as the majority of the perspectives of the different agents involved is believed, and Disbelieved, otherwise;

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– The At Least One (ALO) criterion - The distributed belief will be Believed as long as at least one of the perspectives of the different agents involved is believed, and Disbelieved, otherwise. By default, i.e., when the distributed belief is consensual, the CON criterion is applied, otherwise the distributed belief results from the resolution of the detected Context Independent Conflict. The methodology we are proposing for solving the Context Independent Conflicts is organized in two steps: first, it establishes the desired outcome of the social conflict episode, and then, it applies the processing criterion that solves the episode accordingly. During the first stage, the conflict episode is analysed to establish the most reasonable outcome. The necessary knowledge is extracted from data dependent features like the agents’ reliability [4] and the endorsements of the beliefs [5], allowing the selection, at runtime, of the most adequate processing criterion. In particular, in our work the reliability of an agent is domain dependent - an agent can be more reliable in some domains than in others. The dynamic selection of the processing criterion is based on assessment of the credibility values associated with each belief status. Two credibility assessment procedures were designed: The Foundations Origin based Procedure (FOR) - where the credibility of the conflicting perspectives is determined based on the strength of the foundations endorsements (observed foundations are stronger than assumed foundations) and on the domain reliability of the source agents; and The Reliability based Procedure (REL) - where the credibility of the conflicting views is based on the reliability of the foundations source agents. The methodology for solving Context Independent Conflicts starts by applying the FOR procedure. If the FOR procedure is able to determine the most credible belief status, then the selected processing criterion is applied and the episode is solved. However, if the result of the application of the FOR procedure is a draw between the conflicting perspectives, the Context Independent conflict solving methodology proceeds with the application of the REL procedure. If the REL procedure is able to establish the most credible belief status, then the selected processing criterion is applied and the episode is solved. The sequential application of these procedures is ordered by the amount of knowledge used to establish the resulting belief status. It starts with the FOR procedure which calculates the credibility of the conflicting perspectives based on the strength of the endorsements and on the domain reliability of the sources (agents) of the foundations. It follows with the REL procedure which computes the credibility of the conflicting beliefs solely based on the domain reliability of the sources of the foundations. We will now describe in detail the procedures for solving Context Independent Conflicts mentioned above. 3.1

The Foundations ORigin Based Procedure (FOR)

Generic beliefs are supported by sets of foundational beliefs which follow directly from observation, assumption or external communication. Since communicated

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beliefs also resulted from some process of observation, assumption or communication of other agents, foundations are, ultimately, composed of just observed or assumed beliefs. Galliers [5] refers to a belief’s process of origin as the belief’s endorsement. When a Context Independent Conflict involving a distributed belief φ occurs the FOR procedure is invoked and the credibility values for each one of the conflicting views regarding φ is computed according to the following formulas: k C(φ, Bel) = Ag=i C(φAg , Bel)/N k C(φ, Dis) = Ag=i C(φAg , Dis)/N where N is the number of agents involved in the conflict. The values of the credibility attached to each agent view are equal to the average of the credibility values of their respective sets of foundations. The credibility of a generic foundation of φ - for example, < αAg , E(αAg ), F(αAg ), Ag > which belongs to domain D - depends on the reliability of the foundation’s source agent in the specified domain (R(D, Ag)), on the foundation’s endorsement (E(αAg )) and on its support set (F(αAg )): C(αAg , Bel) = 1 × R(D, Ag), if F(αAg ) = {∅} and E(αAg ) = obs; C(αAg , Bel) = 1/2 × R(D, Ag), if F(αAg ) = {∅} and E(αAg ) = ass; C(αAg , Bel) = 0 if F(αAg ) = {∅}; C(αAg , Dis) = 1 × R(D, Ag), if F(αAg ) = {∅} and E(αAg ) = obs; C(αAg , Dis) = 1/2 × R(D, Ag), if F(αAg ) = {∅} and E(αAg ) = ass; C(αAg , Dis) = 0 if F(αAg ) = {∅}; Within this procedure, the credibility granted, a priori, to observed foundations and assumed foundations was, respectively, 1 and 1/2. The credibility of each foundation is also affected by the reliability of the origin agent (source agent) for the domain under consideration. As a result, each perspective is assigned a credibility value equal to the average of the credibility values of its support foundations. The credibility of any perspective has, then, a value between 0 and 1. A credibility value of 1 means that perspective is 100% credible (it solely depends on observed foundations generated by agents fully reliable on the data domain), whereas a credibility value of 0 means that no credibility whatsoever is associated with the perspective. Semantically, the 1 and 1/2 values granted to observed and assumed foundations have the following meaning: evidences corroborated by perception are 100% credible, whereas assumptions have a 50% chance of being confirmed or contradicted through perception. The FOR procedure calculates the credibility attached to the each one of the conflicting belief statuses (Believed and Disbelieved), and chooses the multiple perspective processing criterion whose outcome results in most credible belief status. If the most credible belief status is: (i) Disbelieved, then the CON criterion is applied to the episode of the conflict; (ii) Believed, then, if the majority of the perspectives are in favour of believing in the belief the MAJ criterion is applied; else the ALO criterion is applied to the episode of the conflict. The agents’ reliability on the domain under consideration is affected by the outcome of the

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Context Independent Conflict episodes processed so far. An episode winning agent increases its reliability in the specified domain, while an episode loosing agent decreases its reliability in the specified domain. At launch time, the agents are assigned a reliability value of 1 to every knowledge domain, which, during runtime, may vary between 0 and 1. If the agent’s view won the conflict episode of domain D then R(D, Ag) = R(D, Ag) × (1 + Nw /N ) × fnorm , where Nw , N and fnorm represent, respectively, the number of agents who won the episode, the total number of agents involved, and a normalization factor needed to keep the resulting values within the interval [0,1]; If agent Ag view lost a Context Independent Conflict episode of domain D then R(D, Ag) = R(D, Ag) × (1 − Nl /N ) × fnorm , where Nl , N and fnorm represent, respectively, the number of agents who lost the episode, the total number of agents involved in the conflict episode and a normalization factor needed to keep the resulting values within the interval [0,1]. A domain reliability value of 1 means that the agent has been fully reliable, and a value near 0 means that the agent has been less than reliable. Example Suppose a multi-agent system composed of three agents, Agent1 , Agent2 and Agent3 , with the following knowledge bases: Agent1 has observed α(a), assumed β(a) and has two knowledge production rules1 , r1,1 : α(X) ∧ β(X) → φ(X) and r1,2 : δ(X) ∧ φ(X) → ψ(X): < α1 (a), obs, {{α1 (a)}}, Agent1 >; < β1 (a), ass, {{β1 (a)}}, Agent1 >; < r1,1 , obs, {{r1,1 }}, Agent1 >; < r1,2 , obs, {{r1,2 }}, Agent1 >; Agent2 has observed α(a), assumed δ(a) and has one knowledge production rule, r2,1 : α(X) ∧ δ(X) → φ(X): < α2 (a), obs, {{α2 (a)}}, Agent2 >; < δ2 (a), ass, {{δ2 (a)}}, Agent2 >; < r2,1 , obs, {{r2,1 }}, Agent2 >; Agent3 has observed φ(a): < φ3 (a), obs, {{φ3 (a)}}, Agent3 >. Agent1 is interested in receiving information regarding α(X), β(X), δ(X), φ(X) and ψ(X), Agent2 is interested in α(X), δ(X) and φ(X), and Agent3 is interested in any information on φ(X). The agents after sharing their results (according to their expressed interests) end up with the following new beliefs: Agent1 has received α2 (a), δ2 (a), r2,1 , φ3 (a), and φ2 (a), and has inferred φ1 (a) and ψ1 (a): 1

rules are also represented as beliefs which may be activated or inhibited (believed/disbelieved).

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< α2 (a), com, {{α2 (a)}}, Agent2 >; < δ2 (a), com, {{δ2 (a)}}, Agent2 >; < r2,1 , com, {{r2,1 }}, Agent2 >; < φ3 (a), com, {{φ3 (a)}}, Agent3 >; < φ1 (a), inf, {{α1 (a), α2 (a), β2 (a), r1,1 }}, Agent1 >; < φ2 (a), com, {{α1 (a), α2 (a), δ2 (a), r2,1 }}, Agent2 >; < ψ1 (a), inf, {{α1 (a), α2 (a), β1 (a), δ2 (a), r1,1 , r2,1 , φ3 (a), r1,2}}, Agent1>; Agent2 has received α1 (a), β1 (a), φ3 (a), r1,1 , and φ1 (a), and has inferred φ2 (a): < α1 (a), com, {{α1 (a)}}, Agent1 >; < β1 (a), com, {{β1 (a)}}, Agent1 >; < r1,1 , com, {{r1,1 }}, Agent1 >; < φ3 (a), com, {{φ3 (a)}}, Agent3 >; < φ2 (a), inf, {{α1 (a), α2 (a), δ2 (a), r2,1 }}, Agent2 >; < φ1 (a), com, {{α1 (a), α2 (a), β1 (a), r1,1 }}, Agent1 >; Agent3 has received α1 (a), α2 (a), β1 (a), δ2 (a), r1,1 , r2,1 , φ1 (a), φ2 (a) r1,1 , φ1 (a), and has inferred φ2 (a): < α1 (a), com, {{α1 (a)}}, Agent1 >; < α2 (a), com, {{α2 (a)}}, Agent2 >; < β1 (a), com, {{β1 (a)}}, Agent1 >; < δ2 (a), com, {{δ2 (a)}}, Agent2 >; < r1,1 , com, {{r1,1 }}, Agent1 >; < r2,1 , com, {{r2,1 }}, Agent2 >; < φ1 (a), com, {{α1 (a), α2 (a), β1 (a), r1,1 }}, Agent1 >; < φ2 (a), com, {{α1 (a), α2 (a), δ2 (a), r2,1 }}, Agent2 >; At some point, Agent3 realizes, via observation, that φ(a) is no longer believed, i.e., < φ3 (a), obs, {∅}, Agent3 >. A first episode of a Context Independent Conflict regarding φ(a) is declared: φ1 (a) and φ2 (a) are believed while φ3 (a) is disbelieved. In the case of our conflict, the credibility values assigned to the believed status is obtained through the following expressions: C(φ1 (a), Bel) = (C(α1 (a), Bel)+C(α2 (a), Bel)+C(β1 (a), Bel)+C(r1,1 , Bel))/4 C(φ2 (a), Bel) = (C(α1 (a), Bel)+C(α2 (a), Bel)+C(δ2 (a), Bel)+C(r2,1 , Bel))/4 C(φ3 (a), Bel) = C(φ3 (a), Bel) As the default reliability values assigned to every agent domain was 1, the credibility values associated to the conflicting perspectives are: C(φ1 (a), Bel) = (1 + 1 + 1/2 + 1)/4 C(φ2 (a), Bel) = (1 + 1 + 1/2 + 1)/4 C(φ3 (a), Bel) = 0

and and and

C(φ1 (a), Dis) = 0 C(φ2 (a), Dis) = 0 C(φ3 (a), Dis) = 1

and

C(φ(a), Dis) = 1/3.

resulting in C(φ(a), Bel) = 7/12

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Since C(φ(a), Bel) > C(φ(a), Dis), the multi-agent system decides to believe in φ(a). The first episode of the conflict regarding φ(a) was successfully solved through the application of the FOR procedure, and the processing criterion that must be applied to generate the adequate social outcome of this conflict episode is the MAJ criterion. Finally, the conflict domain reliability values of the agents involved in the conflict episode are updated accordingly. So Agent1 , Agent2 and Agent3 updated credibility values for the domain under consideration (D) are: R(D, Agent1 ) = 1 × (1 + 2/3)/(1 + 2/3), i.e., R(D, Agent1 ) = 1, R(D, Agent2 ) = 1 × (1 + 2/3)/(1 + 2/3), i.e., R(D, Agent2 ) = 1, and R(D, Agent3 ) = 1 × (1 − 1/3)/(1 + 2/3), i.e., R(D, Agent3 ) = 6/15. 3.2

The RELiability Based Procedure (REL)

The REL procedure assigns each conflicting view a credibility value equal to the average of the reliability values of the source agents of its foundations. The credibility associated with the different perspectives that contribute to each belief status are added and the REL procedure chooses the processing criterion whose outcome results in adopting the most credible belief status. If the most credible belief status is: (i) Disbelieved, then the CON criterion is applied to the episode of the conflict; (ii) Believed, then, if the majority of the perspectives are in favour of believing in the belief the MAJ criterion is applied, else the ALO criterion is applied to the episode of the conflict. The reliability of the agents in the domain conflict is also affected by the outcome of the conflict episodes solved so far. Episode winning agents increase their reliability in the conflict domain, while episode loosing agents decrease their reliability in the conflict domain (see previous sub-section).

4

Context Dependent Conflicts

The detection of contradictory distinct beliefs naturally unchains the reason maintenance mechanism. However, in the case of the Context Dependent Conflicts, consistency preservation is not immediately followed the application of conflict resolution strategies. The agents postpone resolution in an effort to preserve their current beliefs since the resolution of Context Dependent Conflicts implies abandoning the foundations of the conflicting beliefs and generating alternative consensual foundational beliefs. Resolution is delayed until the moment when the system concludes that it cannot fulfil its goals unless it tries to solve the latent conflicts. To solve this type of conflicts the agents need to know how to provide alternative support to the invalidated conclusions. This search for ”next best” solutions is a relaxation mechanism called Preference ORder based procedure (POR). Each knowledge domain has lists of ordered candidate attribute values for some domain concepts. These lists contain sets of possible instances ordered by preference (the first element is the best candidate, the second element is the

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second best, and so forth) for the attribute values of the specified concepts. The preference order values are affected by the proposing agents’ reliability in the domain under consideration. In the case of a foundational belief maintained by a single agent, the process is just a next best candidate retrieval operation. In the case of a distributed foundation, a consensual candidate has to be found. If the gathered proposals are: – Identical, then the new foundation has been found; – Different, then the agents that proposed higher preference order candidates generate new next best proposals, until they run out of candidates or a consensual candidate is found. The alternative foundations found through this strategy are then assumed by the system. The credibility measure of the resulting new foundations is a function of the lowest preference order candidate used and of the involved agents’ reliability. The agents’ reliability values in the domain under consideration are not affected by the resolution of Context Dependent Conflicts.

5

Related Work

Although the work presented in this paper was inspired by many previous contributions from research fields such as belief revision, argumentation based negotiation and multi-agent systems, the approach followed is, as far as we know, novel. Authors like [16], [15] or [17] propose argumentation based negotiation protocols for solving conflicts in multi-agent systems. However, they do not address the problem of how to solve already declared conflicts, but concentrate in avoiding the possible declaration of future conflicts. Several approaches to argumentation have been proposed: the definition of logics [10], detailed agent mental states formalisation or the construction and structure of valid arguments [17]. Nevertheless, we believe that argumentation as distributed belief revision has additional advantages over other argumentation protocols implementations. This claim is supported by the fact that in our computational model the supporting arguments are automatically shared during co-operation. For instance, when a context independent conflict occurs, since the arguments in favour of the conflicting beliefs have already been exchanged, the FOR and REL conflict resolution strategies are immediately applied speeding up the process. Furthermore, argumentation as distributed belief revision allows pro-active context independent conflict resolution, since when this type of conflict occurs the agents accept the social conflict outcome while retaining their own individual perspectives. As a result, the smallest change will trigger the re-evaluation of the conflict status. The implemented autonomous belief revision strategies were also build on the proposals of other authors. The idea of using endorsements for determining preferred revisions was first proposed by Cohen [1] and, later, by Galliers in [5]. However, while Galliers proposes several types of endorsements according to the process of origin of the foundational beliefs (communicated, given, assumed,

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etc.), we only consider two kinds of endorsement: perception or assumption. We base this decision on the fact that beliefs result from some process of observation, assumption or external communication, and since communicated perspectives also resulted from some process of observation, assumption or communication of other agents, ultimately, the foundations set of any belief is solely made of observed and assumed beliefs. Similarly, Gaspar [6] determines the preferred belief revisions according to a belief change function which is based on a set of basic principles and heuristic criteria (sincerity of the sending agent, confidence and credulity of the receiving agent) that allow the agents to establish preferences between contradictory beliefs. Beliefs are associated to information topics and different credibility values are assigned to the agents in these topics. More recently, Dragoni and Giorgini [4] proposed the use of a belief function formalism to establish the credibility of the beliefs involved in conflicts according to the reliability of the source of belief and to the involved beliefs credibility. Each agent is assigned a global reliability value which is updated by the belief function formalism after each conflict. Our agents, like Gaspar’s, have domain dependent reliability values because we believe that agents tend to be more reliable in some domains than others and that the assignment of a global agent reliability (like Dragoni and Giorgini do) would mask these different expertise levels. We also guarantee, unlike Dragoni and Giorgini, that communicated foundations are only affected by the reliability of the foundation source agent, and not by the reliability of agent that communicated the foundation (which may be different). Finally, a quite interesting approach is presented by [9] where argumentation is also regarded as an extension to an existing distributed computational model. The authors regard argumentation as constraint propagation and use, consequently, a distributed constraint satisfaction computational model.

6

Conclusion

This research was motivated by the need to design a co-operative decentralised multi-agent system where dynamic, incomplete data could be adequately represented, used and maintained. The idea of using argumentation as a distributed belief revision protocol to solve information conflicts was a natural consequence of the adopted approach since the autonomous agents were modelled as individual reason maintenance systems. An important advantage of this approach lies on the fact that arguments are automatically exchanged during co-operation and are already available when conflicts occur. As a result, the declaration of conflicts results in the immediate application of the implemented evaluation strategies. The belief revision strategies designed for the resolution of the identified types of negative conflicts are based on data dependent features or explicit knowledge rather than belief semantics. The data features used to solve conflicting beliefs have been previously proposed by other authors (source agent reliability by Dragoni and Giorgini [4], endorsements by Galliers [5], and specification of preferences

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between beliefs by Gaspar [6]). However, we believe that we are combining them in a novel and more efficient manner. These argumentation protocols, which are implemented in the DIPLoMAT system, are under test and evaluation. They attempt to solve the detected conflicting beliefs but cannot, beforehand, guarantee whether their effort will be successful or not.

References 1. Cohen, P. R.; Heuristic Reasoning about Uncertainty: an Artificial Intelligence Approach. Pitman, Boston (1985). 2. de Kleer, J.; An Assumption-Based Truth Maintenance System. Artificial Intelligence 28(2):127-224 (1986). 3. Dragoni, A. F. Giorgini, P. and Puliti, P.; Distributed Belief Revision versus Distributed Truth Maintenance. In Proceedings of the Sixth IEEE Conference on Tools with Artificial Intelligence, IEEE Computer Press (1994). 4. Dragoni, A. F. and Giorgini, P.; Belief Revision through the Belief Function Formalism in a Multi-Agent Environment. Third International Workshop on Agent Theories, Architectures and Languages, LNAI N. 1193, Springer-Verlag, (1997). 5. Galliers, R; Autonomous belief revision and communication, G¨ardenfors, P. ed. Belief Revision. Cambridge Tracts in Theoretical Computer Science, Cambridge University Press, N. 29 (1992). 6. Gaspar, G.; Communication and Belief Changes in a Society of Agents: Towards a Formal Model of an Autonomous Agent, Demazeau, Y. and M¨ uller, J. P. eds. Decentralized A. I., Vol. 2, North-Holland Elsevier Science Publishers (1991). 7. Kinny, D. N. and Georgeff M. P.; Commitment and effectiveness of situated agents. In Proceedings of the Twelfth International Joint Conference on Artificial Intelligence (IJCAI’91), Sydney, Australia (1991). 8. Jennings, N. R., Parsons, S., Noriega, P. and Sierra, C.; On Argumentation-Based Negotiation. In Proceedings of the International Workshop on Multi-Agent Systems, Boston, USA (1998). 9. Jung, H., Tambe, T., Parsons, S., and Kulkarni, S.; Argumentation as Distributed Constraint Satisfaction: Applications and Results. In Proceedings of the International Conference on Autonomous Agents (Agents’01), Montreal, Quebec, Canada (2001). 10. Kraus, S., Sycara, K., and Evenchik, A.; Reaching agreements through argumentation: a logical model and implementation. Artificial Intelligence, 104 (1998). 11. Malheiro, B. and Oliveira, E.; Consistency and Context Management in a MultiAgent Belief Revision Tesbed. Wooldridge, M., M¨ uller, J. P. and Tambe, M. eds. Agent Theories, Architectures and Languages, Lecture Notes in Artificial Intelligence, Vol. 1037. Springer-Verlag, Berlin Heidelberg New York (1996). 12. Malheiro, B., Oliveira, E.; Environmental Decision Support: a Multi-Agent Approach, The First International Conference on Autonomous Agents (Agents’97), Marina del Rey, California, USA (1997). 13. Malheiro, B., Oliveira, E.; Solving Conflicting Beliefs with a Distributed Belief Revision Approach, Monard, M. C., Sichman, J. S. eds. Proceedings of The International Joint Conference 7th Ibero-American Conference on AI 15th Brazilian Symposium on AI (IBERAMIA-SBIA’2000), Atibaia, S. Paulo, Brazil. Lecture Notes in Artificial Intelligence, Vol. 1952. Springer-Verlag, Berlin Heidelberg New York (2000).

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14. Oliveira, E., Mouta, F. and Rocha, A. P.; Negotiation and Conflict Resolution within a Community of Cooperative Agents. In Proceedings of the International Symposium on autonomous Decentralized Systems, Kawasaki, Japan (1993). 15. Parsons, S., Sierra, C. and Jennings, N. R. 1998. Agents that reason and negotiate by arguing, Journal of Logic and computation 8(3)(1998), 261-292. 16. Sycara, K. 1990. Persuasive Argumentation in negotiation, Theory and Decision. 28:203-242. 17. Vreeswijk, A. W. 1997. Abstract argumentation systems. Artificial Intelligence 90(1-2). 18. Wittig, T. ed. 1992. ARCHON: An Architecture for Multi-Agent Systems, Ellis Horwood.

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Abs tr a ct. I n t h i s a r t i c l e w e d e s c r i b e a m u l t i - a g e n t d y n a m i c s c h e d u l i n g e n v iro n m e n t w h e re a u to n o m o u s a g e n ts re p re s e n t e n te rp ris e s a n d m a n a g e th e c a p a c ity o f in d iv id u a l m a c ro -re s o u rc e s in a p ro d u c tio n -d is trib u tio n c o n te x t. T h e a g e n ts a re lin k e d b y c lie n t-s u p p lie r re la tio n s h ip s a n d in te r-a g e n t c o m m u n ic a tio n m u s t ta k e p la c e . T h e m o d e l o f th e e n v iro n m e n t, th e a p p ro p ria te a g e n t in te ra c tio n p ro to c o l a n d a c o o p e ra tiv e s c h e d u lin g a p p ro a c h , e m p h a s iz in g a te m p o ra l s c h e d u lin g p e rs p e c tiv e o f s c h e d u lin g p ro b le m s , a re d e s c rib e d . T h e s c h e d u lin g a p p ro a c h is b a s e d o n a c o o rd in a tio n m e c h a n is m s u p p o rte d b y th e in te rc h a n g e o f c e rta in te m p o ra l in fo rm a tio n a m o n g p a irs o f c lie n t-s u p p lie r a g e n ts in v o lv e d . T h is in fo rm a tio n a llo w s th e a g e n ts to lo c a lly p e rc e iv e h a rd g lo b a l te m p o ra l c o n s tra in ts a n d re c o g n iz e n o n o v e r-c o n s tra in e d p ro b le m s a n d , in th is c a s e , ru le o u t n o n te m p o ra lly -fe a s ib le s o lu tio n s a n d e s ta b lis h a n in itia l s o lu tio n . T h e s a m e k in d o f in fo rm a tio n is th e n u s e d to g u id e re -s c h e d u lin g to re p a ir th e in itia l s o lu tio n a n d c o n v e rg e to a fin a l o n e . K ey w or d s . S c h e d u l i n g , M u l t i - A g e n t S y s t e m s , S u p p l y - C h a i n M a n a g e m e n t .

1

In tr od u cti on S c h e d u lin g is th e a llo c a tio n o f re s o u rc e s o v e r tim e to p e rfo rm a c o lle c tio n o f ta s k s , s u b je c t to te m p o ra l a n d c a p a c ity c o n s tra in ts . In c la s s ic a l/O p e ra tio n s R e s e a rc h (O R ) s c h e d u lin g a p p ro a c h e s , a c e n tra liz e d p e rs p e c tiv e is a s s u m e d : a ll p ro b le m d a ta is k n o w n b y a c e n tra l e n tity a n d s c h e d u lin g d e c is io n s a re ta k e n b y th e s a m e e n tity , b a s e d o n a w e ll d e fin e d c rite ria . S o m e tim e s , in m o re m o d e rn A rtific ia l In te llig e n c e (A I), o r m ix e d O R /A I, b a s e d a p p ro a c h e s , th e s a m e k in d o f c e n tra liz e d p e rs p e c tiv e is a s s u m e d to o . F o r a g e n e ra l in tro d u c tio n to O R a p p ro a c h e s to s c h e d u lin g p ro b le m s s e e [9 ] o r [2 ]; A I b a s e d a p p r o a c h e s c a n b e f o u n d i n [5 ], [2 5 ] o r [1 0 ], f o r i n s t a n c e . P la n n in g a n d c o o rd in a tio n o f lo g is tic s a c tiv itie s h a s b e e n , in th e a re a s o f O R / M a n a g e m e n t S c i e n c e , t h e s u b j e c t o f i n v e s t i g a t i o n s i n c e t h e s i x t i e s [8 ]. T h e p ro b le m o f s c h e d u lin g in th is k in d o f e n v iro n m e n ts h a s h a d , re c e n tly , a m o re d e d i c a t e d a t t e n t i o n ; s e e [6 ], [1 ], [1 1 ] o r [1 5 ], f o r i n s t a n c e . I n t h i s a r t i c l e , t h e s p e c i f i c

P. Brazdil and A. Jorge (Eds.): EPIA 2001, LNAI 2258, pp. 219–231, 2001. c Springer-Verlag Berlin Heidelberg 2001 

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l o g i s t i c s c o n t e x t o f t h e s u p p l y - c h a i n / E x t e n d e d E n t e r p r i s e ( E E ) [1 4 ] i s c o n s i d e r e d , fo r th e s h o rt-te rm a c tiv ity o f s c h e d u lin g o f p ro d u c tio n -d is trib u tio n ta s k s . T h e E E is u s u a lly a s s u m e d to b e a k in d o f c o o p e ra tiv e V irtu a l O rg a n iz a tio n , o r V irtu a l E n te rp ris e , w h e re th e s e t o f in te r-d e p e n d e n t p a rtic ip a n t e n te rp ris e s is re la tiv e ly s t a b l e ; f o r c o n c e p t s , t e r m i n o l o g y a n d c l a s s i f i c a t i o n s e e [3 ]; i n [4 ] o t h e r a p p r o a c h e s t o s c h e d u lin g in th is k in d o f c o n te x t c a n b e fo u n d . A d is trib u te d a p p ro a c h is m o re n a tu ra l in th is c a s e , b e c a u s e s c h e d u lin g d a ta a n d d e c is io n s a re in h e re n tly d is trib u te d , a s re s o u rc e s a re m a n a g e d b y in d iv id u a l, g e o g ra p h ic a lly d e c e n tra liz e d a n d a u to n o m o u s e n titie s (e n te rp ris e s , o rg a n iz a tio n s ). S o , in o u r a p p ro a c h , w e a d o p te d t h e A I M u l t i - A g e n t S y s t e m s p a r a d i g m ( s e e [1 3 ] o r [2 4 ]) . I n t h e f o l l o w i n g , w e d e s c rib e o n g o in g in v e s tig a tio n d e v e lo p in g fro m w o rk p u b lis h e d o n th e s u b je c t o f m u l t i - a g e n t s c h e d u l i n g i n p r o d u c t i o n - d i s t r i b u t i o n e n v i r o n m e n t s ( s e e [1 6 ], [1 7 ], [1 8 ], [1 9 ], [2 0 ] a n d [2 1 ]) . T h e s c h e d u lin g p ro b le m s w e c o n s id e r h a v e th e fo llo w in g fe a tu re s : a ) C o m m u n ic a tio n is in v o lv e d - A g e n ts m u s t c o m m u n ic a te (a t le a s t to e x c h a n g e p ro d u c t o rd e rs w ith c lie n ts /s u p p lie rs ); b ) C o o p e ra tio n is in v o lv e d - E a c h a g e n t m u s t c o o p e ra te s o th a t it w o n ’t in v a lid a te fe a s ib le s c h e d u lin g s o lu tio n s ; c ) S c h e d u lin g a c tiv ity is h ig h ly d y n a m ic - P ro b le m s o lu tio n d e v e lo p m e n t is a n e v e n ts m u s t a lw a y s b e o n -g o in g p ro c e s s d u rin g w h ic h u n fo re se e n a c c o m m o d a te d , a n d re -s c h e d u lin g a n d g iv in g u p a s c h e d u lin g p ro b le m a re o p tio n s to b e c o n s id e re d . T h e fo llo w in g s e c tio n s p re s e n t: a b rie f d e s c rip tio n o f th e m o d e l o f th e m u lti-a g e n t s c h e d u lin g e n v iro n m e n t (s e c .2 ), th e a g e n t in te ra c tio n p ro to c o l (s e c .3 ), th e c o o p e ra tiv e a p p ro a c h p ro p o s e d fo r m u lti-a g e n t s c h e d u lin g p ro b le m s (s e c .4 ), th e in itia l s c h e d u lin g s te p (s e c .5 ) a n d th e re -s c h e d u lin g (s e c .6 ), b o th fro m a n in d iv id u a l a g e n t p e rs p e c tiv e , a n d fin a lly , fu tu re w o rk a n d c o n c lu s io n s (s e c .7 ). S e c s . 5 a n d 6 a re p re s e n te d w ith e x a m p le s b a s e d o n s im u la tio n s .

T he S ched u li n g E n v i r on m en t Mod el In p a s t w o rk (re fe rre d a b o v e ) w e h a v e p ro p o s e d a m o d e l o f th e E E s c h e d u lin g e n v iro n m e n t b a s e d o n a n a g e n t n e tw o r k , w ith e a c h a g e n t m a n a g in g a n a g g re g a te s c h e d u lin g re s o u rc e , re p re s e n tin g a p r o d u c tio n , a tr a n s p o r ta tio n , o r a s to r e re s o u rc e , a n d lin k e d th ro u g h c lie n t-s u p p lie r re la tio n s h ip s . A s c h e d u lin g re s o u rc e is ju s t a n in d iv id u a l n o d e o f a p h y s ic a l n e tw o r k o f re s o u rc e s , a n d a c c o m m o d a te s th e re p re s e n ta tio n o f th e a g e n t ta s k s s c h e d u le d a n d th e a v a ila b le c a p a c ity a lo n g a c e rta in s c h e d u lin g te m p o ra l h o riz o n . O rd in a ry n e tw o rk a g e n ts a re n a m e d c a p a c ity , o r m a n a g e r , a g e n ts , b e c a u s e th e y a re re s p o n s ib le fo r m a n a g in g th e c a p a c ity o f a re s o u rc e , a n d th e y c a n b e p r o d u c tio n , tr a n s p o r ta tio n o r s to r e c la s s a g e n ts ; p ro d u c tio n a n d tra n s p o rta tio n c la s s a g e n ts a re g ro u p e d u n d e r th e p r o c e s s o r a g e n t c la s s , b e c a u s e th e c a p a c ity th e y m a n a g e is b a s e d o n a ra te . A s p e c ia l s u p e r v is io n a g e n t, w ith n o re s o u rc e , p la y s th e ro le o f a n in te rfa c e w ith th e o u ts id e , a n d c a n in tro d u c e n e w s c h e d u lin g p ro b le m s in to th e a g e n t n e tw o rk .

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P a irs o f c lie n t-s u p p lie r c a p a c ity a g e n ts c a n c o m m u n ic a te , b a s ic a lly th ro u g h th e h a n g e o f p ro d u c t re q u e s t m e s s a g e s (s e e n e x t s e c tio n ), w h ic h c o n ta in p ro d u c t, n tity o f p ro d u c t a n d p ro p o s e d d u e -d a te in fo rm a tio n . T h e s u p e rv is io n a g e n t m u n ic a te s w ith s p e c ia l a g e n ts p la y in g th e ro le s o f r e ta il a n d r a w -m a te r ia l n ts , lo c a te d a t th e d o w n s tre a m a n d th e u p s tre a m e n d o f th e a g e n t n e tw o rk (w h ic h p u re c lie n ts a n d p u re s u p p lie rs fo r th e n e tw o rk ), re s p e c tiv e ly . A s c h e d u lin g p ro b le m is d e fin e d b y a g lo b a l p r o d u c t r e q u e s t fr o m th e o u ts id e o f th e a g e n t n e tw o rk (i.e ., a re q u e s t o f a fin a l p ro d u c t o f th e n e tw o rk ), th e g lo b a l d u e - d a t e DD, a n d t h e g l o b a l r e l e a s e d a t e RD. T h e s e t w o d a t e s a r e t h e l i m i t s o f t h e s c h e d u lin g te m p o ra l h o riz o n a n d a re c o n s id e re d th e h a rd g lo b a l te m p o ra l c o n s tra in ts o f th e p ro b le m . T h e s u p e rv is io n a g e n t in tro d u c e s a n e w s c h e d u lin g p ro b le m b y c o m m u n ic a tin g a g lo b a l p ro d u c t re q u e s t fro m o u ts id e to th e a p p ro p ria te re ta il a g e n t (n e tw o rk s c a n b e m u lti-p ro d u c t s o , th e s e t o f p ro d u c ts d e liv e ra b le c a n d e p e n d o n th e re ta il a g e n t); la te r, a fte r th e c a p a c ity a g e n ts h a v e p ro p a g a te d a m o n g th e m , u p s tre a m th e a g e n t n e tw o rk , th e n e c e s s a ry lo c a l p r o d u c t r e q u e s ts , th e s u p e rv is io n a g e n t w ill c o lle c t g lo b a l p r o d u c t r e q u e s ts to o u ts id e fro m ra w -m a te ria l a g e n ts . A s c h e d u lin g p ro b le m w ill c e a s e to e x is t in th e n e tw o rk w h e n th e tim e o f th e la s t o f th e lo c a l d u e -d a te c o m e s , o r if s o m e lo c a l re q u e s ts a re re je c te d , o r a c c e p te d a n d th e n c a n c e le d (th e s u p e rv is io n a g e n t k n o w s th is a s m e s s a g e s o f s a tis fa c tio n , re je c tio n a n d c a n c e lla tio n w ill b e p ro p a g a te d to re ta il a n d ra w -m a te ria l a g e n ts a n d th e n c o m m u n ic a te d to it). In o rd e r to s a tis fy a p ro d u c t re q u e s t fro m a c lie n t a c a p a c ity a g e n t m u s t s c h e d u le a ta s k o n its re s o u rc e . A ta s k n e e d s a s u p p ly o f o n e (in th e c a s e o f a s to re o r tra n s p o rta tio n a g e n t), o r o n e o r m o re p ro d u c ts (in th e c a s e o f a p ro d u c tio n a g e n t a n d d e p e n d in g o n th e c o m p o n e n ts /m a te ria ls fo r th e ta s k p ro d u c t). F o r th o s e s u p p lie s th e a g e n t m u s t s e n d th e a p p ro p ria te p ro d u c t re q u e s ts to th e a p p ro p ria te s u p p lie rs .1 T h e ta s k c o n s u m e s a n o n -c h a n g in g a m o u n t o f re s o u rc e c a p a c ity d u rin g its te m p o ra l in te rv a l. T h e d u ra tio n o f th e ta s k d e p e n d s o n th e p ro d u c t, th e q u a n tity o f p ro d u c t a n d a d d itio n a l p a ra m e te rs re la te d to th e c h a ra c te ris tic s o f th e re s o u rc e a n d , in th e c a s e o f p ro c e s s o r a g e n ts , to th e a m o u n t o f c a p a c ity d e d ic a te d to th e ta s k .2 T h e d e ta ils o f th e s e la tte r p a ra m e te rs a re o m itte d h e re to a llo w s im p lic ity o f e x p la n a tio n , a n d w e w ill a s s u m e a n o n -c h a n g in g d u ra tio n fo r a ll ta s k s , e x c e p t fo r s to re ta s k s (w ith fle x ib le d u ra tio n , a n d m in im u m o f 1 tim e u n it). A lth o u g h ta s k s a re p riv a te to th e a g e n ts (o n ly th e c o m m u n ic a tio n m e s s a g e s a re p e rc e iv e d b y m o re th a n o n e a g e n t), w e c a n v ie w th e s e t o f ta s k s th a t s o m e a g e n ts o f th e n e tw o rk s c h e d u le to s a tis fy a g lo b a l p ro d u c t re q u e s t fro m o u ts id e , a s w h o le , a s b e lo n g in g to a n e tw o r k jo b , s e e e x a m p le in F ig . 1 . T h is is a ju s t a n a n a lo g u e o f th e c o n c e p t o f jo b u s e d in c la s s ic a l p ro d u c tio n s c h e d u lin g p ro b le m s .

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W e a s s u m e th a t th e re is , fo r e a c h c a p a c ity a g e n t, a u n iq u A s a re s u lt o f th is s im p lify in g a s s u m p tio n , th e la c k o re s u lt, th e n e tw o rk b e in g u n a b le to s a tis fy a g lo b a l A llo w in g m u ltip le s u p p lie rs fo r th e s a m e s u p p ly p ro d u (lik e c h o o s in g th e p re fe rre d s u p p lie r, p o s s ib ly w ith d u e -d a te s ), in w h ic h w e a re n o t in te re s te d , fo r n o w . B a s ic a lly , m o re c a p a c ity in v e s te d g iv e s a s h o rte r ta s k d u

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222

Joaquim Reis and Nuno Mamede

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c a p a c ity o v e r-a llo c a tio n m u s t o c c u r w ith a n y ta s k o f th e s o lu tio n , fo r a n y a g e n t, a t a n y m o m e n t o f th e s c h e d u lin g te m p o ra l h o riz o n . F o r te m p o ra l c o n s tra in ts to b e re s p e c te d , a ll lo c a l p ro d u c t re q u e s ts o f th e s o lu tio n m u s t fa ll w ith in th e g lo b a l re le a s e d a te a n d g lo b a l d u e -d a te o f th e p ro b le m ; a ls o , fo r e a c h a g e n t, th e in te rv a l o f its ta s k m u s t fa ll in b e tw e e n th e d u e -d a te a g re e d fo r th e c lie n t re q u e s t a n d (th e la te s t o f) th e d u e -d a te (s ) a g re e d fo r th e re q u e s t(s ) m a d e to th e s u p p lie r(s ), a n d th e la tte r d u e -d a te (s ) m u s t p re c e d e th e fo rm e r. M o r e d e t a i l s o n t h e r e s o u r c e s a n d t h e p h y s i c a l n e t w o r k a r e g i v e n i n [1 6 ] a n d [1 8 ]; a b o u t t h e a g e n t n e t w o r k a n d a g e n t a r c h i t e c t u r e s e e [1 7 ], [1 8 ], a n d [1 9 ].

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s e c tio n w e e x p o s e th e h ig h le v e l in te r-a g e n t p ro to c o l u s e d fo r s c h e d u lin g in n e tw o rk . a g e n t in te ra c tio n a c tiv ity fo r s c h e d u lin g o c c u rs th ro u g h th e in te rc h a n g e o f e s , o f p re d e te rm in e d ty p e s , b e tw e e n p a irs o f c lie n t-s u p p lie r a g e n ts . T h e g e o f a m e s s a g e a lw a y s o c c u rs in th e c o n te x t o f a c o n v e r s a tio n b e tw e e n th e a n d th e re c e iv e r a g e n ts . A c o n v e rs a tio n h a s a c o n v e r s a tio n m o d e l, w h ic h s in fo rm a tio n a b o u t th e p re d e te rm in e d s e q u e n c e s o f th e ty p e s o f m e s s a g e s g e a b le a n d is d e fin e d th ro u g h a fin ite s ta te m a c h in e . A n in te r a c tio n p r o to c o l e d a s a s e t o f c o n v e rs a tio n m o d e ls . F o r th e in te ra c tio n o f c a p a c ity a g e n ts w e th e M a n a g e r -M a n a g e r in te ra c tio n p ro to c o l, re p re s e n te d in F ig . 2 .

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r ej ection - r e j e c t i o n o f a p re v io u sly re c e iv e d p ro d u c t re q u e s t, s e n t b y th e s u p p lie r to th e c lie n t.

c ) M e ssa g e ty p e s a n d d e sc rip tio n .

a ccep ta n ce - a c c e p t a n c e o f a p re v io u s ly re c e iv e d p ro d u c t re q u e s t, s e n t b y th e s u p p lie r to th e c lie n t.

3

r e- r eq u es t re -s c h e d u lin g re q u e s t, se n t b y th e su p p lie r (c lie n t) to th e c lie n t (su p p lie r), a sk in g to r e - s c h e d u l e a p re v io u sly a c c e p te d p ro d u c t re q u e st to a g iv e n d u e -d a te .

b ) R e q u e st-to -S u p p lie r c o n v e rsa tio n m o d e l.

/

e- a cc ep ta n ce

/r

4 5

e- r ej ection

e- r eq u es t

e- r ej ection

2

5

/

r e- r ej ection

1

r e- r eq u e s t

/r

/r

4

r e- r eq u es t

a ) R e q u e st-fro m -C lie n t c o n v e rsa tio n m o d e l.

e- a ccep ta n ce

r e- a cc ep ta n ce

/

/

a ccep ta n ce

/

3

eq u es t

r e- r ej ection

2

e- r eq u es t

/

n cela tion

ca n cela tion

/r

ccep ta n ce

/r 1

s a tis f a ction

/ca

/

ca n cela tion

/a

r eq u es t /

/

ce r e- a ccep ta n

/r

223

tr a n s itio n s (m e s s a g e ty p e s ): r eceive / s en d

6

r e- r ej ection - r e j e c t i o n o f a p re v io u s ly re c e iv e d re -s c h e d u lin g re q u e s t, se n t b y th e re c e iv e r to th e se n d e r o f th e re -s c h e d u lin g re q u e s t.

ca n cela tion - s i g n a l s g i v i n g u p a p re v io u s ly a c c e p te d p ro d u c t re q u e s t, s e n t b y th e s u p p lie r (c lie n t) to th e c lie n t (s u p p lie r).

r e- a ccep ta n ce - a c c e p t a n c e o f a p re v io u s ly re c e iv e d re -s c h e d u lin g re q u e s t, se n t b y th e re c e iv e r to th e se n d e r o f th e re -s c h e d u lin g re q u e s t.

s a tis f a ction - s i g n a l s d e l i v e r y o f a p re v io u s ly a c c e p te d p ro d u c t re q u e s t, s e n t b y s u p p lie r to c lie n t a t th e tim e o f th e d u e -d a te o f th e p ro d u c t re q u e s t.

F ig .2 .C o n v e rs a tio n m o d e ls a n d m e s s a g e s fo r th e M a n a g e r -M a n a g e r in te ra c tio n p ro to c o l. T h e p ro to c o l h a s R e q u e s t-to -S u p p lie r , 2 -b , a n d to b e u s e d a g e n t, re s p e c tiv e ly . F

4

th d e b y ig

e sc a . 2

a s s o c ia te d rib e d a s fin n a g e n t w h -c d e s c rib e

c o ite e n s th

n v e rs a tio s ta te m a p la y in g e ty p e s o

n m o c h in e th e ro f m e s

d e ls R e q u e s t-fr o m d ia g ra m s in F ig . le s o f a s u p p lie r sa g e s e x c h a n g e a b

-C lie n t a n d 2 -a a n d F ig . a n d a c lie n t le .

A Coop er a ti v e Mu lti -a g en t S ched u li n g Ap p r oa ch

C l a s s i c a l l y , s c h e d u l i n g i s c o n s i d e r e d a d i f f i c u l t p r o b l e m [7 ]. I n g e n e r a l , s o l u t i o n s f o r a s c h e d u lin g p ro b le m h a v e to b e s e a rc h e d fo r, a n d th e s e a rc h s p a c e c a n b e v e ry la rg e . A d d itio n a lly , fo r a m u lti-a g e n t s c h e d u lin g p ro b le m , a p a rt o f th e e ffo rt is in v e s te d in c o o rd in a tio n o f th e a g e n ts in v o lv e d w h ic h , in o u r c a s e , m e a n s s h a rin g in fo rm a tio n th ro u g h m e s s a g e e x c h a n g e . M e s s a g e e x c h a n g e is c o n s id e re d c o s tly s o , m e th o d s o f p ru n in g th e s e a rc h s p a c e fo r fin d in g a t le a s t a firs t fe a s ib le s o lu tio n w ith m in im a l c o o rd in a tio n e ffo rts a re c o n s id e re d s a tis fa c to ry . T h e a p p ro a c h w e p ro p o s e in th is a rtic le , fo r th e c o o p e ra tiv e in d iv id u a l (a g e n t) s c h e d u lin g b e h a v io r, is a m in im a l a p p r o a c h , th a t is , a n a g e n t v ie w in g a s c h e d u lin g p r o b l e m s o l u t i o n a s f e a s i b l e w o n 't d o a n y t h i n g r e s p e c t i n g t o t h e s c h e d u l i n g p r o b l e m . A f i r s t v e r s i o n o f t h i s a p p r o a c h a p p e a r e d i n [2 0 ]; i n [2 1 ] w e p r e s e n t e d a r e f i n e d a p p ro a c h o n ly fo r p ro c e s s o r, i.e ., p ro d u c tio n o r tra n s p o rta tio n , a g e n ts ; in th e p re s e n t a rtic le w e c o v e r a ls o s to re a g e n ts a n d , a d d itio n a lly , in c lu d e th e re s p e c tiv e m in im a l re -s c h e d u lin g a c tio n s fo r p ro c e s s o r a n d s to re a g e n t c a s e s . C o n s id e r tw o s e ts o f s o lu tio n s fo r a s c h e d u lin g p ro b le m : th e s e t o f tim e -fe a s ib le s o lu tio n s , w h ic h re s p e c t a ll te m p o ra l c o n s tra in ts , a n d th e s e t o f r e s o u r c e -fe a s ib le s o lu tio n s , w h ic h re s p e c t a ll c a p a c ity c o n s tra in ts . A fe a s ib le s o lu tio n is o n e th a t is

224

Joaquim Reis and Nuno Mamede

b o th tim e -fe a s ib le a n d re s o u rc e -fe a s ib le s o , th e s e t o f fe a s ib le s o lu tio n s is th e in te rs e c tio n o f th o s e tw o s e ts . A p ro b le m is te m p o r a lly o v e r -c o n s tr a in e d if th e s e t o f tim e -fe a s ib le s o lu tio n s is e m p ty , a n d is r e s o u r c e o v e r -c o n s tr a in e d if th e s e t o f re s o u rc e -fe a s ib le s o lu tio n s is e m p ty . If a p ro b le m h a s b o th n o n -e m p ty tim e -fe a s ib le a n d re s o u rc e -fe a s ib le s o lu tio n s e ts , a n d th e ir in te rs e c tio n is n o n -e m p ty , th e n th e p ro b le m h a s fe a s ib le s o lu tio n s . W e p ro p o s e a n a p p ro a c h u s in g th e fo llo w in g th re e s te p p ro c e d u re , fo r e a c h in d iv id u a l c a p a c ity a g e n t: S te p 1 . A c c e p ta n c e a n d in itia l s o lu tio n - D e te c t if th e p ro b le m is te m p o ra lly o v e r-c o n s tra in e d , a n d if it is n ’t, e s ta b lis h a n in itia l s o lu tio n , a n d p ro c e e d in th e n e x t s te p ; if it is , te rm in a te th e p ro c e d u re b y re je c tin g th e p ro b le m , b e c a u s e it h a s n o fe a s ib le s o lu tio n ; S te p 2 . R e -s c h e d u le to fin d a tim e -fe a s ib le s o lu tio n - If th e e s ta b lis h e d s o lu tio n is tim e -fe a s ib le , p ro c e e d in th e n e x t s te p ; if it is n ’t, re -s c h e d u le to re m o v e a ll te m p o ra l c o n flic ts ; S te p 3 . R e -s c h e d u le to fin d a fe a s ib le s o lu tio n - F o r a re s o u rc e -fe a s ib le s o lu tio n , te rm in a te th e p ro c e d u re ; o th e rw is e , try to re -s c h e d u le to re m o v e a ll c a p a c ity c o n flic ts w ith o u t c re a tin g te m p o ra l c o n flic ts , re s o rtin g to c a n c e lla tio n , w ith ta s k u n -s c h e d u lin g , a s a la s t c h o ic e , if n e c e s s a ry . A s s o m e a p p ro a c h e s in th e lite ra tu re , th is p ro c e d u re s ta rts b y e s ta b lis h in g o n e in itia l, p o s s ib ly n o n -fe a s ib le , s o lu tio n w h ic h is th e n re p a ire d in o rd e r to re m o v e c o n f l i c t s ; s e e , f o r i n s t a n c e , [1 2 ]. S t e p s 1 a n d 2 o f t h e p r o c e d u r e a r e o r i e n t e d f o r a te m p o ra l s c h e d u lin g p e rs p e c tiv e a n d c o n c e rn o n ly to a s in g le s c h e d u lin g p ro b le m o f th e a g e n t. S te p 3 is o rie n te d fo r a re s o u rc e s c h e d u lin g p e rs p e c tiv e a n d c a n in v o lv e a ll s c h e d u lin g p ro b le m s o f th e a g e n t a t s te p 3 , a s a ll ta s k s o f th e a g e n t c o m p e te fo r th e a g e n t re s o u rc e c a p a c ity .

5

S tep 1 : S ched u li n g a n In i ti a l S olu ti on W e n o w c a n lo c a c o n trib u F o r a

s h o w , th ro u g lly re c o g n iz e te to e s ta b lis h p ro c e sso r a g

p ro c e s s o r ta s k

2 7i ,1 4

h e x a m p le a n o n te m a n in itia l e n t, s u p p o

s fo r p r p o ra lly s o lu tio n se a n a

o c e s s o r a n d s to re c la s s a g e n ts , h o w a n a g e n t o v e r-c o n s tra in e d p ro b le m a n d , in th a t c a s e , (s te p 1 ). g e n t g 7 h a s a s c h e d u lin g p ro b le m w ith th e

o f n e tw o rk jo b in F ig . 1 . In F ig . 3 -a , a p o s s ib le s itu a tio n fo r

th is ta s k (w h ic h a ls o re p re s e n ts a fe a s ib le s o lu tio n fo r th e p ro b le m ) is re p re s e n te d o n a tim e lin e . A s g 7 h a s tw o s u p p lie rs fo r th e ta s k , tw o re q u e s ts to tw o s u p p lie rs a re

G 7i ,8,1 4 a n d G 7i ,9,1 4 , te d b y Ka n d +s y m b o

G 4i ,7,1 4

sh o w n ,

b e s id e s th e re q u e s t fro m

(d e fi s la s la th e

ls ) a n d te m p o ra l s la c k s a re s h o w n in F ig a n d FM d e n o t e , r e s p e c t i v e l y , t h e i n t e r n la c k s , e x te r n a l d o w n s tr e a m s la c k , e x te n d u p s tr e a m s la c k s . F o r e a c h k in d o f u r (s la c k s a re re p re s e n te d b y a rro w s ). B y d

n o

j , fi c k , in c k s, d re is o

m , te r o w n e

FE J , n a l u n s tr e a p e r e a

FE M, FJ p s tr e a m s m s la c k a c h s u p p lie

th e c lie n t,

. In te rv a ls

. 3 -a . S y m b a l d o w n s tr e r n a l u p s tr e p s tre a m s la e fin itio n :

o ls a m a m c k s

Scheduling, Re-scheduling and Communication 7

FJ

7 ,j FM i ,1 4

th e a g e n e g d u e +' s th e

In te rn ta s k n ts o a tiv e -d a te is a n ta s k

7

= FE J

i ,1 4

i ,1 4

a l s la c k a n d m a f th e n e in te r n a s a n d th in te rv a (1 0 a n d

G

re q u e sts to su p p lie rs

7

,

= TIME (G i

7

fi j

i ,1 4

4 ,7 ,1 4

i ,1 4

)- E NDTIME (2 i 7

+ fi m

G

7 ,9 i ,1 4

7 ,j i ,1 4

,

= S TA RTTIME (2 i

)

,1 4

)- TIME (G ) (j = 8 ,9 ) s a re in s e rte d lo c a lly , b y th e in itia tiv e o f th e a g e n t, w h e n s c h e d u lin g k in g re q u e s ts to s u p p lie rs ; e x te rn a l s la c k s a re im p o s e d b y th e o th e r tw o rk . It is a s s u m e d th a t, in a n y c a s e , th e a g e n t w ill m a in ta in n o n l s l a c k s . E a c h o f t h e K' s i s a n i n t e r v a l b e t w e e n o n e o f t h e s u p p l i e r e c lie n t d u e -d a te (1 3 a n d 1 9 , a n d 1 2 a n d 1 9 , in F ig . 3 -a ); e a c h o f th e l b e tw e e n o n e o f th e e a rlie s t s ta rt tim e s a n d th e la te s t fin is h tim e fo r 2 1 , a n d 1 1 a n d 2 1 , in F ig . 3 -a ). E a c h o f th e la tte r p a irs o f te m p o ra l

7 ,j M i ,1 4

= FE

+ fi j

225

7 ,j i ,1 4

fi m

7

,1 4

G

7 i ,1 4

7 ,8 i ,1 4

7 ,j i ,1 4

4 ,7 i ,1 4

re q u e st fro m c lie n t ti m e

1 0

1 1

1 2

1 3

1 5

fi m 7i ,8,1 4 FM7i ,8,1 4 fi m 7i ,9,1 4 FMi7 ,1,9 4

FE Mi7 ,1,8 4

FE M7i

1 4

,9 ,1 4

1 8

1 9

7 i ,1 4

2 0

2 1

FE J i 7 ,1 FJ i 7 ,1 4 4

K

K

+

1 7

fi j

7 ,8 i ,1 4

7 ,9 i ,1 4

7 ,8 i ,1 4

1 6

+

7 ,9 i ,1 4

a ) P ro c e sso r sc h e d u lin g p ro b le m .

G

re q u e st to su p p lie r

1 ,4 i ,1 4

G

1 4 ,1 i ,1 4

1 i ,1 4

re q u e st fro m c lie n t ti m e

2 0

2 1

2 2

2 3

FE Mi

2 4

1 ,1 4

2 5

fi m FMi

2 6

2 7

1 i ,1 4

2 8

fi j

1 ,1 4

K

2 9

1 i ,1 4

3 0

3 1

FE J i 1 ,1 FJ i 1 ,1 4 4

1 i ,1 4

b ) S to re sc h e d u lin g p ro b le m .

+

1 i ,1 4

F ig .3 .S c h e d u lin g p ro b le m

p a ra m e te rs : a ) fo r p ro c e s s o r a g e n t g 7, a n d b ) fo r s to re a g e n t g (fo r th e v a lu e s in th e tim e lin e s o f th e s e tw o c a s e s n o re la tio n s h ip is in te n d e d ).

1

p o in ts a re h a rd te m p o ra l c o n s tra in ts fo r o n e o f th e fo rm e r p a irs o f d u e -d a te s . A ls o , th e te m p o ra l e n d p o in ts o f th e m o s t re s tric tiv e +in te rv a l (1 1 a n d 2 1 in F ig . 3 -a ) a re 7

h a r d t e m p o r a l c o n s t r a i n t s f o r t h e t a s k ; l e t u s d e n o t e t h e s e b y RD i fo r th e u p s tre a m

a n d d o w n s tre a m

p o in t, re s p e c tiv e ly .

7

,1 4

a n d DD i

,1 4

,

226

Joaquim Reis and Nuno Mamede

It is e a s y to s e e th a t, in o ta s k m u s t b e c o n ta in e d in th c o n ta in e d in th e c o rre s p o n te m p o ra l s la c k c a n b e n e g in te rv a l is le s s th a n th e ta s a n d th e a g e n t c a n re je c t it. W e p ro p o s e th a t p ro d u c t re q u e s t in fo rm a tio n , c a r r y m e s s a g e s fro m s u p p lie rs w

DD i

,1 4

7

w o u l d t h e n c a l c u l a t e t h e DD i

= TIME (G 7 ,j ,1 4

w h e re :

RD i

4 ,7 i ,1 4

s ib le , th e in te rv a l o f th e e a c h Kin te rv a l m u s t b e l. F o r th is to h o ld , n o th e m o s t re s tric tiv e + o ra lly o v e r-c o n s tra in e d ,

re q u e s t m e s s a g e s fro m th e c lie n t, a d d itio n a lly to p ro d u c t t h e v a l u e o f t h e FE J s l a c k ; a l s o , r e q u e s t a c c e p t a n c e i l l c a r r y t h e v a l u e o f t h e r e s p e c t i v e FE M s l a c k . I n o u r 7

e x a m p le , a g e n t g 7

rd e r fo r a s o lu tio n to b e tim e -fe a e m o s t re s tric te d Kin te rv a l, a n d d in g (s a m e s u p p lie r) + in te rv a a tiv e . A ls o , if th e d u ra tio n o f k d u ra tio n , th e p ro b le m is te m p

7

)+ FE J

7 ,j ,1 4

a n d RD i 7

a n d

i ,1 4

= TIME (G i

7

,1 4

RD i 7 ,j ,1 4

)- FE M i

G

W h e n th e a g e n t re c e iv e s re q u e s t

4 ,7 i ,1 4

fro m

,1 4

,1 4

v a lu e s b y : 7 ,j ,1 4

= MA X (RD i j = 8 ,9

)

(j = 8 ,9 ) th e c lie n t, it w ill, g u a ra n te e in g

n o n - n e g a t i v e v a l u e s o f fi j a n d fi m f o r t h e t a s k t o b e s c h e d u l e d , m a k e r e q u e s t s

G 7i

,8 ,1 4

FJ

7 i ,1 4

G 7i

a n d + fi m

,9 ,1 4

7 ,j i ,1 4

to

s u p p lie rs , p a s s in g

th e m

a ls o

th e

(s u p p lie r

FE J )

v a lu e

( f o r j = 8 ,9 ) . W h e n t h e a g e n t r e c e i v e s a l l t h e r e q u e s t a c c e p t a n c e s

fro m th e s u p p lie rs , v e rifie s firs t if th e p ro b le m is te m p o ra lly o v e r-c o n s tra in e d , b y 7 7 7 t e s t i n g i f DD i ,1 4 - RD i ,1 4 < DU RA TION(2 i ,1 4 ). I f t h i s i s t r u e t h e p r o b l e m m u s t b e re je c te d . O th e rw is e , th e a g e n t w ill s e n d th e a c c e p ta n c e m e s s a g e to th e c lie n t, 7 7 p a s s in g it a ls o th e (c lie n t FE M) v a lu e FM i ,1 4 + fi j i ,1 4 , w h e re 7

FM i

= S TA RTIME (2 i 7

,1 4

o v e r-c o n s tra in e d
, w h ic h re p re s e n ts

th e a g e n t lo c a l p e rs p e c tiv e o f th e s c h e d u lin g p ro b le m , a n d a ls o in c lu d e s (a p a rt o f) th e in itia l s o lu tio n . F o r a s to re a g e n t, s u p p o s e a n a g e n t g 1 h a s a s c h e d u lin g p ro b le m w ith th e s to re ta s k

2 1i

,1 4

(w h ic h a ls o tim e lin e . T h in th e fo llo w in te rn a l s la c in te rv a l, a n d g re a te r th a n

o f n e tw o rk jo b in F ig . 1 . In F ig . 3 -b , a p o s s ib le s itu a tio n fo r th is ta s k

re p re s e n ts a fe a s ib le s o lu tio n fo r th e p r e c a s e is s im ila r to th e o n e fo r a g e n t g 7 , w in g . T h e re is o n ly o n e re q u e s t to a s u p p lie k s a re d e fin e d d iffe re n tly : th e ta s k in te rv a p a rt o f th e ta s k d u ra tio n is c o n s id e re d a s in 1 , w h ic h is th e m in im u m a s s u m in g th e 1 1 1 r e l a t i o n s h i p fi j i , 1 4 + fi m i , 1 4 = DU RA TION(2 i , 1 4 )- 1

o b le m ) is re p re s e n te d o n a ith th e e x c e p tio n s d e s c rib e d r, a s g 1 is a s to re a g e n t. T h e l is e q u a l to th e (u n iq u e ) K te rn a l s la c k (if its d u ra tio n is ta s k m u s t e x is t), w ith th e a lw a y s

h o ld in g . F ig . 3 -b

s u g g e s t s s y m m e t r i c a l d e f i n i t i o n s f o r fi j a n d fi m s l a c k s , w i t h t h e m i n i m u m d u ra tio n in te rv a l " c e n te re d " in th e Kin te rv a l b u t, fo r p u rp o s e s o f te m p o ra l c o n s tra in t

Scheduling, Re-scheduling and Communication

227

v io la tio n id e n tific a tio n (s e e n e x t s e c tio n ), th e fo llo w in g d e fin itio n s m u s t b e u s e d . F o r t h e d o w n s t r e a m s i d e v i o l a t i o n s ( c a s e s 1 a n d 3 , i n t h e n e x t s e c t i o n ) , fi j a n d fi m a r e d e f i n e d b y ( t h e m i n i m u m d u r a t i o n i n t e r v a l i s s h i f t e d t o t h e l e f t ) : 1

fi j

i ,1 4

= DU RA TION(

1 i ,1 4

)- 1 , a n d

1

fi m

= 0

i ,1 4

F o r t h e u p s t r e a m s i d e v i o l a t i o n s ( c a s e s 2 a n d 4 , i n t h e n e x t s e c t i o n ) , fi j fi m a r e d e f i n e d b y ( t h e m i n i m u m d u r a t i o n i n t e r v a l i s s h i f t e d t o t h e r i g h t ) : fi j

1 i ,1 4

= 0 ,

T h e p ro b le m o f FE J

1 i ,1 4

a n d

fi m

1

= DU RA TION(

i ,1 4 7

i s t e m p o r a l l y o v e r - c o n s t r a i n e d i f DD i

+ DU RA TION(

1 i ,1 4

1

a n d FE M i

)- 1

,1 4

7

,1 4

- RD i


.

S tep 2 : R e-s ched u li n g for a T i m e-F ea s i ble S olu ti on

In th is s e c tio n w e s h o w h o w , s ta rtin g fro m a n in itia l s o lu tio n w ith te m p o ra l c o n flic ts , a g e n ts g 7 a n d g 1 c a n lo c a lly c o n trib u te to o b ta in a tim e -fe a s ib le s o lu tio n (s te p 2 ). F o r th e lo c a l s itu a tio n s re p re s e n te d in F ig . 3 -a a n d F ig . 3 -b , a ll s la c k s a re p o s itiv e s o , th e s o lu tio n is s e e n a s te m p o ra lly -fe a s ib le (b y a g e n t g 7 , a n d a g e n t g 1 , re s p e c tiv e ly ). In th e s e c a s e s , a n a g e n t w ill d o n o th in g , u n le s s it re c e iv e s a n y re -s c h e d u lin g re q u e s t, w h ic h it c o u ld a c c e p t p ro v id e d n o n -n e g a tiv e in te rn a l s la c k s c a n b e m a in ta in e d , fo r a p ro c e s s o r a g e n t, o r a ta s k w ith d u ra tio n g re a te r th a n 0 is p o s s ib le , in th e c a s e o f a s to re a g e n t. O th e rw is e , fo u r k in d s o f p o s s ib le lo c a l s itu a tio n s c a n o c c u r w h e re th e a g e n t its e lf m u s t ta k e th e in itia tiv e o f s o m e re -s c h e d u lin g a c tio n s . T h e s itu a tio n s re fe rre d a re d e s c rib e d b y th e re -s c h e d u lin g c a s e s 1 , 2 , 3 a n d 4 , fo r w h ic h w e s h o w e x a m p le s in F ig . 4 fo r p ro c e s s o r a g e n ts (fo r a g e n t g 7 ), a n d in F ig . 5 fo r s to re a g e n ts (fo r a g e n t g 1 ). E a c h fig u re re p re s e n ts , fo r e a c h c a s e : a ) th e s itu a tio n d e te c te d , a n d b ) th e s itu a tio n a fte r a m in im a l re -s c h e d u lin g a c tio n . N o re la tio n s h ip is in te n d e d a m o n g tim e lin e v a lu e s o f th e p ro c e s s o r a n d th e s to re a g e n t c a s e s . In th e te x t fo llo w in g , u p p e r in d e x e s a re o m itte d in s la c k s y m b o ls in o rd e r to c o v e r b o th , p ro c e s s o r a n d s to re , a g e n t c a s e s . C a s e s 1 a n d 2 m u s t b e c o n s id e r e d fir s t, b y th e a g e n t. C a s e 1 o c c u r s i f FJ i , 1 4 < 0 a n d FE J i , 1 4 < 0 ( t h e t a s k a n d t h e c l i e n t r e q u e s t v i o l a t e th e h a rd te m p o ra l c o n s tra in t d o w n s tre a m , 1 7 in F ig . 4 -1 -a , a n d 2 0 in F ig . 5 -1 -a ). T h e d e te c tio n o f c a s e 1 m u s t b e fo llo w e d b y th e a p p ro p ria te ta s k re -s c h e d u lin g a n d c lie n t

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3 m u s t b e fo llo w e d b y th e a p p ro p ria te c lie n t re q u e s t re -s c h e d u lin g to a n e a rlie r tim e (re s u ltin g in th e s itu a tio n s h o w n in F ig . 4 -3 -b , a n d F ig . 5 -3 -b ). C a s e 4 o c c u r s i f , f o r s o m e s u p p l i e r , FE M i , 1 4 < 0 ( s o m e r e q u e s t s t o s u p p l i e r s v io la te h a T h e d e te c o ffe n d in g 4 -4 -b , a n d

rd te m p o tio n o f c re q u e s ts F ig . 5 -4

ra l c o n s tra in ts u p s tre a m , 1 3 in F ig . 4 -4 -a , a n d 2 3 in F ig . 5 -4 -a ). a s e 4 m u s t b e fo llo w e d b y th e a p p ro p ria te re -s c h e d u lin g o f th e to s u p p lie rs to la te r tim e s (re s u ltin g in th e s itu a tio n s h o w n in F ig . -b ).

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Joaquim Reis and Nuno Mamede

Con clu s i on a n d F u tu r e W or k W e d e s c rib e d a m u lti-a g e n t d y n a m ic s c h e d u lin g e n v iro n m e n t in v o lv in g c o m m u n ic a tio n a n d c o o p e ra tio n , a n d a n a p p ro a c h fo r m u lti-a g e n t c o o p e ra tiv e s c h e d u lin g b a s e d o n a th re e s te p p ro c e d u re fo r in d iv id u a l a g e n ts . S te p 1 a llo w s a g e n ts to d e te c t lo c a lly if th e p ro b le m is te m p o ra lly o v e r-c o n s tra in e d a n d , in th e c a s e i t i s n 't , s c h e d u l e a n i n i t i a l , p o s s i b l y n o n t i m e - f e a s i b l e , s o l u t i o n . B y l o c a l l y e x c h a n g in g s p e c ific te m p o ra l s la c k v a lu e s , a g e n ts a re a b le to lo c a lly p e rc e iv e th e h a rd g lo b a l te m p o ra l c o n s tra in ts o f a p ro b le m , a n d ru le o u t n o n tim e -fe a s ib le s o lu tio n s in th e s u b s e q u e n t s te p s . E a c h o f th e s la c k v a lu e s e x c h a n g e d in s te p 1 c o rre s p o n d s , fo r a p a rtic u la r a g e n t, to a s u m o f s la c k s , d o w n s tre a m a n d u p s tre a m th e a g e n t n e tw o rk , a n d s o , th e y c a n n o t b e c o n s id e re d p riv a te in fo rm a tio n o f a n y a g e n t in p a rtic u la r. In s te p 2 , if n e c e s s a ry , a g e n ts re p a ir th e in itia l s o lu tio n to o b ta in a tim e -fe a s ib le o n e . T h e p ro c e d u re is v e ry g e n e ra l w ith re s p e c t to its s te p 3 . T h is s te p c a n b e re fin e d to a c c o m m o d a te a d d itio n a l im p ro v e d c o o rd in a tio n m e c h a n is m s fo r im p le m e n tin g c e r t a i n s e a r c h s t r a t e g i e s , b a s e d o n c a p a c i t y / r e s o u r c e c o n s t r a i n e d n e s s ( e . g . , s e e [2 3 ] o r [2 2 ]) , l e a d i n g t h e a g e n t s o n a f a s t c o n v e r g e n c e t o s p e c i f i c f e a s i b l e s o l u t i o n s . F o r in s ta n c e , fe a s ib le s o lu tio n s s a tis fy in g s o m e s c h e d u lin g p re fe re n c e s o r o p tim iz in g s o m e c rite ria , e ith e r fro m a n in d iv id u a l a g e n t p e rs p e c tiv e , o r fro m a g lo b a l o n e , o r b o th . T h is is a s u b je c t fo r o u r fu tu re w o rk .

R efer en ces 1 . 2 . 3 .

4 .

5 . 6 . 7 . 8 .

9 .

A rn o ld , J ö rg , e t a l, P r o d u c tio n P la n n in g a n d C o n tr o l w ith in S u p p ly C h a in s , E S P R IT p ro je c t 2 0 5 4 4 , X -C IT T IC , 1 9 9 7 . B la z e w ic z , J .; E c k e r, K .H .; S c h m id t, G .; W e g la rz , J ., S c h e d u lin g in C o m p u te r a n d M a n u fa c tu r in g S y s te m s , S p rin g e r V e rla g , 1 9 9 4 C a m a r in h a - M a to s , L u ís M .; A fs a r m a n e s h , H a m id e h , T h e V ir tu a l E n te r p r is e C o n c e p t, in I n f r a s tr u c tu re s f o r V ir tu a l E n te r p r is e s , C a m a r in h a - M a to s , L .M . a n d A fs a r m a n e s h , H . ( e d s .) , K lu w e r A c a d e m ic P u b lis h e r s , D o r d r e c h t, T h e N e th e r la n d s , 1 9 9 9 , 3 - 1 4 . C a m a r in h a - M a to s , L u ís M .; A fs a r m a n e s h , H a m id e h , I n fr a s tr u c tu r e s fo r V ir tu a l E n te r p r is e s , N e tw o r k in g In d u s tr ia l E n te r p r is e s , L u ís M . C a m a rin h a -M a to s , H a m id e h A f s a r m a n e s h ( e d s .) , K lu w e r A c a d e m ic P u b lis h e r s , D o r d r e c h t, T h e N e th e r la n d s , 1 9 9 9 . D o r n , J .; F r o e s c h e l, K ., S c h e d u lin g o f P r o d u c tio n P r o c e s s e s , D o r n , J .; F r o e s c h e l, K . ( e d s .) , E lis H o r w o o d , L d ., 1 9 9 3 . F o x , M a r k S ., e t a l, T h e I n te g r a te d S u p p ly C h a in M a n a g e m e n t S y s te m , D e p a r tm e n t o f In d u s tria l E n g in e e rin g , U n iv e rs ity o f T o ro n to , C a n a d a , 1 9 9 3 . G a re y , M .R .; J o h n s o n , D .S ., C o m p u te r s a n d In tr a c ta b ility : A G u id e to th e T h e o r y o f N P C o m p le te n e s s , W .H . F r e e m a n a n d C o ., N e w Y o r k , 1 9 7 9 . G ra v e s , S .C .; K a n , A .H .G . R in n o o y ; Z ip k in , P .H ., (e d s .), L o g is tic s o f P r o d u c tio n a n d In v e n to r y , H a n d b o o k s in O p e ra tio n s R e s e a rc h a n d M a n a g e m e n t S c ie n c e , V o lu m e 4 , N o rth -H o lla n d , A m s te rd a m , 1 9 9 3 . K a n , A .H .G . R in n o o y , M a c h in e S c h e d u lin g P r o b le m s , M a rtin u s N ijh o ff, T h e H a g u e , 1 9 7 6 .

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1 0 . K e rr, R o g e r; S z e lk e , E liz a b e th (e d s .), A r tific ia l I n te llig e n c e in R e a c tiv e S c h e d u lin g , C h a p m a n & H a ll, 1 9 9 5 . 1 1 . K je n s ta d , D a g , C o o r d in a te d S u p p ly C h a in S c h e d u lin g , P h D . T h e s is , N o rw e g ia n U n iv e rs ity o f S c ie n c e a n d T e c h n o lo g y , T ro n d h e im , N o rw a y , 1 9 9 8 . 1 2 . M in to n , S te v e n , e t a l, M in im iz in g C o n flic ts : a H e u r is tic R e p a ir M e th o d fo r C o n s tr a in t S a tis fa c tio n a n d S c h e d u lin g P r o b le m s , A rtific ia l In te llig e n c e 5 8 , 1 9 9 2 , 1 6 1 -2 0 5 . 1 3 . O 'H a r e , G . M . P . ; J e n n i n g s , N . R . , F o u n d a t i o n s o f D i s t r i b u t e d A r t i f i c i a l I n t e l l i g e n c e , J o h n W ile y & S o n s , I n c ., 1 9 9 6 , N e w Y o r k , U S A . 1 4 . O 'N e i l l , H . ; S a c k e t t , P . , T h e E x t e n d e d E n t e r p r i s e R e f e r e n c e F r a m e w o r k , B a l a n c e d A u to m a tio n S y s te m s II, C a m a rin h a -M a to s , L .M . a n d A fs a rm a n e s h , H . (e d s .), 1 9 9 6 , C h a p m a n & H a ll, L o n d o n , U K , 4 0 1 -4 1 2 1 5 . R a b e lo , R ic a rd o J .; C a m a r in h a - M a to s , L u is M .; A fs a r m a n e s h , H a m id e h , M u ltia g e n t P e r s p e c t i v e s t o A g i l e S c h e d u l i n g , B a s y s '9 8 I n t e r n a t i o n a l C o n f e r e n c e o n B a l a n c e d A u to m a tio n S y s te m s , P ra g u e , C z e c h R e p u b lic , 1 9 9 8 . 1 6 . R e i s , J . ; M a m e d e , N . ; O 'N e i l l , H . , O n t o l o g i a p a r a u m M o d e l o d e P l a n e a m e n t o e C o n t r o l o n a E m p r e s a E s t e n d i d a , P r o c e e d i n g s o f t h e I B E R A M I A '9 8 , L i s b o n , P o r t u g a l , 1 9 9 8 , H e ld e r C o e lh o ( e d .) , E d iç õ e s C o lib r i, L is b o n , P o r tu g a l, 4 3 - 5 4 ( in p o r tu g u e s e ) . 1 7 . R e is , J .; M a m e d e , N .; O ’ N e ill, H ., A g e n t C o m m u n ic a tio n fo r S c h e d u lin g in th e E x te n d e d T C 5 W G 5 .3 /P R O D N E T C o n fe re n c e o n E n te r p r is e , P ro c e e d in g s o f th e IF IP In fra s tru c tu re s fo r V irtu a l E n te rp ris e s , P o rto , P o rtu g a l, 1 9 9 9 , C a m a rin h a -M a to s , L .M ., A fs a rm a n e s h H . (e d s .), K lu w e r A c a d e m ic P u b lis h e rs , D o rd re c h t, T h e N e th e rla n d s , 1 9 9 9 , 3 5 3 -3 6 4 . 1 8 . R e is , J .; M a m e d e , N ., W h a t’ s in a N o d e , N o d e s a n d A g e n ts in L o g is tic N e tw o r k s , P ro c e e d in g s o f th e IC E IS ’9 9 , 1 s t In te rn a tio n a l C o n fe re n c e o n E n te rp ris e In fo rm a tio n S y s te m s , S e tú b a l, P o r tu g a l, 1 9 9 9 , F ilip e , J . a n d C o r d e ir o , J . ( e d s .) , 2 8 5 - 2 9 1 . 1 9 . R e is , J .; M a m e d e , N ., A n A g e n t A r c h ite c tu r e fo r M u lti A g e n t D y n a m ic S c h e d u lin g , P ro c e e d in g s o f th e IC E IS ’2 0 0 0 , 2 n d . In te rn a tio n a l C o n fe re n c e o n E n te rp ris e In fo rm a tio n S y s te m s , S ta f f o r d , U K , 2 0 0 0 , S h a r p , B ., C o r d e ir o , J . a n d F ilip e , J . ( e d s .) , 2 0 3 - 2 0 8 . 2 0 . R e is , J .; M a m e d e , N .; O ’ N e ill, H ., L o c a lly P e r c e iv in g H a r d G lo b a l C o n s tr a in ts in M u ltiA g e n t S c h e d u lin g , J o u rn a l o f In te llig e n t M a n u fa c tu rin g , V o l. 1 2 , N o . 2 , 2 0 0 1 , 2 2 7 -2 4 0 . 2 1 . R e is , J .; M a m e d e , N ., M u lti- A g e n t D y n a m ic S c h e d u lin g a n d R e - S c h e d u lin g w ith G lo b a l T e m p o r a l C o n s tr a in ts , P ro c e e d in g s o f th e IC E IS ’2 0 0 1 , 3 rd In te rn a tio n a l C o n fe re n c e o n E n te rp ris e In fo rm a tio n S y s te m s , S e tú b a l, P o rtu g a l, 2 0 0 1 , M ira n d a , P ., S h a rp , B ., P a k s ta s , A . a n d F ilip e , J ( e d s .) , V o l. I , 3 1 5 3 2 1 . 2 2 . S a d e h , N o rm a n , M ic r o -O p o r tu n is tic S c h e d u lin g : T h e M ic r o -B o s s F a c to r y S c h e d u le r , In te llig e n t S c h e d u lin g , M o rg a n K a u fm a n , 1 9 9 4 , C h a p te r 4 . 2 3 . S y c a ra , K a tia P .; R o th , S te v e n F .; S a d e h , N o rm a n ; F o x , M a rk S ., R e s o u r c e A llo c a tio n in D is tr ib u te d F a c to r y S c h e d u lin g , IE E E E x p e rt, F e b ru a ry , 1 9 9 1 , 2 9 -4 0 . 2 4 . W e is s , G e r h a rd ( e d .) , M u ltia g e n t S y s te m s , A M o d e r n A p p r o a c h to D is tr ib u te d A r tific ia l In te llig e n c e , T h e M IT P re s s , 1 9 9 9 . 2 5 . Z w e b e n , M o n te ; F o x , M a rk S ., I n te llig e n t S c h e d u lin g , M o rg a n K a u fm a n n P u b lis h e rs , I n c ., S a n F r a n c is c o , C a lif o r n ia , 1 9 9 4 .

E lectr on i c In s ti tu ti on s a s a F r a m ew or k for Ag en ts ’ N eg oti a ti on a n d Mu tu a l Com m i tm en t A n a P a u la R o c h a , E u g é n io O liv e ira L IA C C , F a c u lty o f E n g in e e rin g , U n iv e rs ity o f P o rto , R. Dr. Roberto Frias, 4 2 0 0 - 4 65 Porto, Portugal {arocha,eco}@fe.up.pt

A b s tra c t. E le c tro n ic tra n s a c tio n s a re o f in c re a s in g u s e d u e to its o p e n n e s s a n d c o n tin u o u s a v a ila b ility . T h e ra p id g ro w th o f in fo rm a tio n a n d c o m m u n ic a tio n te c h n o lo g ie s h a s h e lp e d th e e x p a n s io n o f th e s e e le c tro n ic tra n s a c tio n s , h o w e v e r, is s u e s re la te d to s e c u rity a n d tru s t a re y e t lim itin g its a c tio n s p a c e , m a in ly in w h a t c o n c e rn s b u s in e s s to b u s in e s s a c tiv ity . T h is p a p e r in tro d u c e s a n E le c tro n ic In s titu tio n fra m e w o rk to h e lp in e le c tro n ic tra n s a c tio n s m a n a g e m e n t m a k in g a v a ila b le n o rm s a n d ru le s a s w e ll a s m o n ito rin g b u s in e s s p a rtic ip a n ts ’ b e h a v io u r in s p e c ific e le c tro n ic b u s in e s s tra n s a c tio n s . V irtu a l O rg a n is a tio n (V O ) life c y c le h a s b e e n u s e d a s a c o m p le x s c e n a rio e n c o m p a s s in g e le c tro n ic tra n s a c tio n s a n d w h e re E le c tro n ic In s titu tio n s h e lp in b o th fo rm a tio n a n d o p e ra tio n p h a s e . A fle x ib le n e g o tia tio n p ro c e s s th a t in c lu d e s m u lti-a ttrib u te a n d le a rn in g c a p a b ilitie s a s w e ll a s d is trib u te d d e p e n d e n c ie s re s o lu tio n is h e re p ro p o s e d fo r V O fo rm a tio n . “ P h a s e d c o m m itm e n t” is a n o th e r c o n c e p t h e re in tro d u c e d fo r V O o p e ra tio n m o n ito rin g th ro u g h th e E le c tro n ic In s titu tio n .

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A n E le c tro n ic In s titu tio n is a fra m e w o rk fo r e n a b lin g , th ro u g h a c o m m u n ic a tio n n e tw o rk , a u to m a tic tra n s a c tio n s b e tw e e n p a rtie s a c c o rd in g to s e ts o f e x p lic it in s titu tio n a l n o rm s a n d ru le s . A n E le c tro n ic In s titu tio n h e lp s o n b o th p ro v id in g to o ls a n d s e rv ic e s fo r a n d o n s u p e rv is in g th e in te n d e d re la tio n s h ip s b e tw e e n th e p a rtie s . U s u a lly , p a rtie s e n g a g e d in e le c tro n ic tra n s a c tio n s a n d jo in t a c tio n s a re s o ftw a re a g e n ts m e d ia te d . W e th e re fo re b e lie v e th a t a n a p p ro p ria te E le c tro n ic In s titu tio n c a n b e im p le m e n te d a s a n a g e n t-b a s e d fra m e w o rk w h e re e x te rn a l a g e n ts c a n m e e t to g e th e r a c c o rd in g to a s e t o f e s ta b lis h e d a n d fu lly a g re e d m u tu a l c o n s tra in ts . A g o o d e x a m p le illu s tra tin g th e n e e d o f a n E le c tro n ic In s titu tio n c a n b e fo u n d in a s o ftw a re fra m e w o rk p ro v id in g th e a u to m a tic s e rv ic e s n e e d e d fo r h e lp in g o n th e V irtu a l O rg a n is a tio n s ’ life c y c le . A V irtu a l O rg a n is a tio n (V O ) is a n a g g re g a tio n o f a u to n o m o u s a n d in d e p e n d e n t o rg a n is a tio n s c o n n e c te d th ro u g h a n e tw o rk (p o s s ib ly a p u b lic n e tw o rk lik e In te rn e t) a n d b ro u g h t to g e th e r to d e liv e r a p ro d u c t o r s e rv ic e in re s p o n s e to a c u s to m e r n e e d . V irtu a l O rg a n is a tio n m a n a g e m e n t s h o u ld b e s u p p o rte d b y e ffic ie n t in fo rm a tio n a n d c o m m u n ic a tio n te c h n o lo g y th ro u g h its e n tire life c y c le .

P. Brazdil and A. Jorge (Eds.): EPIA 2001, LNAI 2258, pp. 232–245, 2001. c Springer-Verlag Berlin Heidelberg 2001 

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T o o ls fo r V irtu a l O rg a n is a tio n s fo rm a tio n p ro c e s s , th ro u g h th e u s e o f a n E le c tro n ic M a rk e t p ro v id in g e n h a n c e d p ro to c o ls fo r a p p ro p ria te n e g o tia tio n c a n e a s ily b e a c c o m m o d a te in to th e E le c tro n ic In s titu tio n a v a ila b le s e rv ic e s . In o u r a p p ro a c h , th e s e s e rv ic e s in c lu d e a u to m a tic c a p a b ilitie s fo r a d a p tiv e b id fo rm u la tio n , a c c e p tin g a q u a lita tiv e fe e d b a c k fo r th e s a k e o f k e e p in g th e in fo rm a tio n a s m u c h a s p o s s ib le p riv a te to e a c h o n e o f th e n e g o tia tin g a g e n ts , a s w e ll a s m u lti-is s u e b id e v a lu a tio n . C o n tra ry to o th e r a p p ro a c h e s [1 , 2 ] th a t u s e a -p rio ri fix e d v a lu e s fo r w e ig h tin g a ttrib u te s ’ v a lu e s in th e b id e v a lu a tio n fu n c tio n , w e h e re a d v o c a te w e ig h tin g th o s e v a lu e s , re fle c tin g th e d e v ia tio n fro m th e p re fe rre d v a lu e s , a c c o rd in g to th e re la tiv e im p o rta n c e o f th e a ttrib u te s . F u rth e r m o re , th e n e g o tia tio n p ro to c o l w e a re in tro d u c in g , h e re c a lle d Q -N e g o tia tio n , in c lu d e s th e c a p a b ility fo r A g e n ts th a t a re try in g to s u p p ly m u tu a lly c o n s tra in e d ite m s , to d e a l w ith th e re s p e c tiv e in te rd e p e n d e n c ie s w h ile k e e p in g th e ir s e lf-in te re s te d n e s s . D u rin g th e s e lf-in te re s te d a g e n ts Q -N e g o tia tio n p ro c e s s , th e y m a y h a v e to a g re e o n s u p p ly in g s e ts o f m u tu a lly c o n s tra in e d ite m s w h o s e v a lu e s , a lth o u g h n o t b e in g o p tim u m fo r e a c h o n e o f th e in d iv id u a l a g e n ts , c o rre s p o n d to a m in im a l jo in t d e c re m e n t o f th e a g e n ts ’ m a x im u m u tility . H o w e v e r, it w o u ld n o t b e fa ir th a t th is a g re e m e n t, in th e n a m e o f th e b e s t p o s s ib le jo in t u tility , b e n e fits o n e a g e n t m o re th a n th e o th e r. W e th e re fo re p ro p o s e th a t, in th e c a s e o f a g re e m e n ts b a s e d o n th e a g e n ts ’ jo in t u tility , th e a g e n ts c o n c e rn e d s h o u ld e q u a lly d is trib u te th e jo in t d e c re m e n t o f th e ir m a x im u m u tility . T h ro u g h th e c a lc u la tio n o f a p p ro p ria te c o m p e n s a tio n s , a g e n ts th a t h a v e th e m o s t b e n e fic ia l, k n o w th e y h a v e to tra n s fe r s o m e u tility to th o s e w h o h a v e th e le a s t. T h e o u tc o m e o f th e V irtu a l O rg a n is a tio n fo rm a tio n s ta g e is , fo r o u r p ro p o s e d E le c tro n ic In s titu tio n , a “ p h a s e d c o m m itm e n t” th ro u g h w h ic h d iffe re n t p a rtie s c o m m it th e m s e lv e s to s p e c ific fu tu re a c tio n s . W e in te n d to lin k c o m m itm e n ts , w h ic h a re th e re s u lt o f p re v io u s n e g o tia tio n d u rin g th e V irtu a l O rg a n is a tio n fo rm a tio n s ta g e , to th e n e x t s ta g e (V O o p e ra tio n ) th ro u g h a m o n ito rin g p ro c e s s . W e a ls o in tro d u c e th e c o n c e p ts o f b o th M e ta In s titu tio n a n d E le c tro n ic In s titu tio n w h ic h is th e re s p o n s ib le fo r m a k in g a v a ila b le fu n c tio n a litie s in c lu d in g a n a d a p tiv e m u lti-c rite ria b a s e d n e g o tia tio n p ro to c o l to g e th e r w ith fe a tu re s fo r s o lv in g a g e n ts m u tu a l d e p e n d e n c ie s . T h is p a p e r in c lu d e s , b e s id e s th e in tro d u c tio n , th re e m o re s e c tio n s . T h e n e x t s e c tio n in tro d u c e s th e c o n c e p ts o f E le c tro n ic In s titu tio n s a n d M e ta In s titu tio n s in th e c o n te x t o f V irtu a l O rg a n is a tio n s . A th ird s e c tio n d e ta ils o u r p ro p o s e d Q -N e g o tia tio n a lg o rith m u s e d in th e V O fo rm a tio n s ta g e . S e c tio n 4 d e s c rib e s p h a s e d c o m m itm e n ts in th e V O o p e ra tio n s ta g e a n d , fin a lly , s e c tio n 5 g iv e s s o m e c o n c lu s io n s a n d d ire c tio n s fo r fu tu re w o rk .

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Ana Paula Rocha and Eug´enio Oliveira

E lectr on i c In s ti tu ti on s a n d Meta In s ti tu ti on s

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It s e e m s in tu itiv e th a t w h e n a u to m a te d a g e n ts ’ in te ra c tio n s b e c o m e m o re s o p h is tic a te d a n d a g e n ts ’ a u to n o m y m o re e v id e n t, a p ro b le m re la te d w ith c o n fid e n c e , tru s t a n d h o n e s ty m a y a ris e . M o re o v e r, a g re e m e n ts lik e d e a ls m a d e b y d iffe re n t c o m p a n ie s o r th e ir d e le g a te s (a u to m a te d o r n o t) a lw a y s c la im fo r a c o m m o n a n d n o n a m b ig u o u s g ro u n d o f u n d e rs ta n d in g . W e n e e d to d e s ig n a fra m e w o rk , a c c e p te d b y a ll th e p a rtie s , to e n c o m p a s s a ll th e a u to m a tic a c tiv itie s th a t a re g o in g to ta k e p la c e b e tw e e n a g e n ts re p re s e n tin g d iffe re n t in d iv id u a l o r c o lle c tiv e e n titie s . A n E le c tro n ic In s titu tio n is a fra m e w o rk fo r e n a b lin g , th ro u g h a c o m m u n ic a tio n n e tw o rk , a u to m a tic tra n s a c tio n s b e tw e e n p a rtie s a c c o rd in g to s e ts o f e x p lic it in s titu tio n a l n o rm s a n d ru le s . A n E le c tro n ic In s titu tio n h e lp s o n b o th p ro v id in g to o ls a n d s e rv ic e s fo r a n d o n s u p e rv is in g th e in te n d e d re la tio n s h ip s b e tw e e n th e p a rtie s . H o w e v e r, e a c h E le c tro n ic In s titu tio n w ill b e , a t le a s t p a rtia lly , d e p e n d e n t o n th e s p e c ific a p p lic a tio n d o m a in o f b u s in e s s it h a s b e e n d e s ig n e d fo r. O u r p ro p o s a l s ta rts w ith th e d e fin itio n o f a M e ta -In s titu tio n , w h ic h h a s to b e in d e p e n d e n t o f th e a p p lic a tio n d o m a in . W e s e e a M e ta -In s titu tio n a s a s h e ll fo r g e n e ra tin g s p e c ific E le c tro n ic In s titu tio n s . A M e ta -In s titu tio n is a s e t o f E le c tro n ic fa c ilitie s to b e re q u e s te d a n d u s e d in o rd e r to h e lp o n th e c re a tio n o f s u ita b le E le c tro n ic In s titu tio n s a c c o rd in g to a s e t o f e s ta b lis h e d s o c ia l ru le s a n d n o rm s o f b e h a v io u r. T h o s e ru le s o f b e h a v io u r s h o u ld a p p ly to m a n y d iffe re n t k in d s o f (a u to m a tic ) e n titie s in te ra c tin g th ro u g h th e w e b . B e s id e s e n fo rc in g th o s e g e n e ra l ru le s in to th e s o c ia l in te ra c tio n s , a M e ta -In s titu tio n a ls o p ro v id e s to o ls fo r s o m e im p o rta n t s ta g e s o f th e in te ra c tio n p ro c e s s . T h e m a in g o a l o f a M e ta -In s titu tio n is , h o w e v e r, to b e a b le to m a k e a v a ila b le s u ita b le E le c tro n ic In s titu tio n s th a t w ill le a v e a ll a lo n g a p a rtic u la r b u s in e s s p ro c e s s in a s p e c ific a p p lic a tio n d o m a in . E le c tro n ic tra n s a c tio n s b e tw e e n d is trib u te d a n d a u to n o m o u s e n titie s a re b e c o m in g m o re a n d m o re s o ftw a re a g e n ts m e d ia te d . W e th e re fo re b e lie v e th a t a n a p p ro p ria te E le c tro n ic In s titu tio n c a n b e im p le m e n te d a s a n a g e n t-b a s e d fra m e w o rk w h e re e x te rn a l a g e n ts c a n m e e t to g e th e r a c c o rd in g to a s e t o f e s ta b lis h e d a n d fu lly a g re e d n o rm s , ru le s , a n d m u tu a l c o n s tra in ts .

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V i r tu a l Or g a n i s a ti on s a n d E lectr on i c In s ti tu ti on s

g o o d e x a m p le illu s tra tin g p ro v id in g th e a u to m a tic s e rv c y c le . T h is a g g re g a tio n o f a u to n w ill re d u c e c o m p le x ity – to d re q u ire c lo s e c o o rd in a tio n a

th e n e e d o f a n E le c tro n ic In s titu tio n (E I) c a n b e fo u n d in ic e s n e e d e d fo r h e lp in g o n th e V irtu a l O rg a n is a tio n s ’ life o m o u s o rg a n is a tio n s is a d v a n ta g e o u s in th e s e n s e th a t it a y ’s p ro d u c ts a n d s e rv ic e s a re in c re a s in g ly c o m p le x a n d c ro s s m a n y d iffe re n t d is c ip lin e s – a n d m o s t im p o rta n t,

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re s p o n s e to ra p id ly c h a n g in g re q u ire m e n ts . V irtu a l O rg a n is a tio n w ill te m p o ra ry tim e d u ra tio n , th a t is th e tim e n e e d e d to s a tis fy its p u rp o s e . c y c le is d e c o m p o s e d in fo u r p h a s e s [3 , 4 ] th a t w ill a ls o b e re fle c te d in rk :

1 . Id e n tific a tio n o f N e e d s : A p p ro p ria te d e s c rip tio n o f th e p ro d u c t o r s e r d e liv e re d b y th e V O , w h ic h g u id e s th e c o n c e p tu a l d e s ig n o f th e V O . o f th e 2 . F o r m a tio n (P a r tn e r s S e le c tio n ): A u to m a tic s e le c tio n o rg a n is a tio n s (p a rtn e rs ), w h ic h b a s e d in its s p e c ific k n o w le d g e , s k ills , c o s ts a n d a v a ila b ility , w ill in te g ra te th e V O . 3 . O p e r a tio n : C o n tro l a n d m o n ito rin g o f th e p a rtn e rs ’ a c tiv itie s , in c lu d in g o f p o te n tia l c o n flic ts , a n d p o s s ib le V O re c o n fig u ra tio n d u e to p a rtia l fa ilu 4 . D is s o lu tio n : B re a k in g u p th e V O , d is trib u tio n o f th e o b ta in e d p ro fits a n d re le v a n t in fo rm a tio n fo r fu tu re u s e o f th e E le c tro n ic In s titu tio n .

v ic e to b e in d iv id u a l re so u rc e s, re s o lu tio n re s. s to ra g e o f

W e e x p e c t fro m a M e ta -In s titu tio n , th e a p p lic a tio n in d e p e n d e n t fra m e w o rk w e h a v e d e f in e d in s e c tio n 2 .1 , th e c a p a b ility to d ir e c tly h e lp o n th e “ I d e n tif ic a tio n o f n e e d s ” s ta g e o f th e V O life c y c le , a s fo llo w s :

− F irs t h e lp in g a g e n ts in d e s b y o th e r p o te n tia l m e m b e r In s titu tio n a n d − S e c o n d , p ro v id in g th e s e a to a c h ie v e th o s e d e s c rib e d T h e M p a rtic u la r th e e x p lic W e c a lig h t o f th

e ta a p it V n s e e

-In s titu tio n p lic a tio n d o O g o a ls . e e b o th th e m e rg e n c e o

c rib in g th e ir n e e d s in s u c h a w a y th a t c a n b e u n d e rs to o d s th a t m a y jo in la te r a s p e c ific a n d a p p ro p ria te E le c tro n ic rc h in g to o ls to lo o k fo r p o te n tia l p a rtn e rs w h o k n o w h o w n e e d s.

w ill th e n g e n e ra te th a t s p e c ific E le c tro n ic In s titu tio n fo r th e m a in th ro u g h th e in s ta n tia tio n o f s o m e m o d u le s a c c o rd in g to g e n e ra l a rc h ite c tu re a n d th e ro le o f a M e ta -In s titu tio n in th e f V irtu a l O rg a n is a tio n s a s it is d e p ic te d in th e fig u re b e lo w :

N o rm s & R u le s O n to lo g y S e rv ic e s

M e ta I n s titu tio n

E le c tro n ic In s titu tio n

Id e n tific a tio n o f N e e d s

L in k s to o th e r In s titu tio n s

F ig .1 .G e n e r a l a r c h ite c tu re a n d r o le o f a M e ta - I n s titu tio n

T h e E le c tro n ic In s titu tio n , in h e rits a p p ro p ria te o th e r in s titu tio n s th a t m a y p la y a c ru c ia l ro le fo r a fro m th e M e ta -In s titu tio n , w ill p ro v id e th e fra m e tw o m a in s ta g e s o f th e V O life c y c le : V O fo rm a tio W e w ill d e s c rib e in d e ta il, in th e n e x t tw o s e c p ro v id e s th e m e a n s fo r h e lp in g o n th o s e tw o s ta g e m a rk e t a g e n t-b a s e d to o l.

ru le s ll th e w o rk n a n d tio n s , s b y m

a s w V O p fo r d V O o h o w a k in

e ll a ro c e e a lin p e ra a n E g a v

s im p o rta n t lin k s to s s , th a t a re in h e rite d g w ith , a t le a s t, th e tio n m o n ito rin g . le c tro n ic In s titu tio n a ila b le a n e le c tro n ic

236

Ana Paula Rocha and Eug´enio Oliveira

F ig u re 2 , b e lo w , s h o w s s h o w s th a t V O fo rm a tio e n a b lin g s e v e ra l o rg a n iz a (M A g t) le a d in g to th e V O c o m m itm e n t m u tu a lly a g o p e ra tio n m o n ito rin g . T h e p u rp o s e s o f c o m p le te n e s s .

th e m a in m o d u le s o f a n E le c tr n m o d u le m a k e s a v a ila b le tio n a g e n ts (O A g t) to m e e t p a rtn e rs s e le c tio n . V O o p e ra re e d b y th e p a rtn e rs a t th e fin a l m o d u le (V O d is s o lu tio n

o n ic In s titu tio n . F ig u re 2 a ls o o u r Q -N e g o tia tio n p ro to c o l to g e th e r th ro u g h a M a rk e t tio n m o d u le u s e s th e p h a s e d e n d o f p re v io u s s ta g e fo r ) is m e n tio n e d h e re o n ly fo r E le c tr o n ic I n s titu tio n

N o rm s & R u le s L in k s to o th e r In s titu tio n s

V O for m a ti on

V O op er a ti on

Q -N e g o tia tio n

M o n ito r in g

V O d i s s olu ti on

le g a l fin a n c ia l

M A g t

O A g t

O A g t

p h a se d c o m m itm e n t

O A g t

F ig .2 .G e n e r a l a r c h ite c tu r e a n d r o le o f a n E le c tr o n ic I n s titu tio n

3

Ad v a n ced fea tu r es f or N eg oti a ti on i n V O for m a ti on

In th e s c e n a rio o f a n n e g o tia tio n m e c h a n is m th a t, b a s e d o n th e ir o w g ro u p to s a tis fy th e p re a u to m a tic n e g o tia tio n im p o rta n t re q u ire m e n ts :

•

•

•

a g e n ts h o u ld n c o m p v io u s ly m e c h a n

b a s e d V irtu a e n a b le th e s e te n c ie s a n d d e s c rib e d V O is m h a s to

l O e le c a v a n e b e

rg a n is a tio n tio n o f th e ila b ility , w e d s. In su c p o w e rfu l

fo in ill h a e n o

rm a tio n p ro c e s s , th e d iv id u a l o rg a n is a tio n s c o n s titu te th e o p tim a l s c e n a rio , th e a d o p te d u g h to s a tis fy th re e

C a p a b ilitie s fo r n e g o tia tin g a b o u t w h a t a re th e m o s t p ro m is in g o rg a n is a tio n s th a t s h o u ld b e lo n g to V O . T h is m e a n s th a t a g e n ts , a s re p re s e n ta tiv e o f o rg a n is a tio n s , h a v e to n e g o tia te o v e r g o o d s o r s e rv ic e s th o s e o rg a n is a tio n s a re a b le to p ro v id e . In re a lis tic s c e n a rio s , g o o d s /s e rv ic e s a re d e s c rib e d th ro u g h m u ltip le a ttrib u te s , w h ic h im p ly th a t th e n e g o tia tio n p ro c e s s m u s t b e e n h a n c e d w ith th e c a p a b ility to b o th e v a lu a te a n d fo rm u la te m u lti-a ttrib u te b a s e d p ro p o s a ls . A g e n ts th a t a re w illin g to b e lo n g to th e V irtu a l O rg a n is a tio n m a y c o m p e te b e tw e e n th e m . A n a g e n t d o e s n o t k n o w o th e r o n e s ’ n e g o tia tio n s tra te g ie s o r e v e n c u rre n t p ro p o s a ls . L e a rn in g te c h n iq u e s c a n h e lp a g e n ts to b e tte r n e g o tia te in th e s e p a rtia lly u n k n o w n e n v iro n m e n ts , b y re a s o n in g a b o u t p a s t n e g o tia tio n e p is o d e s a s w e ll a s a b o u t th e c u rre n t o n e im p ro v in g its o w n b e h a v io u r. In th e V O fo rm a tio n p ro c e s s , e a c h o n e o f th e in d iv id u a l o rg a n is a tio n s w ill c o n trib u te w ith a t le a s t o n e o f its o w n c a p a b ilitie s (g o o d o r s e rv ic e ) to th e V O . A ll th e s e c o n trib u tio n s m a y b e , a n d th e y u s u a lly a re , m u tu a lly d e p e n d e n t. T h e n e g o tia tio n p ro c e s s h a s to b e a b le to d e a l w ith th o s e in te r-d e p e n d e n c ie s , re a c h in g a c o h e re n t s o lu tio n a s th e fin a l o n e to b e a c c e p te d b y a ll th e a g e n ts .

Electronic Institutions

237

A n im p o rta n t c h a ra c te ris tic th a t m u s t b e c o n s id e re d in V O s c e n a rio is th e fa c t th a t y o rg a n is a tio n h a s a s its m a in o b je c tiv e to m a x im iz e its o w n p ro fit. In o rd e r to d o a t, n e g o tia tio n p ro c e s s h a s to ta k e in to a c c o u n t a g e n ts in d iv id u a l ra tio n a lity a n d lf-in te re s te d n e s s . K e e p in g in fo rm a tio n p riv a te p re v e n ts lo o s in g n e g o tia tio n p o w e r c o m p e tito rs , s in c e o th e rs w ill n e v e r k n o w o r b e a b le to d e d u c e h o w c lo s e th e y a re a n o th e r a g e n t’s p re fe re n c e s . It is o u r c la im th a t o u r p ro p o s e d n e g o tia tio n a lg o rith m c a n e ffe c tiv e ly d e a l w ith th e s e th re e im p o rta n t re q u ire m e n ts in th e V O s c e n a rio w h ile k e e p in g a g e n ts ’ in fo rm a tio n p riv a te a s m u c h a s p o s s ib le . In th e n e x t s e c tio n s , w e fu rth e r d e ta il th e p ro p o s e d m o d e l fo r a g e n ts ’ n e g o tia tio n . F irs t, w e p re s e n t a fo rm a l d e s c rip tio n o f o u r n e g o tia tio n m o d e l. T h e n w e d e s c rib e h o w to s p e c ific a lly d e a l w ith e a c h o n e o f th e th re e re q u ire m e n ts m e n tio n e d a b o v e (m u lti-a ttrib u te b id d in g , a d a p tiv e b id d in g a n d m u tu a l d e p e n d e n c ie s re s o lu tio n ).

a n th se to to

3 .1

T he N eg oti a ti on Mod el

In th e V O fo rm a tio n p ro c e s s , p a rtic ip a n ts in th e n e g o tia tio n c a n b e e ith e r m a rk e t o r o rg a n is a tio n a g e n ts . T h e M a rk e t A g e n t p la y s th e ro le o f o rg a n iz e r, m e a n in g th a t it is th e a g e n t th a t s ta rts a n d g u id e s a ll th e n e g o tia tio n p ro c e s s . T h e O rg a n is a tio n A g e n ts p la y th e ro le o f re s p o n d e n ts , m e a n in g th a t th e y a re th o s e w h o a re w illin g to b e lo n g to th e fu tu re V O a n d , th e re fo re , th e y h a v e to s u b m it p ro p o s a ls d u rin g th e n e g o tia tio n p h a se . In o rd e r to a g re e in a V O s tru c tu re , a g e n ts (M a rk e t a n d s e v e ra l O rg a n is a tio n s ) n a tu ra lly e n g a g e th e m s e lv e s in a s e q u e n tia l n e g o tia tio n p ro c e s s c o m p o s e d o f m u ltip le ro u n d s o f p ro p o s a ls (s e n t b y O rg a n is a tio n s to M a rk e t) a n d c o u n te r-p ro p o s a ls w h ic h a re a c tu a lly c o m m e n ts to p a s t p ro p o s a ls (s e n t b y M a rk e t to O rg a n is a tio n s ). T h e M a rk e t A g e n t p la y in g a c e n tra l ro le a s o rg a n iz e r, m o d e ls th e n e g o tia tio n p ro c e s s th ro u g h th e N e g M A trip le t a s fo llo w s : N e g w h e re : • C m p t id e • L A g ts is C m p t. • H is th e s in g le n e d u rin g th

M A

(1 )

n tifie s th e c o m p o n e n t u n d e r n e g o tia tio n th e lis t o f re s p o n d e n t (o rg a n is a tio n ) a g e n ts th a t c a n p ro v id e c o m p o n e n t n e g o tia tio n h is to ry . E a c h e le m e n t o f H c o n ta in s in fo rm a tio n re la te d to a g o tia tio n ro u n d . E a c h n e g o tia tio n ro u n d in c lu d e s a ll p ro p o s a ls re c e iv e d a t ro u n d . H = { H t} ,

w h • • •

= < C m p t, L A g ts , H >

H t

= { < P r o p ti, E v a l ti> }

P ro p

ti

= { V 1

, …, V n

(2 )

}

e re : P r o p ti i s t h e p r o p o s a l s e n t b y o r g a n i s a t i o n a g e n t i , i n t h e n e g o t i a t i o n r o u n d t . V x is th e p ro p o s a l’s v a lu e o f a ttrib u te x . E v a l ti i s t h e e v a l u a t i o n v a l u e o f p r o p o s a l P r o p ti, f r o m t h e M a r k e t A g e n t p o i n t o f v ie w .

238

N e g

Ana Paula Rocha and Eug´enio Oliveira

E a c h o n e o f th e O rg a n is a tio n A g e n ts m o d e l th e n e g o tia tio n p ro c e s s th ro u g h th e O A n -u p le a s fo llo w s : N e g

•

O A

C m p t id e n tifie s th e c o m p o n e n t u n d M A g t id e n tifie s M a rk e t A g e n t th a t H is th e n e g o tia tio n h is to ry . E a c h s in g le n e g o tia tio n ro u n d . E a c h n e a c h s p e c ific O rg a n is a tio n A g e n t re c e iv e d fro m th e M a rk e t A g e n t.

• •

H = { < P r o p t, C o m m e n t t> } ,

e r is e e g to

n e g th e le m o tia th e

o tia tio n o rg a n iz e r e n t o f H tio n ro u n M a rk e t A

Q = { Q t} , 3 .2

o f th c o n ta d in c g e n t

is in lu p

n e g o tia tio n p ro c s in fo rm a tio n re d e s th e p ro p o s a lu s th e fe e d b a c k

C o m m e n t t ∈ { w i n n e r , < E v a l t 1 , …, E v a l t n > }

w h e re : • P r o p t is th e p ro p o s a l s e n t d u rin g th e n e g o • C o m m e n tt is th e c o m m e n t re c e iv e d fro m c o m m e n t in d ic a te s if th e p ro p o s a l is e (w in n e r ) o r in c lu d e s a q u a lita tiv e a p p r v a lu e s u n d e r n e g o tia tio n . T h e Q p a ra m e te r in c lu d e s re le v a n t in fo a lg o rith m u s e d fo r n e x t b id fo rm u la tio n . T h s e c tio n . A t th is p o in t, it is o n ly im p o rta n t to

•

(3 )

= < C m p t, M A g t, H , Q >

tia tio n ro M a rk e t ith e r th e e c ia tio n

e ss. la te d to a l se n t b y c o m m e n t (4 )

u n d t. A g e n t t o p r o p o s a l P r o p t. T h i s w in n e r in th e c u rre n t ro u n d fo r e a c h o n e o f th e a ttrib u te

rm a tio n to b e u s e d b y th e le a rn in g is p a rtic u la r to p ic is d is c u s s e d in a la te r s a y th a t Q is d e s c rib e d a s fo llo w s :

Q t = { < S t a t e t, A c t i o n t, Q V a l u e t > }

Mu lti -Attr i bu te B i d E v a lu a ti on

N e g o tia tio n im p lie s , fo r th e V O s c e n a rio a s w e ll a s fo r m o s t o f th e e c o n o m ic tra n s a c tio n s , to ta k e in to c o n s id e ra tio n n o t o n ly o n e , b u t m u ltip le a ttrib u te s fo r d e fin in g th e te rm s (g o o d s /s e rv ic e s ) u n d e r d is c u s s io n . F o r in s ta n c e , a lth o u g h th e p ric e o f a n y g o o d is a n im p o rta n t (p e rh a p s th e m o s t im p o rta n t) a ttrib u te , a b o u t d e liv e ry tim e o r q u a lity c a n a ls o b e , a n d g e n e ra lly a re , c o m p le m e n ta ry is s u e s to in c lu d e in th e d e c is io n a b o u t to b u y /s e ll o r n o t a s p e c ific g o o d . A tta c h in g u tility v a lu e s to d iffe re n t a ttrib u te s u n d e r n e g o tia tio n s o lv e s th e p ro b le m o f m u lti-a ttrib u te e v a lu a tio n . G e n e ra lly , a n e v a lu a tio n fo rm u la is a lin e a r c o m b in a tio n o f th e a ttrib u te s ’ v a lu e s w e ig h te d b y th e ir c o rre s p o n d in g u tility v a lu e s . In th is w a y , a m u lti-a ttrib u te n e g o tia tio n is s im p ly c o n v e rte d in a s in g le a ttrib u te n e g o tia tio n , w h e re th e re s u lt o f th e e v a lu a tio n fu n c tio n c a n b e s e e n a s th is s in g le is s u e . E x a m p le s o f th is m e th o d a re p re s e n te d in [1 , 2 ]. H o w e v e r, in s o m e c a s e s , it c o u ld b e d iffic u lt to s p e c ify a b s o lu te n u m e ric v a lu e s to q u a n tify th e a ttrib u te s ’ u tility . A m o re n a tu ra l a n d re a lis tic w a y is to s im p ly im p o s e a p re fe re n c e o rd e r o v e r a ttrib u te s . T h e m u lti-a ttrib u te fu n c tio n p re s e n te d in fo rm u la (5 ) e n c o d e s th e a ttrib u te s ’ a n d a ttrib u te s v a lu e s ’ p re fe re n c e s in a q u a lita tiv e w a y a n d , a t th e s a m e tim e , a c c o m m o d a te s a ttrib u te s in tra -d e p e n d e n c ie s .

Electronic Institutions

E v

1

=

D e v ia tio n

,

D e v ia tio n

1

=

w h e re : n = n u m b e r o f a ttrib u te s th a t d e fin e s a V x = f (V 1 , V, n ), x ∉{1 , , n } 1 , a n d ⎧V i −P r e f V i ⎪⎪ d i f ( P r e f V i , V i ) = ⎨m a x i − m i n i ⎪ P o s ( V i ) −P o n v a lu ⎩⎪

n

*

∑

n

i

i =1 n

239

(5 )

* d if ( P r e fV i ,V i ) ,

s p e c ific c o m p o n e n t,

,

if c o n tin u o u s d o m a in

s ( P r e fV i ) e s ,

if d is c r e te d o m a in

A p ro p o s a l’s e v a lu a tio n v a lu e is c a lc u la te d b y th e M a rk e t A g e n t, a s th e in v e rs e o f t h e w e i g h t e d s u m o f t h e d i f f e r e n c e s b e t w e e n t h e o p t i m a l ( P r e f V i) a n d t h e r e a l ( V i) v a lu e o f e a c h o n e o f th e a ttrib u te s . In th e fo rm u la , e a c h p a rc e l s h o u ld b e p re s e n te d in in c re a s in g o rd e r o f p re fe re n c e , th a t is , a ttrib u te s id e n tifie d b y lo w e r in d e x e s a re le a s t im p o rta n t th a n a ttrib u te s id e n tifie d w ith h ig h e r in d e x e s . T h e p ro p o s a l w ith th e h ig h e s t e v a lu a tio n v a lu e s o fa r is th e w in n e r, s in c e it is th e o n e th a t c o n ta in s th e a ttrib u te s ’ v a lu e s m o re c lo s e ly re la te d to th e o p tim a l o n e s fro m th e M a rk e t A g e n t p o in t o f v ie w . T h e n e g o tia tio n p ro c e s s is re a liz e d a s a s e t o f ro u n d s w h e re O rg a n is a tio n A g e n ts c o n c e d e , fro m ro u n d to ro u n d , a little b it m o re try in g to a p p ro a c h th e M a rk e t A g e n t p re fe re n c e s , in o rd e r to b e s e le c te d a s p a rtn e rs o f th e V O . T h e M a rk e t A g e n t h e lp s O rg a n is a tio n A g e n ts in th e ir ta s k o f fo rm u la tin g n e w p ro p o s a ls b y g iv in g th e m s o m e h in ts a b o u t th e d ire c tio n th e y s h o u ld fo llo w in th e ir n e g o tia tio n s p a c e . T h e s e h in ts a re g iv e n , b y th e M a rk e t A g e n t, a s c o m m e n ts a b o u t a ttrib u te s ’ v a lu e s in c lu d e d in c u rre n t p ro p o s a ls . Q u a li ta ti v e F eed ba ck F or m u la ti on T h e re s p o n s e to p ro p o s e d b id s is fo rm u la te d b y th e M a rk e t A g e n t a s a q u a lita tiv e fe e d b a c k , w h ic h re fle c ts th e d is ta n c e b e tw e e n th e v a lu e s in d ic a te d in a s p e c ific p ro p o s a l a n d th e o p tim a l o n e re c e iv e d s o fa r. T h e re a s o n w h y th e M a rk e t A g e n t c o m p a re s a p a rtic u la r p ro p o s a l w ith , n o t its o p tim a l, b u t th e b e s t o n e re c e iv e d s o fa r, c a n b e e x p la in e d b y th e fa c t th a t it is m o re c o n v in c in g to s a y to a n O rg a n is a tio n A g e n t th a t th e re is a b e tte r p ro p o s a l in th e m a rk e t th a n s a y in g th a t its p ro p o s a l is n o t th e o p tim a l o n e . A q u a lita tiv e fe e d b a c k is th e n fo rm u la te d b y th e M a rk e t A g e n t a s a q u a lita tiv e c o m m e n t o n e a c h o f th e p ro p o s a l’ a ttrib u te s v a lu e s , w h ic h c a n b e c la s s ifie d in o n e o f th re e c a te g o rie s : s u ffic ie n t, b a d o r v e r y _ b a d . O rg a n is a tio n A g e n ts w ill u s e th is fe e d b a c k in fo rm a tio n to its p a s t p ro p o s a ls , in o rd e r to fo rm u la te , in th e n e x t n e g o tia tio n ro u n d s , n e w p ro p o s a ls try in g to fo llo w th e h in ts in c lu d e d in th e fe e d b a c k c o m m e n ts .

1

E a c h a ttrib u te V x

m a y d e p e n d o n s e v e ra l o th e r a ttrib u te s th ro u g h fu n c tio n f.

240

3 .3

Ana Paula Rocha and Eug´enio Oliveira

L ea r n i n g i n B i d F or m u la ti on

T h e Q -N e g o tia tio n a lg o rith m u s e s a re in fo rc e m e n t le a rn in g s tra te g y b a s e d in Q le a rn in g fo r th e fo rm u la tio n o f n e w p ro p o s a ls . T h e Q -le a rn in g a lg o rith m [6 ] is a w e ll k n o w n re in fo rc e m e n t le a rn in g a lg o rith m th a t m a p s e v a lu a tio n v a lu e s (Q -v a lu e s ) to p a irs s ta te /a c tio n . T h e s e le c tio n o f a re in fo rc e m e n t le a rn in g a lg o rith m s e e m s to b e a p p ro p ria te in th e n e g o tia tio n p ro c e s s th a t c o n d u its to th e V O fo rm a tio n , s in c e o rg a n iz a tio n a g e n ts e v o lv e in a n , a t le a s t, p a rtia lly u n k n o w n e n v iro n m e n t. A n d in p a rtic u la r, Q -le a rn in g e n a b le s o n -lin e le a rn in g , w h ic h is a n im p o rta n t c a p a b ility in o u r s p e c ific s c e n a rio w h e re a g e n ts w ill le a rn in a c o n tin u o u s w a y d u rin g a ll th e n e g o tia tio n p ro c e s s , w ith in fo rm a tio n e x tra c te d fro m e a c h o n e o f th e n e g o tia tio n ro u n d s , a n d n o t o n ly in th e e n d w ith th e n e g o tia tio n re s u lt. Q -le a rn in g is b a s e d in th e id e a o f re w a rd in g a c tio n s th a t p ro d u c e s g o o d re s u lts , a n d p u n is h in g th o s e th a t p ro d u c e b a d re s u lts , a s in d ic a te d b y p a ra m e te r r in th e c o rre s p o n d e n t fo rm u la (s e e e q u a tio n (6 )).

Q (s,a )

In th e Q -N e g o tia tio n p ro c e s s , w e a s s u m A s ta te is d e fin e d b y a s e t o f a ttrib u te s ’ , n =n u m s = v 1 ,v 2 , ,v n , v x :v a lu

•




•

e th a t: v a lu e s , th u s re p re s e n tin g a p ro p o s a l. b e r o f a ttr ib u te s e o f a ttr ib u te x

A n a c tio n is a re la tio n s h ip th a t is a m o d ific th e a p p lic a tio n o f o n e o f th e fu n c tio n s : in c re a , n =n u m b e r o a = f1 , f 2 , , f n , f x ∈{i n c r e a s 

T h e a d a p ta tio n o f th e fo rm a tio n n e g o tia tio n , le a d e n u m e ra te in n e x t p a ra g ra p T h e re w a rd v a lu e fo r a fe e d b a c k re c e iv e d fro m th th is s ta te (s e e fo rm u la 7 ).

Q s to h s, p a e M

le a rn in g th e in c a n d a re rtic u la r a rk e t A

⎧n r

T h e e to le a rn , p ro m is in s ta te p ro a g e n t. A v a lu e o f a ttrib u te

=

(6 )

⎛ ⎞ = Q ( s , a ) +α ⎜ r +γ m a x Q ( s ’ , b ) −Q ( s , a ) ⎟ b ⎝ ⎠

⎪ n ⎨ − p e n a lty i ⎪ 2 ∑ i ⎩

a tio n o se , d e c f a ttr ib e ,d e c r e

f th e a ttrib u te s ’ v a lu e s th ro u g h re a s e , o r m a in ta in . u te s a s e ,m a i n t a i n }

a lg o rith m to o u r s p e c ific s c e n a rio , th e V O lu s io n o f tw o im p o rta n t fe a tu re s w e w ill b rie fly d e ta ile d e ls e w h e re [6 ]. s ta te is c a lc u la te d a c c o rd in g to th e q u a lita tiv e g e n t, in re s p o n s e to th e p ro p o s a l d e riv e d fro m (7 )

,

if w in n e r ,

if n o t w in n e r

x p lo ra tio n s p a c e , w h ic h c a n b e c a m e v e ry is re d u c e d in o rd e r to in c lu d e o n ly th o s g a c tio n s . A p ro m is in g a c tio n is a n a c tio p o s e d to th e M a rk e t A g e n t h in ts in c lu d e d s a n e x a m p le , if th e M a rk e t A g e n t, a s a a ttrib u te x a s b a d , o n e p ro m is in g a c tio n a n d m a in ta in a ll th e o th e rs .

(0

≤ p e n a l t y i ≤1

la rg e a n d th u e a c tio n s th a t n th a t c a n b e in th e fe e d b a p ro p o s a l’s fe s h o u ld b e in

)

s im p lie s a lo n g tim e c a n b e c o n s id e re d a s a p p lie d to a p re v io u s c k fo rm u la te d b y th is e d b a c k , c la s s ifie s th e c re a s e a little b it th is

Electronic Institutions

3 .4

241

D i s tr i bu ted D ep en d en ci es R es olu ti on

O n e o f th e re q u ire m e n ts fo r th e n e g o tia tio n p ro to c o l w e a re h e re p ro p o s in g , b e s id e s d e a lin g w ith a ttrib u te s in tra -d e p e n d e n c ie s , is th e c a p a b ility to d e a l w ith a ttrib u te s ’ in te r-d e p e n d e n c ie s . T h is is a n im p o rta n t re q u ire m e n t to b e c o n s id e re d in o u r s c e n a rio , b e c a u s e in th e V O fo rm a tio n p ro c e s s in te rd e p e n d e n t n e g o tia tio n s ta k e p la c e s im u lta n e o u s ly , a n d p ro p o s a ls re c e iv e d fro m d iffe re n t o rg a n is a tio n a g e n ts m a y h a v e in c o m p a tib le d e p e n d e n t a ttrib u te s ’ v a lu e s . T h e re fo re , a g e n ts s h o u ld n e g o tia te in o rd e r to a g re e b e tw e e n th e m o n m u tu a l a d m is s ib le v a lu e s , w h a t c a n b e s e e n a s a d is trib u te d d e p e n d e n c ie s s a tis fa c tio n p ro b le m . T h e d is trib u te d d e p e n d e n c ie s s a tis fa c tio n p ro b le m h a s b e e n th e s u b je c t o f a tte n tio n o f o th e r re s e a rc h e rs , a d d re s s in g th e s tu d y o f b o th s in g le [7 ] a n d m u ltip le d e p e n d e n t v a ria b le s [8 , 9 , 1 0 ]. In th e V O fo rm a tio n p ro c e s s , d e p e n d e n c ie s m a y o c c u r b e tw e e n m u ltip le v a ria b le s , m a k in g th e la tte r a p p ro a c h e s m o re re le v a n t to o u r re s e a rc h . T h e firs t tw o m e n tio n e d p a p e rs , [8 , 9 ] d e s c rib e a lg o rith m s to re a c h o n e p o s s ib le s o lu tio n , n o t th e o p tim a l o n e . T h e th ird p a p e r [1 0 ] in tro d u c e s a n a lg o rith m th a t, a lth o u g h re a c h in g th e o p tim a l s o lu tio n , im p o s e s th a t a ll a g e n ts in v o lv e d in th e m u tu a l d e p e n d e n c ie s re s o lu tio n p ro c e s s h a v e to k n o w a ll a g e n ts ’ p riv a te u tility fu n c tio n s . D iffe re n tly fro m a ll th e s e p ro p o s a ls , o u r d is trib u te d d e p e n d e n c ie s s a tis fa c tio n a lg o rith m , b e s id e s re a c h in g th e o p tim a l s o lu tio n , k e e p s a g e n ts ’ in fo rm a tio n a s m u c h a s p o s s ib le p riv a te . E a c h a g e n t in v o lv e d in th e d is trib u te d d e p e n d e n t p ro b le m re s o lu tio n s h o u ld k n o w its s p a c e o f s ta te s , th a t is , a ll p o s s ib le v a lu e s fo r its o w n d e p e n d e n t a ttrib u te s . A g e n ts w ill th e n e x c h a n g e b e tw e e n th e m a lte rn a tiv e v a lu e s fo r th e d e p e n d e n t a ttrib u te s , in o rd e r to a p p ro a c h a n a g re e m e n t. A s in a n y ite ra tiv e n e g o tia tio n p ro c e s s , a g e n ts s ta rt th e n e g o tia tio n b y p ro p o s in g its o p tim a l (fro m a lo c a l p o in t o f v ie w ) s o lu tio n a n d , in th e n e x t ro u n d s s ta rt c o n c e d in g try in g to re a c h a c o n s e n s u s . In o rd e r to p ro p e rly u n d e rs ta n d th e w a y th e a lg o rith m w o rk s , firs t w e s h o u ld in tro d u c e th e c o n c e p t o f “ d e c r e m e n t o f th e m a x im u m u tility ” o f a n a lte rn a tiv e s ta te . S ta te tra n s itio n s a re d u e to re la x a tio n o f o n e o r m o re s ta te v a ria b le s . T h e d e c re m e n t o f th e m a x im u m u tility o f a p a rtic u la r a lte rn a tiv e p ro p o s a l c a n b e c a lc u la te d a s th e d iffe re n c e b e tw e e n th e e v a lu a tio n v a lu e s o f th is a lte rn a tiv e p ro p o s a l a n d th e o p tim a l o n e . W e w ill a b b re v ia te “ d e c re m e n t o f th e m a x im u m u tility ” to “ d e c re m e n t o f th e u tility ” m e a n in g th e s u c c e s s iv e a m o u n t o f u tility a g e n ts h a s to c o n c e d e c o m p a re d to th e (lo c a l) o p tim a l b id . F o rm u la (8 ) re p re s e n ts th e d e c re m e n t o f u tility fo r a g e n t i, c o rre s p o n d in g to th e p a rtic u la r s ta te s k, w h e re s * is th e a g e n t’s o p tim a l s ta te (p ro p o s a l).

d u ik A t e a c h n e g o lo w e s t d e c re m e p ro c e s s , a g e n ts u tility , w h a t e n a T h is p ro c e s s p ro p o s e d in th e

=

( ) − E v (s k )

(8 )

E v s *

tia tio n s te p , th e a g e n t s e le c ts a s a n e w n t o f th e u tility o f th o s e n o t y e t p ro d o n o t re v e a l th e ir o w n s ta te ’s u tility , b le s k e e p in g im p o rta n t in fo rm a tio n p riv e n d s w h e n a ll a g e n ts c a n n o t s e le c t a n e p a s t. In th is w a y , a g e n ts , a lth o u g h

p ro p o s a l th e o n e th a t h a s p o s e d . D u rin g th e n e g o tia b u t o n ly th e s ta te ’s d e c re m a te . x t s ta te b e tte r th a n o n e a lre re m a in in g s e lf-in te re s te d ,

th e tio n e n t a d y w ill

242

Ana Paula Rocha and Eug´enio Oliveira

c o n v e rg e fo r a s o lu tio n th a t is th e b e s t p o s s ib le fo r a ll o f th e m re p re s e n ts th e m in im u m jo in t o f d e c re m e n t o f th e u tility . T h e p ro p o s e d d is trib u te d d e p e n d e n c ie s s a tis fa c tio n a lg o rith m fo llo w s : 1 . E a c h a g e n t i s e le c t its n e x t p re fe ra b le a lte rn a tiv e s ta te , fro m b e fo re . L e t u s s u p p o s e th is is s ta te a .

d u ia 2 . E a − − 3 . W

c h its its h e n

to g e th e r, b e c a u s e it c a n b e d e s c rib e d a s th o s e n o t y e t p ro p o s e d

( )

= m i n d u is s

a g e o w o w a g

n t i s n p re n lo c e n t j

e n fe a l re

d s o u t ra b le s d e c re m c e iv e s

to o th e ta te a s e n t o f th e p ro

rs: a n e w p ro p o sa l th e u tility fo r th a t s ta te p o s a l (s ta te a ) fro m a g e n t i, it c a lc u la te s :

− i t s o w n l o c a l d e c r e m e n t o f u t i l i t y ( d u aj ) − th e jo in t d e c re m e n t o f th e u tility : j d u a = ∑ d u da a g , d a g = {1 n }s e t o f m u t u a l d e p e n d e n t a g e n t s 

d a g

− th e m in im u m jo in t o f th e d e c re m e n t o f th e u tility a lre a d y k n o w n ( jd u m ) 4 . a n d s e le c ts : − its n e x t p re fe ra b le s ta te . S u p p o s e it is s ta te b . − i f d u bj < j d u m , a g e n t j p r o p o s e s s t a t e b t o o t h e r a g e n t s − e ls e a g e n t j a c c e p ts s ta te m a s th e fin a l p ro p o s a l a n d n e g o tia tio n e n d s . T r a n s fer of Com p en s a ti on s A fte r a g re e in p ro c e s s , g e n e ra lly a g e n ts b e c o m e m in v o lv e d in th e d u tility (r d u ), th e a c c o rd in g to fo rm

a g lo b a l s o lu tio n , a g e t d iffe re n t lo c a l d o re p e n a liz e d th a n is trib u te d d e p e n d e n c jo in t d e c re m e n t o f u la (9 ):

rd u

=

jd u m n ,

g e n ts in v o lv e d in th e c re m e n t o f u tility v o th e rs . In o rd e r to ie s re s o lu tio n g e t th th e u tility w ill b e

n =n u m b e r o f a g e n ts

e d a lu g u e s d is

e p e n d e n c ie s re s o lu tio n e s a n d , th e re fo re , s o m e a ra n te e th a t a ll a g e n ts a m e re a l d e c re m e n t o f trib u te d b e tw e e n th e m (9 )

A s a c o n s e q u e n c e , s o m e a g e n ts h a v e to p a y o r g e t a c o m p e n s a tio n v a lu e to o th e rs . O n c e a g e n t i h a s p r e v i o u s l y c a l c u l a t e d d u im a s i t s l o c a l d e c r e m e n t o f u t i l i t y , t h e c o m p e n s a tio n v a lu e is c a lc u la te d a c c o rd in g to fo rm u la (1 0 ).

c V a lu e i

= r d u − d u im

(1 0 )

If th e a g e n t’ re a l d e c re m e n t o f th e u tility is g re a te r th a n its lo c a l d e c re m e n t o f th e u tility , it w ill p a y a c o m p e n s a tio n v a lu e to o th e rs , th a t h a s c a lc u la te d a s th e d iffe re n c e o f th e s e tw o v a lu e s . If n o t, th e a g e n t w ill g e t a c o m p e n s a tio n v a lu e .

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243

P ha s ed Com m i tm en ts W e h a v e s e e n h o w a g e n ts , re p re s e n tin g in d iv id u a l a u to n o m o u s e n te rp ris e s , m a y re a c h a n a g re e m e n t th ro u g h a p p ro p ria te n e g o tia tio n p ro c e d u re s . T h e c o n tra c t th a t fo rm a lis e s th a t a g re e m e n t s h o u ld e x p lic itly s ta te a ll th e c o m m itm e n ts th a t th o s e a g e n ts a re d u e to s a tis fy a ll a lo n g th e V O life c y c le . A fu ll c o m m itm e n t c o n tra c t m a y b e u n a b le to d e a l w ith p o s s ib le fu tu re , p a rtia lly u n e x p e c te d , e v e n ts . T h is fa c t h a s a lre a d y b e e n re c o g n iz e d s in c e th e d e fin itio n o f th e o ld c o n tra c t n e t p ro to c o l [1 1 ] w h e re th e p o s s ib ility o f a c o n tra c t c a n c e lla tio n w a s e n v is a g e d . M o re re c e n tly , o th e r a u th o rs lik e [1 2 ] h a v e a p p ro a c h e d th is s u b je c t in th e c o n te x t o f d e c o m m itin g in th e m e e tin g s c h e d u lin g a p p lic a tio n . H o w e v e r, it w a s S a n d h o lm [1 3 , 1 4 ] w h o g a v e a m o re s y s te m a tic a n d re le v a n t c o n trib u tio n fo r th is is s u e th ro u g h th e in tro d u c tio n o f th e c o n c e p t o f “ le v e le d c o m m itm e n t” a n d a s s o c ia te d p e n a ltie s . C o n tra ry to th e g a m e th e o re tic a p p ro a c h w h e re c o n tin g e n c y c o n tra c ts a re e s ta b lis h e d a c c o rd in g to th e e x is te n c e o r n o t o f fu tu re e v e n ts , S a n d h o lm [1 4 ] a llo w s u n ila te ra l d e c o m m itm e n ts th ro u g h th e p a y m e n t o f c a lc u la te d p e n a ltie s . R e s u ltin g c o n tra c ts a re th e n c a lle d “ le v e le d c o m m itm e n t c o n tra c ts ” . T h re e m a in a s p e c ts a re re la te d to th is is s u e :

•

F irs t, th e p ro b le m o f h o w to re p re s e n t, in a n u n a m b ig u o u s fo rm , s u c h a c o m m itm e n t in c lu d in g a ll re le v a n t in fo rm a tio n a b o u t fu tu re a g e n ts ’ a ttitu d e s . S e c o n d , h o w to e x p lo re th is k n o w le d g e in o rd e r to c o rre c tly m o n ito rin g th e n e x t s ta g e s o f th e V O life c y c le ? T h ird , w h a t to d o in c a s e o f fa ilu re o f w h a t w a s p re v io u s ly n e g o tia te d a n d a g re e d a n d fin a lly s ta te d in th e a c c e p te d c o n tra c t. C a n p a rtie s b a c k o u t? In w h a t c irc u m s ta n c e s c a n th a t h a p p e n ? A n d , if th e a n s w e r is y e s , w h a t p ro c e d u re s h o u ld fo llo w ? S h o u ld a n e w n e g o tia tio n p ro c e s s s ta rt o r (a n d ) s h o u ld a p p ro p ria te p e n a ltie s b e e n fo rc e d o n th e a g e n ts ?

• •

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o m m itm e n ts h a v e to b e a g re e d a n d re p re s e n te d in s u c h a w a y th a re n t fu tu re p o in ts in tim e , th e y c a n b e v e rifie d . W h ic h p ro c e d u re to v e rific a tio n s h o u ld a ls o b e c o n s id e re d in th e a g re e d c o n tra c t. e e n v is a g e re p re s e n tin g th e n e g o tia tio n o u tc o m e (th e a g re e d c o n tra c a m e w h e re e a c h s lo t re p re s e n ts p re -c o n d itio n s p lu s a s e t o f ru le s to b e ib le a p p lic a tio n . T h o s e ru le s w h o s e c o n d itio n a l p a rt h a s b e e n v e rifie d o p ria te a c tio n to b e ta k e n in th o s e s p e c ific c irc u m s ta n c e s . c o n tra c t, in c lu d in g a s e t o f p h a s e d c o m m itm e n ts , c a n b e re p re s e n te d a

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C o n t r a c t = L A g t s , A g t s −P / S , V e r i f i c a t i o n _ p r o c e d u r e

t a t se v e ra l fo llo w a fte r t) a s a k in d s e le c te d fo r in d ic a te th e s:

, w h e re :

L A g ts re p re s e n ts th e lis t o f a g e n ts th a t a c c e p t th a t c o n tra c t. A g t-P /S tie s e a c h a g e n t to g e th e r w ith th e c o n trib u tio n (p ro d u c t o r s e rv ic e ) is c o m m ite d to g iv e to th e V O .

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A g t − P / S = {A g t − P / S i },

A g t −P / S i ={ A g t i , P r o d / S e r v i

}

V e r ific a tio n _ p r o c e d u r e in d ic a te s h o w a n d w h e n to m o n ito rin g th e o p e ra tio n p ro c e d u re s a g re e d th ro u g h th e c o n tra c t. V e r ific a tio n _ p r o c e d u r e is re p re s e n te d a s :

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Ana Paula Rocha and Eug´enio Oliveira

V e rific a tio n _ p ro c e d u re = < P re -c o n d , R u le -s e t> , w h e re : • P r e - c o n d ∈{ e v e n t, tim e _ p o in t} • e v e n t is a s p e c ific ty p e o f a rriv e d m e s s a g e s . • tim e _ p o in t is a p re -s p e c ifie d p o in t in tim e fo r c h e c k • R u l e - s e t = { < c o n d i, a c t i o n i> } • c o n d i is a s e t o f c o n d itio n s to b e c h e c k e d a fte r P r e -c • a c tio n i ∈{ d p e n a lty , d p e n a lty + r e _ n e g t, n o a c t} , a n d − d p e n a lty re p re s e n ts a d e c o m m itm e n t p e n a lty v a lu − r e _ n e g t re p re s e n ts th e re -n e g o tia tio n a c tio n . − n o a c t re p re s e n ts th e c a s e w h e re n o a c tio n is to b e

in g c u rre n t c o n d itio n s . o n d is tru e . : e . d o n e .

D e c o m m itm e n t p e n a ltie s h a v e to b e c a lc u la te d a c c o rd in g to th e o th e r V O p a rtn e rs ’ re s p e c tiv e lo s s e s . It is o u r in te n tio n to e n h a n c e th e n e g o tia tio n p ro to c o l in s u c h a w a y th a t th e a g e n ts a lre a d y k n o w th e s e p e n a ltie s a t th e e n d o f th e n e g o tia tio n p h a s e .

5

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E le c tro n ic In s titu tio n s a re g e n e ra l fra m e w o rk s fo r h e lp in g in c o lla b o ra tiv e w o rk in e le c tro n ic e n v iro n m e n ts . E le c tro n ic In s titu tio n s p ro v id e , s o m e tim e s e n fo rc e , ru le s a n d n o rm s o f b e h a v io u r a n d m a k e a v a ila b le s e rv ic e fa c ilitie s s u p p o rtin g b o th in te ra c tio n a n d o p e ra tio n m o n ito rin g o f c o m p u ta tio n a l e n titie s . A V irtu a l O rg a n iz a tio n is a p o w e rfu l e x a m p le o f th e n e e d o f s u c h c o lla b o ra tiv e w o rk , o n c e d iffe re n t e n te rp ris e s h a v e to jo in to g e th e r, te m p o ra rily , to a c h ie v e a c o m m o n b u s in e s s o rie n te d g o a l. T h is p a p e r e la b o ra te s o n h o w E le c tro n ic In s titu tio n s c a n e ffe c tiv e ly h e lp d u rin g th e V O life c y c le . F o r th e V O fo rm a tio n s ta g e w e h a v e in tro d u c e d a n e w n e g o tia tio n a lg o rith m , c a lle d Q -N e g o tia tio n , w h ic h in c lu d e s a p p ro p ria te fe a tu re s fo r d e a lin g w ith th e s p e c ific re q u ire m e n ts o f th e V O s c e n a rio . A n im p o rta n t re q u ire m e n t in th e V O s c e n a rio , is th a t in fo rm a tio n m u s t b e k e p t p riv a te to in d iv id u a l e n te rp ris e s , s in c e th e y a re c o m p e titiv e b y n a tu re a n d d o n o t w a n t to re v e a l th e ir m a rk e t s tra te g y to o th e rs . T h e Q -N e g o tia tio n a lg o rith m h a s th e a b ility to m a in ta in in fo rm a tio n p riv a te to in d iv id u a l e n te rp ris e s , a n d a t th e s a m e tim e , in c lu d e s th e c a p a b ility to e v a lu a te m u ltia ttrib u te p ro p o s a ls , to le a rn d u rin g th e n e g o tia tio n p ro c e s s , a n d to re s o lv e a ttrib u te s ’ in te r d e p e n d e n c ie s . L e t u s d is c u s s e a c h o n e o f th e s e fe a tu re s s e p a ra te ly . F irs t, m u ltia ttrib u te e v a lu a tio n is d o n e a s s ig n in g re la tiv e p re fe re n c e s to a ttrib u te s . O th e r s tu d ie s in m u lti-a ttrib u te e v a lu a tio n [1 , 2 ] g e n e ra lly im p o s e th e u s e o f a re a l c o n c re te v a lu e th a t c a p tu re s e a c h a ttrib u te ’s im p o rta n c e , w h ic h s o m e tim e s c a n b e d iffic u lt to q u a n tify . S e c o n d , le a rn in g is p e rfo rm e d b y u s in g a n o n -lin e re in fo rc e m e n t le a rn in g a lg o rith m d u rin g th e n e g o tia tio n p ro c e s s , th ro u g h a q u a lita tiv e fe e d b a c k th a t is th e o p p o n e n t’s c o m m e n t to e a c h p ro p o s a l. T h ird , th e in te r a ttrib u te s ’ d e p e n d e n c ie s re s o lu tio n p ro c e s s p ro p o s e d in Q -N e g o tia tio n re a c h th e o p tim a l s o lu tio n k e e p in g in fo rm a tio n p riv a te a s m u c h a s p o s s ib le . O th e r k n o w n a p p ro a c h e s re la te d w ith d is trib u te d d e p e n d e n c ie s re s o lu tio n , e ith e r re a c h n o n -o p tim a l s o lu tio n s [8 , 9 ], o r im p o s e th e k n o w le d g e o f o th e r a g e n ts ’ p riv a te in fo rm a tio n to b e m a d e p u b lic [1 0 ].

Electronic Institutions

F o r th e V O o p e ra tio n s ta g m m itm e n t th a t is e s ta b lis h e d c le p re v io u s s ta g e . T h is c o m a s e d c o m m itm e n ts , th e E le c h a v io u r o f th e p a rtic ip a n t e n tra c t a c c o rd in g to tim e p o in ts W e in te n d to d e v e lo p in th e s e rv ic e s a p p ro p ria te fo r E le c tro n

c o c y p h b e c o

e w e h e re p ro p in th e e n d o f th e m itm e n t is th e n tro n ic In s titu tio n n titie s a t p re -s p e o r fu tu re e v e n ts . fu tu re k n o w le d g ic In s titu tio n s .

o s e th e e x n e g o tia tio n s p e c ifie d h a s th e c a c ifie d m o m

p lo ra tio p ro c e ss in a c o p a b ility e n ts p r

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o f a p h a se d d u rin g V O life n tra c t. T h ro u g h to m o n ito r th e e v ie w e d in th e

e re p re s e n ta tio n a n d o n to lo g y [1 5 ]

R efer en ces 1 . V u lk a n , N ., J e n n in g s , N .R .: E f f ic ie n t M e c h a n is m s f o r th e S u p p ly o f S e r v ic e s in M u lti- A g e n t E n v iro n m e n ts . 1 s t In t C o n f. o n In fo rm a tio n a n d C o m p u ta tio n E c o n o m ic s , C h a rle s to n (1 9 9 8 ) 2 . M a to s , S ., S ie r r a , C .: E v o lu tio n a r y C o m p u tin g a n d N e g o tia tio n A g e n ts . W o r k s h o p o n A g e n t M e d ia te d E le c tro n ic T ra d in g , M in n e a p o lis , U S A (1 9 9 8 ) 3 . F a is s t, W .: In fo rm a tio n T e c h n o lo g y a s a n E n a b le r o f V ir tu a l E n te r p r is e s : A L if e - c y c le o rie n te d D e s c rip tio n . E u ro p e a n C o n fe re n c e o n V irtu a l E n te rp ris e s a n d N e tw o rk S o lu tio n s , P a d e rb o rn , G e rm a n y (1 9 9 7 ) 4 . F is c h e r , K ., M u lle r , J .P ., H e im ig , I ., S c h e e r , A .: I n te llig e n t A g e n ts in V ir tu a l E n te r p r is e s . 1 s t In te rn a tio n a l C o n fe re n c e o n th e P ra tic a l A p p lic a tio n o f In te llig e n t A g e n ts a n d M u lti-A g e n t T e c h n o lo g y , L o n d o n , U K (1 9 9 6 ) 5 . W a tk in s , C .J .C .H ., D a y a n , P .: Q - L e a r n in g . M a c h in e L e a r n in g , V o l. 8 , N . 3 /4 . K lu w e r A c a d e m ic P u b lis h e rs , B o s to n (1 9 9 2 ) 2 7 9 -2 9 2 6 . O liv e ira , E ., R o c h a , A .P .: A g e n ts a d v a n c e d fe a tu re s fo r n e g o tia tio n in E le c tro n ic C o m m e rc e a n d V ir tu a l O r g a n is a tio n s f o r m a tio n p r o c e s s . I n : D ig n u m , F ., S ie r r a , C . ( e d s .) : A g e n t M e d ia te d E le c tro n ic C o m m e rc e , th e E u ro p e a n A g e n tL in k P e rs p e c tiv e . L e c tu re s N o te s in A rtific ia l In te llig e n c e , V o l. 1 9 9 1 . S p rin g e r-V e rla g (2 0 0 0 ) 7 7 -9 6 7 . Y o k o o , M ., D u r f e e , E ., I s h id a , T ., K u w a b a r a , K .: D is tr ib u te d C o n s tr a in t S a tis f a c tio n f o r F o rm a liz in g D is trib u te d P ro b le m S o lv in g . 1 2 th In te rn a tio n a l C o n fe re n c e o n D is trib u te d C o m p u tin g S y s te m s , Y o k o h a m a , J a p a n (1 9 9 2 ) 8 . A r m s tr o n g , A ., D u r f e e , E .: D y n a m ic P r io r itiz a tio n o f C o m p le x A g e n ts in D is tr ib u te d C o n s tra in t S a tis fa c tio n P ro b le m s . 1 5 th In te rn a tio n a l J o in t C o n fe re n c e o n A rtific ia l In te llig e n c e , N a g o y a , J a p a n (1 9 9 7 ) 9 . Y o k o o , M ., H ir a y a m a , K .: D is tr ib u te d C o n s tr a in t S a tis f a c tio n A lg o r ith m f o r C o m p le x L o c a l P ro b le m s . 3 rd In te rn a tio n a l C o n fe re n c e o n M u lti-A g e n t S y s te m s , P a ris , F ra n c e (1 9 9 8 ) 1 0 .P a r u n a k , H .V .D ., W a r d , A ., S a u te r , J .: T h e M a r C o n A lg o r ith m : A S y s te m a tic M a r k e t A p p ro a c h to D is trib u te d C o n s tra in t P ro b le m s . A rtific ia l In te llig e n c e fo r E n g in e e rin g D e s ig n , A n a ly s is a n d M a n u f a c tu r in g J ., V o l. 1 3 . C a m b r id g e U n iv . P r e s s ( 1 9 9 9 ) 2 1 7 - 2 3 4 1 1 .S m ith , R .G .: T h e C o n tr a c t N e t P r o to c o l: H ig h - L e v e l C o m m u n ic a tio n a n d C o n tr o l in a D is tr ib u te d P r o b le m S o lv e r . I E E E T r a n s . o n C o m p u te r s , V o l.2 9 , N .1 2 ( 1 9 8 0 ) 1 1 0 4 - 1 1 1 3 1 2 .S e n , S ., D u r f e e , E .: T h e r o le o f c o m m itm e n t in c o o p e r a tiv e n e g o tia tio n . I n te r n a tio n a l J o u r n a l o n I n te llig e n t C o o p e r a tiv e I n f o r m a tio n S y s te m s , V o l.3 , N .1 (1 9 9 4 ) 6 7 -8 1 1 3 .S a n d h o lm , T .W ., L e s s e r , V .R .: A d v a n ta g e s o f a L e v e le d C o m m itm e n t C o n tr a c tin g P r o to c o l. In P ro c e e d in g s o f th e N a t. C o n f. o n A rtific ia l In te llig e n c e (A A A I), P o rtla n d (1 9 9 6 ) 1 2 6 -1 3 3 1 4 .S a n d h o lm , T .: A g e n ts in E le c tr o n ic C o m m e r c e : C o m p o n e n t T e c h n o lo g ie s f o r A u to m a te d N e g o tia tio n a n d C o a litio n F o r m a tio n . A u to n o m o u s A g e n ts a n d M u lti- A g e n t S y s te m s , V o l,3 , N .1 . K lu w e r A c a d e m ic P u b lis h e r s ( 2 0 0 0 ) 7 3 - 9 6 1 5 .G r u b e r , T .R .: A T r a n s la tio n A p p r o a c h to P o r ta b le O n to lo g y S p e c if ic a tio n s . K n o w le d g e A c q u is itio n , V o l.5 , N .2 , ( 1 9 9 3 ) 1 9 9 - 2 2 0

An Im i ta ti on -B a s ed Ap p r oa ch to Mod eli n g H om og en ou s Ag en ts S oci eti es G o ra n T ra jk o v s k i W e s t V irg in ia U n iv e rs ity - P , 3 0 0 C a m p u s D riv e , P a rk e rs b u rg , W V , 2 6 1 0 4 , U S A E- mail: [email protected]

Abs tr a ct. T h e p r e s e n t p a p e r c o n c e n t r a t e s o n o n e m o d e l i n g a p p r o a c h f o r h o m o g e n o u s s o c ie tie s o f a g e n ts in a g iv e n e n v iro n m e n t. It is a n e x te n s io n o f th e e x is tin g In te ra c tiv is t-E x p e c ta tiv e T h e o ry o n A g e n c y a n d L e a rn in g to m u ltia g e n t e n v iro n m e n ts . T h e u n ia g e n t th e o ry ’s k e y p h ra s e s a re e x p e c ta n c y a n d le a rn in g th ro u g h in te ra c tio n s w ith th e e n v iro n m e n t. M o tiv a te d b y th e re s e a rc h d o n e in th e d o m a in o f im ita tio n in h u m a n s , th is p a p e r in tro d u c e s le a rn in g b y im ita tio n th ro u g h in te ra c tio n b e tw e e n a k in a g e n ts . T h e s o c ia l c o n s e q u e n c e s o f s u c h a n e n v iro n m e n t fro m th e p e rs p e c tiv e o f le a rn in g a n d e m e rg e n c e o f la n g u a g e a re d is c u s s e d a s w e ll.

1 In tr od u cti on In o u r w o rk o n w ith in th e In te ra c tiv is t-E x p e c ta tiv e T h e o ry o f A g e n c y a n d L e a rn in g (IE T A L ) [8 ], w e p ro p o s e d a n d in v e s tig a te d a le a rn in g p a ra d ig m in a u to n o m o u s a g e n ts in a u n ia g e n t e n v iro n m e n t. T h e k e y c o n c e p ts o f th is th e o ry a re e x p e c ta n c y a n d le a rn in g th e e n v iro n m e n t th ro u g h in te ra c tio n s , w h ile b u ild in g a n in trin s ic m o d e l o f it. D e p e n d in g o n th e s e t o f a c tiv e d riv e s , th e a g e n t u s e s th e a p p ro p ria te p ro je c tio n o f its in trin s ic m o d e l in o rd e r to n a v ig a te w ith in th e e n v iro n m e n t o n its q u e s t to s a tis fy th e s e t o f a c tiv e d riv e s . In th is p a p e r w e ta k e o ff w ith th e e x is tin g re s u lts o f th e th e o ry a n d p ro p o s e th e b a s is o f a m u ltia g e n t th e o ry , w h e re a p a rt fro m th e n o tio n s o f e x p e c ta n c y a n d le a rn in g th ro u g h in te ra c tio n s w ith th e e n v iro n m e n t, w e in tro d u c e in te ra c tio n , [2 ], b e tw e e n a lik e a g e n ts , in s p ire d b y re s e a rc h re s u lts o n th e p h e n o m e n o n o f im ita tio n [1 ], [4 ], in b o th n e u ro p h y s io lo g y a n d p s y c h o lo g y . T h e p a p e r is o rg a n iz e d a s fo llo w s . S e c tio n 2 s u m m a riz e s s o m e o f th e re le v a n t re s u lts in re s e a rc h o f th e p h e n o m e n o n o f im ita tio n in h u m a n s . In S e c tio n 3 , w e g iv e th e in tro d u c tio n to th e IE T A L T h e o ry . In S e c tio n 4 , w e fo rm a liz e a n in s ta n tia tio n o f th e IE T A L th e o ry in th e a g e n t th a t w e c a ll P e tita g é , w h ic h in te ra c ts w ith th e e n v iro n m e n t it is in , a n d b u ild s its in trin s ic m o d e l o f it. B y e q u ip p in g th e a g e n t w ith a s p e c ia l s e n s o r fo r s e n s in g th e a lik e a g e n ts , a n d e n a b lin g th e a g e n ts to e x c h a n g e e a c h o th e r’s c o n tin g e n c y ta b le s , w e a llo w th e u n it in a n e n v iro n m e n t in h a b ite d w ith P e tita g é -lik e a g e n ts to fu n c tio n a s a h o m o g e n o u s m u ltia g e n t w o rld w ith s o c ia lly a c tiv e a g e n ts . T h is e n v iro n m e n t a n d th e e m e rg e n c e o f la n g u a g e is th e fo c u s o f d is c u s s io n in S e c tio n 5 . T h e la s t s e c tio n o v e rv ie w s th e p a p e r, a n d s ta te s d ire c tio n s fo r fu rth e r in v e s tig a tio n in th e d o m a in .

P. Brazdil and A. Jorge (Eds.): EPIA 2001, LNAI 2258, pp. 246–252, 2001. c Springer-Verlag Berlin Heidelberg 2001 

An Imitation-Based Approach to Modeling Homogenous Agents Societies

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2 Im i ta ti on R ev i s i ted In a n d m o a m

th is s e c tio n w e s u m m a riz e re le v a n t re s u lts fro m re s e a rc h fro m n e u ro p h y s io lo g y p s y c h o lo g y a p p lic a b le in th e d o m a in o f im ita tio n , in o u r a p p ro a c h to w a rd s th e d e lin g o f th e m u ltia g e n t s o c ie ty . T h is a p p ro a c h is ju s tifia b le b y th e e ffo rts to w a rd s o re e ffic ie n t le a rn in g p a ra d ig m in a g e n ts w ith th e e m b o d ie d m in d p a ra d ig m . T h e c o n c e p t o f le a rn in g b y im ita tio n (le a rn in g b y w a tc h in g , , te a c h in g b y s h o w in g ) is c e rta in ly n o t a n e w o n e . T h o rn d ik e [1 0 ] d e fin e s it a s “ [im ita tio n is ] le a rn in g to d o a n a c t fro m s e e in g it d o n e , w h e re a s P ia g e t [5 ] m e n tio n e d a s a m a jo r p a rt w h e n o ffe rin g h is th e o ry fo r d e v e lo p m e n t o f th e a b ility to im ita te g o in g th ro u g h s ix s ta g e s . A fte r P ia g e t th e in te re s t in (m o v e m e n t) im ita tio n d im in is h e d , p a rtia lly b e c a u s e o f th e p re ju d ic e th a t “ m im ic k in g ” o r “ im ita tin g ” is n o t a n e x p re s s io n o f h ig h e r in te llig e n c e , [7 ]. Im ita tio n is , th o u g h , fa r fro m b e in g a triv ia l ta s k . It is ra th e r a h ig h ly c re a tiv e m a p p in g b e tw e e n th e a c tio n s a n d th e ir c o n s e q u e n c e s o f th e o th e r a n d o f o n e -s e lf’s (v is u a l in p u t-m o to r c o m m a n d s -c o n s e q u e n c e s e v a lu a tio n ). R iz z o la tti e t a l, [6 ], d is c o v e r th e s o c a lle d “ m irro r n e u ro n s ” - n e u ro n s th a t fire w h ile o n e is p e rfo rm in g s o m e m o to r a c tio n s o r lo o k a t s o m e b o d y e ls e d o in g th e s a m e a c tio n . T h is fin d in g o f R iz z o la tti m a y g iv e in s ig h ts in o u r e m p a th iz in g a b ilitie s a s w e ll a s o u r “ o th e r m in d re a d in g ” a b ilitie s . It s ta te s th a t in th e a d d itio n o f th e firs t p e rs o n p o in t o f v ie w (s u b je c tiv e e x p e rie n c e ) a n d th e th ird p e rs o n p o in t o f v ie w (s c ie n tific , o r o b je c tiv e s ta n c e ) w e h a v e a s p e c ia l w ith in -th e -s p e c ie s s h a re d p o in t o f v ie w d e d ic a te d o n u n d e rs ta n d in g o th e rs o f th e s a m e s p e c ie s . C o n s e q u e n c e s fo r c o g n itiv e s c ie n c e a n d A I in c lu d e p u ttin g ra d ic a l c o n s tra in ts w ith in th e s p a c e o f p o s s ib le m o d e ls o f th e m in d W ith in th e c la s s ic a l, d is e m b o d ie d a p p ro a c h re c o g n iz in g a n d c o m m u n ic a tin g w ith o th e r s w a s n o t a r e a l p r o b le m . N e w k n o w le d g e ( i.e . n e w c o m b in a tio n s o f s y m b o ls ) w a s e a s ily c o m m u n ic a te d v ia in h e re n tly lin g u is tic te rm s , d u e to th e a s s u m p tio n th a t e v e ry b o d y a n d e v e ry th in g h a v e a c c e s s to s o m e in te rn a l m irro r re p re s e n ta tio n , [3 ].

3 B a s i cs of the U n i Ag en t T heor y In th is s e c tio n w e s u m m a riz e th e u n ia g e n t IE T A L th e o ry in o rd e r to fa c ilita te th e c o m m u n ic a tio n o f id e a s in th e re m a in in g p a rt o f th e p a p e r. T h e n o tio n o f e x p e c ta n c y h a s a c e n tra l ro le in th is th e o ry , a n d th e a g e n t, w h ile b e in g in th e e n v iro n m e n t, a n tic ip a te s th e e ffe c ts o f its o w n a c tio n s in th e w o rld . In o rd e r to a v o id a n y p o s s ib le te rm in o lo g ic a l c o n fu s io n , w e g iv e th e fo llo w in g e x p la n a tio n . A n a g e n t is s a id to b e a w a r e o f th e e n v iro n m e n t it in h a b its if it c a n a n tic ip a te th e re s u lts o f h is o w n a c tio n s . T h is m e a n s th a t, g iv e n s o m e c u rre n t p e rc e p t p th e a g e n t c a n g e n e r a te e x p e c ta n c ie s a b o u t th e r e s u ltin g p e r c e p ts p 1, p 2,... if it a p p lie s a c tio n s a 1, a 2... A f te r in h a b itin g s o m e e n v ir o n m e n t f o r c e r ta in tim e , a n a g e n t b u ild s a n e t w o r k o f s u c h e x p e c t a n c y t r i p l e t s p i- a j- p k . T h i s b r i n g s u s t o t h e s e c o n d k e y c o n c e p t in o u r th e o ry o f a g e n c y , n a m e ly th e c o n c e p t o f a g e n t e n v iro n m e n t in te ra c tio n .A s w e s e e , th e m a in p ro b le m s a re : firs t, to le a rn th e g ra p h a n d s e c o n d , to k n o w h o w to u s e it.

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4 F or m a li z a ti on of the Ag en t In m fo a g

th is S e c tio n w e g iv e a n a lg e b ra ic fo rm a liz a tio n o f th e a g e n t th a t in h a b its th e u ltia g e n t e n v iro n m e n t, [1 1 ]. F o rm a liz in g th e a g e n t a n d its in te ra c tio n (s ) is c ru c ia l r th e e x p e rim e n ta l s e tu p s in th e e x p lo ra tio n o f th e e ffic ie n c y o f th e a p p ro a c h . T h e e n t is g a in in g its k n o w le d g e th ro u g h o u t its s ta y in th e e n v iro n m e n t. If w e s p e a k in te rm s o f g ra p h s , w e m a y d e p ic t th is s itu a tio n w ith a g ra p h w h o s e n o d e s a re la b e le d a n d th e s e la b e ls m a y b e s a m e fo r d iffe re n t n o d e s . T h e o n ly w a y a n o d e c a n b e re c o g n iz e d a s d iffe re n t th e n is to e x a m in e its c o n te x t. C o n te x t o f a n o d e is a tre e -lik e d a ta s tru c tu re d e fin e d re c u rs iv e ly a s a ll fo llo w e rs o f th e n o d e to g e th e r w ith th e ir c o n te x ts . In [1 1 ], w e h a v e p re s e n te d le a rn in g a lg o rith m s in s p ire d b y b io lo g ic a l s y s te m s . L e t V = { v , v , ..., v } b e a f in ite n o n e m p ty s e t o f v e r tic e s a n d A = { s ,s , ... , s } a 1 2 n 1 2 m fin ite n o n e m p ty s e t o f a c tio n s w ith im p lic it o rd e rin g in d u c e d b y th e in d e x in g . L e t th e p a i r G s = ( V , r ) , s ∈A , w h e r e r ⊆V ×V , b e o r i e n t e d r e g u l a r g r a p h w i t h m a t r i x o f s

s

i n c i d e n c e o f t h e r e l a t i o n r f o r e v e r y s ∈A s c o lu m n . T h e g ra p h G ' =

(V ,

th a t c o n ta in s e x a c tly o n e e le m e n t 1 in e a c h

U r s ) w ill b e c a lle d g r a p h o f g e n e r a l c o n n e c tiv ity o f th e s ∈V

fa m ily o f g ra p h s { G r ⊆( V ×V ) ×A , re p re s e n ts a n s e t o f a c tio n s L e t L = { l , 1 o f th e v e rte x a lia s in g . T h e g ra p h is th e D e s ig n V is ib le E n v ir D u rin g its a n d b u ild s its

s

d e fin e d o r ie n te d o f G .. l , ..., l } 2 k se t o f

: s ∈A } . I f t h e g r a p h G ' i s c o n n e c t e d , t h e n t h e t r i p l e t G = ( V , A , r ) , a s f o l l o w s ( ( v , v ) , s ) ∈r i f a n d o n l y i f ( v , v ) ∈r v , v ∈V , s ∈A , 1 2 1 2 s 1 2 g r a p h w ith m a r k e d e d g e s . V is s e t o f v e rtic e s , r re la tio n , a n d A b e a s e t o f l a b e l s ( a n d f : V →L a s u r j e c t i o n . F i s c a l l e d l a b e l i n g G , a n d it e n d o rs e s th e p o s s ib ility o f m o d e lin g th e p e rc e p tu a l

th a t w e , a s d e s ig n e rs o f e r V is ib le E n v iro n m e n o n m e n t (m o d e l). T h is is s ta y in th e e n v iro n m e n in trin s ic re p re s e n ta tio n

th e e x p e r t, a n d th e w h a t th e t, th e a g e o f th e e n v

im e n ta l s e tu p , s e e g r a p h G ''' = ( L , a g e n t is a b le to “ s n t is in te ra c tin g w iro n m e n t (F ig 1 ).

G " = (V , A , L , r, f) is r ''', A ) i s t h e A g e n t e e ” . ith th e e n v iro n m e n t,

W h e n th e , s a y , h u n g e r d riv e is a c tiv a te d fo r th e firs t tim e , th e a g e n t p e rfo rm s ra n d o m w a lk d u rin g w h ic h e x p e c ta n c ie s a re s to re d in th e a s s o c ia tiv e m e m o ry . T h e e m o tio n a l c o n te x ts o f th e s e e x p e c ta n c ie s a re n e u tra l u n til fo o d is s e n s e d . O n c e th is h a p p e n s , c u rre n t e x p e c ta n c y e m o tio n a l c o n te x t is s e t to p o s itiv e v a lu e . T h is v a lu e is th e n e x p o n e n tia lly d e c re m e n te d a n d p ro p a g a te d b a c k w a rd s fo llo w in g th e re c e n t p e rc e p ts . E v e ry n e x t fu tu re tim e th e h u n g e r d riv e is a c tiv a te d , th e a g e n t u s e s th e c o n te x t v a lu e s o f th e e x p e c ta n c ie s to d ire c t its a c tio n s . It c h o o s e s , o f c o u rs e , th e a c tio n th a t w ill le a d to e x p e c ta n c y w ith m a x im u m c o n te x t v a lu e . If a ll th e e x p e c ta n c ie s fo r th e c u rre n t p e rc e p tu a l s ta te a re n e u tra l, ra n d o m w a lk is p e rfo rm e d . A g a in , w h e n fo o d is s e n s e d e m o tio n a l c o n te x ts a re a d ju s te d in th e p re v io u s ly d e s c rib e d m a n n e r. Generate_Intrinsic_Representation (G: Interaction_Graph, ξ: Schema; GIR: Assotiative_Memory)

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BEGIN_P ROCEDURE Initialize (RΔ= ∅); Initialize_Position (G; Position); Try (Position, ξ; (B1 , S1 )); Add ( [(λ, λ), (B1 ,S1 )]; RΔ); WHILE (Active_Drive_Not_Satisfied) DO Try (Position, ξ; (B2 , S2 )); Add ([(B1 , S1 ), (B2 , S2 )]; RΔ); (B1 , S1 ):= (B2 , S2 ); END_WHILE Propagate_Context ( (B1 , S1 ), drive; GIR). END_P ROCEDURE Try (Position: Location_In_Interaction_Graph, ξ: Schema; (B, S): Percepts_Actions_Pair) BEGIN_P ROCEDURE S:= λ; TryIn (Position, ξ; (Add (S, Current_Percept), B)); REPEAT TryIn (Position, B; (Add (S, Current_Percept), B) U NTIL NOT enabled (B) END_P ROCEDURE P ropagate_Context (d: drive; GIR: Assotiative_Memory) BEGIN_PROCEDU RE N:= 0 ; WHILE (B1 , S1 ) ∈Projection2 (GIR) DO Projection3(GIR) := exp(- N); INC (N) END_WHILE END_P ROCEDURE F ig .1 .A p o s s ib le im p le m e n ta tio n o f th e le a r n in g p r o c e d u r e f o r th e a u to n o m o u s a g e n t.

T h e w a y th e a g e n t “ p e rc e iv e s ” th e e n v iro n m e n t is d iffe re n t w h e n d iffe re n t d riv e s a re a c tiv e . T h a t m e a n s th a t it u s e s d iffe re n t in s ta n tia tio n s , d e p e n d in g o n th e g iv e n s e t o f d riv e s . It is re a lis tic to a s s u m e th a t th e d riv e s a re o rd e re d in a c o m p le te s u b -s e m ila ttic e m a n n e r (m e a n in g th a t e v e ry s u b s e t o f d riv e s h a s its m a x im u m w ith in th e s tru c tu re o f d riv e s ). T h e to p o f th e d riv e s tru c tu re in a ll a g e n ts in th e m u ltia g e n t s o c ie ty is th e d riv e to im ita te th e a g e n ts “ in s ig h t” . O n c e tw o a g e n ts s e n s e e a c h o th e r, th e y s h ift to th e im ita tio n m o d e , in w h ic h th e y e x c h a n g e th e ir c o n tin g e n c y ta b le s . T h e d is c u s s io n s o n th e c o n s e q u e n c e s o f th e in te r-a g e n t in te ra c tio n a re d is c u s s e d in th e fo llo w in g s e c tio n .

5 T he Mu lti a g en t S oci ety In th is S e c tio n w e g iv e a P e tita g é -lik e a g e n ts , th a t a in tra a g e n t c o m m u n ic a tio n in th e e n d o f th e S e c tio n . A s d is c u s s e d b e fo re , th e o th e r P e tita g é -lik e a g e n ts in

d e s c rip tio n o f a m u ltia g e n t e n v iro n m e n t in h a b ite d b y re a b le to im ita te th e ir c o h a b ita n ts . T h e p ro b le m s o f h e te ro g e n e o u s m u ltia g e n t e n v iro n m e n ts a re d is c u s s e d a t a g e n t is e q u ip p e d w ith a s p e c ia l s e n s o r th a t is s e n s in g th e s a m e e n v iro n m e n t. T h e s e n s o r is w o rk in g in p a ra lle l

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w ith th e o th e r s e n s o rs . S e n s in g a n o th e r P e tita g é ta k e s th e a g e n t in to its im ita tin g m o d e , d u rin g w h ic h th e a g e n ts e x c h a n g e th e ir c o n tin g e n c y ta b le s . T h e ta b le s a re b e in g u p d a te d b y n e w ro w s . L e t u s s u p p o s e th a t th e c o n tin g e n c y ta b le o f o n e o f th e a g e n t h a s M ro w s , a n d o f th e o th e r N ro w s . A fte r th e p ro c e s s o f e x c h a n g e o f th e c o n tin g e n c y ta b le , b o th o f th e a g e n ts u p d a te th e ir ta b le s , w ith th e u n io n o f th e ir in d iv id u a l ta b le s . In m a th e m a tic a l te rm s , th a t w o u ld m e a n th a t th e c a rd in a lity o f th e re la tio n s (n u m b e r o f ro w s o f th e c o n tin g e n c y ta b le ) w ill b e a t m o s t M + N . T h e a g e n ts m ig h t h a v e b e e n v is itin g d iffe re n t a re a s o f th e e n v iro n m e n t d u rin g th e ir w a lk th ro u g h th e e n v iro n m e n t, o r a re a s th a t a re p e rc e p tu a lly v e ry s im ila r to e a c h o th e r , w h ic h th e y h a v e in h a b ite d f o r d u r a tio n s o f tim e T 1, a n d T 2 r e s p e c tiv e ly . D e p e n d in g o n th e to p o lo g y o f th o s e a re a s o f th e e n v iro n m e n t, a n d th e ir s im ila rity , th e in te rs e c tio n o f th e re la tio n s c a n ra n g e b e tw e e n 0 a n d m in { M , N } , th e firs t c o rre s p o n d in g to a v is ita tio n to p e rc e p tu a lly d iffe re n t e n v iro n m e n ts , a n d th e la tte r to v is ita tio n o f p e rc e p tu a lly v e ry s im ila r e n v iro n m e n ts . T h e re s u lts fo rm th e u n ia g e n t IE T A L c a n n o t b e g e n e ra liz e d to s ta te th a t th e lo n g e r a n a g e n t h a s b e e n in th e e n v iro n m e n t, th e “ lo n g e r” th e c o n tin g e n c y ta b le w ill b e . T h e r e f o r e , th e “ a g e d iff e r e n c e ” a b s ( T 1- T 2) h a s n o in f lu e n c e o n th e s h a p e s o n th e le a rn in g c u rv e s . O n th e o th e r h a n d , th e le a rn in g c u rv e d e c re a s e s in tim e , [8 ]. H o w e v e r, d u e to th e s o lu tio n o f th e p ro b le m o f c y c lin g in a s im u la te d e n v iro n m e n t b y in tro d u c tio n o f ra n d o m m o v e s o n c e c y c lin g is d e te c te d , th e o d d s o f th e a g e n t to e x p lo re a m o re c o m p re h e n s iv e p a rt o f th e w h o le e n v iro n m e n t a re in c re a s e d . N e v e rth e le s s , a fte r th e p ro c e s s o f in fo rm a tio n in te rc h a n g e , th e le a rn in g c u rv e d ro p s , a n d is in th e b a n d b e tw e e n th e tim e a x is a n d th e lo w e r o f th e in d iv id u a l le a rn in g c u rv e s o f e a c h o f th e a g e n ts . U p o n th e firs t lo o k th e s o c ie ty o f P e tita g é s w o u ld b e e a s ily o rd e re d b y th e a m o u n t o f in fo rm a tio n c o n ta in e d in th e c o n tin g e n c y ta b le s . H o w e v e r, d u e to th e h is to ry o f th e a g e n t a n d th e p a rt o f th e e n v iro n m e n t v is ite d s in c e , th e a g e n ts in th e e n v iro n m e n t c a n n o t b e o rd e re d in a lin e a r m a n n e r b y in c lu s io n o f th e c o n tin g e n c y ta b le s . A lg e b ra ic a lly , th e s tru c tu re w ith a c a rrie r a ll p o s s ib le c o n tin g e n c y ta b le s in a g iv e n e n v iro n m e n t, o rd e re d b y s e t in c lu s io n , fro m th e d e s ig n e r’s p o in t o f v ie w , is a la ttic e th a t w e re fe r to a s th e la ttic e P o f a ll P e tita g é s . T h e b o tto m e le m e n t a n a g e n t w ith n o k n o w le d g e o f th e e n v iro n m e n t, w h ic h h a s b e e n m a d e in h a b ita n t o f th e e n v iro n m e n t, a n d to p a n a g e n t th a t h a s b e e n in th e e n v iro n m e n t lo n g e n o u g h to k n o w e v e ry th in g . T h e a g e n ts w ill c lu s te riz e in s u b la ttic e s o f a g e n ts th a t h a v e b e e n v is itin g s im ila r a re a s o f th e e n v iro n m e n t. A s a g e n ts c o m e in to th e e n v iro n m e n t a n d s ta rt le a rn in g , th e y w a lk th ro u g h P , to o , m o v in g in th e d ire c tio n o f th e to p e le m e n t. A ll th e a g e n ts in th e e n v iro n m e n t a t a g iv e n tim e t, c o n s is t a s tru c tu re S (t), th a t is a g e n e ra l p a rtia lly o rd e re d s e t b y in c lu s io n , w ith b o th c o m p a ra b le a n d in c o m p a ra b le e le m e n ts . In o th e r te rm s , a s a g ra p h it m a y n o t b e c o n n e c te d a t a g iv e n p o in t in tim e . E v e ry e le m e n t o f th e s u b s tru c tu re o f th e h ie ra rc h y ro o te d a t a g iv e n a g e n t A , k n o w s w h a t A k n o w s a t l e a s t w h a t A k n o w s . Its c o n tin g e n c y ta b le is s u b s e t o f th e ta b le s o f th e a g e n ts c o m p a ra b le a n d h ig h e r to A in P . T h e c o n tin g e n c y ta b le o f th e r o o t o f t h e c l a s s o f a g e n t s r o o t e d a t A a t i n P w i l l b e r e f e r r e d a s t o a n en tr y i n t h e i r lex i con . A f t e r a n i m i t a t i o n i n s t a n c e , t h e i r l e x i c o n w i l l n a t u r a l l y c h a n g e b y e x p a n d i n g th e le x ic o n .

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F ig . 2 . T h e la ttic e o f h ie ra rc h y o f a ll p o s s ib le a g e n ts (le ft). A fte r th e im ita tio n , b o th a g e n ts in v o lv e d in th e c o n tin g e n c y ta b le in te rc h a n g e , a re p ro p a g a te d u p w a rd s in th e la ttic e P . C T s ta n d s fo r c o n tin g e n c y ta b le , A 1 a n d A 2 a re a g e n ts .

T h e le x ic o n s h o u ld b e u n d e rs to o d a s a s y s te m o f a c tiv itie s th a t a ll th e a g e n ts in th e c la s s c a n p e rfo rm . T h e la n g u a g e o f th e A A s o c ie ty w ill c o n s is t o f th e u n io n o f le x ic o g ra p h ic e n trie s o f a ll a g e n ts c u rre n tly in th e e n v iro n m e n t. N o g e n e ra l in te rre la tio n c a n b e s ta te d b e tw e e n th e k n o w le d g e a n d th e a g e h ie ra rc h ie s o f th e a g e n ts in th e w o rld o f P e tita g é s . A s s ta te d b e fo re , n o g u a ra n te e c a n b e g iv e n th a t th e lo n g e r a n a g e n t in h a b its th e e n v iro n m e n t, th e m o re it “ k n o w s ” . T h e s a m e s ta te m e n t h o ld s e v e n f o r a g e n ts w ith th e s a m e le x ic o n s , i.e . b e lo n g in g to a c la s s ro o te d a t th e s a m e a g e n t in P o r S (t). T h e p ro b le m o f in a b ility to e x c h a n g e th e w h o le c o n tin g e n c y ta b le s d u e to h a rd w a re o r tim e c o n s tra in ts is a p ra c tic a l c o n s tra in t th a t n e e d s to b e ta k e n in to s e rio u s c o n s id e ra tio n s w h ile s im u la tin g a m u ltia g e n t e n v iro n m e n t in h a b ite d b y P e tita g é -lik e a g e n ts . T h e p ro b le m o ff la c k o f tim e fo r c o n v e n tio n (th e o th e r a g e n t g o t o u t o f s ig h t b e fo re th e c o n tin g e n c y ta b le s w e re e x c h a n g e d ) is n o t a s s e v e re a s th e p ro b le m o f h a rd w a re m e m o ry c o n s tra in ts . T h e im ita tio n s ta g e p u lls b o th a g e n ts h ig h e r in P ; th e y a c tu a lly g a in m o re k n o w le d g e o f th e e n v iro n m e n t. W h ile a d d re s s in g th e m e m o ry p ro b le m , p o lic ie s o f fo rg e ttin g n e e d to b e d e v is e d .

6 Con clu s i on s a n d D i r ecti on s for F u r ther W

or k

In th is p a p e r w e p ro p o s e d a m o d e l fo r a m u ltia g e n t s o c ie ty , b a s e d o n e x p e c ta n c y a n d in te ra c tio n . B a s e d o n re s u lts o n im ita tio n s , w e p ro p o s e d a m u ltia g e n t v e rs io n o f th e IE T A L th e o ry . T h e P e tita g é -lik e a g e n ts in h a b it th e s a m e e n v iro n m e n t a n d in te ra c t w ith e a c h o th e r u s in g im ita tio n . T h e d riv e to im ita te is th e h ig h e s t o n th e h ie ra rc h y o f d riv e s o f a ll a g e n ts . A fte r th e c o n v e n tio n o f tw o a g e n ts , th e y in te rc h a n g e th e ir c o n tin g e n c y ta b le s , a n d c o n tin u e to e x p lo re th e e n v iro n m e n t. T h e p ro b le m s a s s o c ia te d w ith th e im ita tio n s ta g e s a n d th e c h a n g e s in th e a g e n ts h a v e b e e n o b s e rv e d fro m d iffe re n t a n g le s . T h e a b u n d a n c e o f a p p ro a c h e s to w a rd s m u ltia g e n t s y s te m s th a t a re n o t n e c e s s a rily c o m p lia n t w ith th e m a in s tre a m A I, g iv e u s th e m o tiv a tio n to e x p lo re fu rth e r th e th e o ry . In a n u p c o m in g s ta g e o f o u r re s e a rc h , w e w ill s im u la te th e W o rld o f P e tita g é s , a n d e x p lo re th e p ro b le m s th a t s u c h a s im u la tio n w ill re v e a l, fo r a la te r im p le m e n ta tio n o f th e a p p ro a c h in ro b o tic a g e n ts .

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Goran Trajkovski

R efer en ces [1 ] [2 ] [3 [4 [5 [6 [7 [8 [9 [1 [1

B y rn e R W , R u s s o n A E , “ L e a rn in g b y Im ita tio n ” , B e h a v io ra l a n d B ra in S c ie n c e s (2 0 0 1 ). F e rb e r J : M u lti-A g e n t S y s te m s : A n In tro d u c tio n to D is trib u te d A rtific ia l In te llig e n c e , A d d is o n -W e s le y , 1 9 9 9 . ] F ik e s R E , N ils s o n N J , ” L e a rn in g a n d e x e c u tin g g e n e ra liz e d ro b o t p la n s ” , A rtific ia l In te llig e n c e , 3 (4 ) (1 9 7 2 ). ] N e h a n iv C , D a u te n h a h n K , “ M a p p in g b e tw e e n d is s im ila r b o d ie s : A ffo rd a n c e s a n d th e a lg e b ra ic fo u n d a tio n s o f im ita tio n ” , P ro c e e d in g s o f th e S e v e n th E u ro p e a n W o rk s h o p o n L e a rn in g R o b o ts E d in b u rg h , U K (1 9 9 8 ) 6 4 --7 2 . ] P ia g e t, J P la y , D re a m s , a n d Im ita tio n in C h ild h o o d , N o rto n , N e w Y o rk , 1 9 4 5 . ] R iz z o la tti G , F a d ig a L , G a lle s e V , F o g a s s i L , P re m o to r c o rte x a n d th e re c o g n itio n o f m o to r a c tio n s . C o g n itiv e B ra in R e s e a rc h , 3 (2 ) (1 9 9 6 ) 1 3 1 -1 4 1 ] S c h a a l S , S te rn a d D , “ P ro g ra m m a b le p a tte rn g e n e ra to rs ” , P ro c e e d in g s , 3 rd In te rn a tio n a l C o n fe re n c e o n C o m p u ta tio n a l In te llig e n c e in N e u ro s c ie n c e ” , R e s e a rc h T ria n g le P a rk , N C , (1 9 9 8 ) 4 8 -5 1 . ] S to ja n o v G , B o z in o v s k i S , T ra jk o v s k i G , “ In te ra c tio n is t-E x p e c ta tiv e V ie w o n A g e n c y a n d L e a rn in g " , IM A C S J o u rn a l fo r M a th e m a tic s a n d C o m p u te rs in S im u la tio n , N o rth -H o lla n d P u b lis h e rs , A m s te rd a m , V o l. 4 4 (1 9 9 7 ). ] S to ja n o v G , T ra jk o v s k i G , B o z in o v s k i S , “ T h e S ta tu s o f R e p re s e n ta tio n in B e h a v io r B a s e d R o b o tic S y s te m s : T h e P ro b le m a n d A S o lu tio n ” , IE E E C o n fe re n c e S y s te m s , M a n , a n d C y b e rn e tic s , O rla n d o (1 9 9 7 ). 0 ] T h o rn d ik e E L , “ A n im a l in te llig e n c e : a n e x p e rim e n ta l s tu d y o f th e a s s o c ia tiv e p ro c e s s in a n im a ls ” P s y c h o lo g ic a l R e v ie w M o n o g ra p h 2 (8 ) (1 8 9 8 ) 5 5 1 -5 5 3 . 1 ] T ra jk o v s k i G , S to ja n o v G , “ A lg e b ra ic F o rm a liz a tio n o f E n v iro n m e n t R e p re s e n ta tio n ” , in : ( T a ta i, G ., G u ly a s , L . ( e d s ) ) A g e n ts E v e r y w h e r e , S p r in g e r , B u d a p e s t, H U ( 1 9 9 8 ) 5 9 - 6 5 .

Situation Calculus as H ybrid Logic: First Steps Patrick Blackburn1 , Jaap Kamps2 , and Maarten Marx2 2

1 INRIA, Lorraine, Nancy, France. [email protected] ILLC, University of Amsterdam, Plantage Muidergracht 24, 1018TV Amsterdam, the Netherlands. {kamps,marx}@science.uva.nl

Abstract. The situation calculus, originally conceived by John McCarthy, is one of the main representation languages in artificial intelligence. The original papers introducing the situation calculus also highlight the connection between the fields of artificial intelligence and philosophical logic (especially modal logics of belief, knowledge, and tense). Modal logic changed enormously since the 60s. This paper sets out to revive the connection between situation calculus and modal logic. In particular, we will show that quantified hybrid logic, QHL, is able to express situation calculus formulas often more natural and concise than the original formulations. The main contribution of this paper is a new quantified hybrid logic with temporal operators and action modalities, tailor-made for expressing the fluents of situation calculus.

1

Introduction

The seminal paper that McCarthy and Hayes published in 1969, Some Philosophical Problems from the Standpoint of Artificial Intelligence, marks a watershed in artificial intelligence. It is the key reference for one of its main representation languages—the situation calculus. We will focus here on the original version of situation calculus ([13,14]; sometimes called the “snapshots” version, to distinguish it from other variants). The most important construct of situation calculus is—no surprise—situations. As [13] has it: One of the basic entities in our theory is the situation. Intuitively, a situation is the complete state of affairs at some instant of time. . . . Since a situation is defined as a complete state of affairs, we can never describe a situation fully; and we therefore provide no notation for doing so in our theory. Instead, we state facts about situations in the language of an extended predicate calculus. Examples of such facts are 1. raining(s) meaning that it is raining in situation s.

The situations are fully informed instances of the world of which we have limited knowledge, but still occur in the object language—this is what modal logicians now call a hybrid language. Precisely the same intuition is present in the writings of Arthur Prior, the founder of temporal logic [17]. McCarthy and Hayes [14] praise Prior’s work. They include his temporal operators into the situation calculus and they note the similarity 

This research was supported by the Netherlands Organization for Scientific Research (NWO, grants # 400-20-036 and # 612-62-001). This work was carried out as part of the INRIA funded partnership between CALG (Computational and Applied Logic Group, University of Amsterdam) and LED (Langue et Dialogue, LORIA, Nancy).

P. Brazdil and A. Jorge (Eds.): EPIA 2001, LNAI 2258, pp. 253–260, 2001. c Springer-Verlag Berlin Heidelberg 2001 

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of their use of situation variables to Prior’s time-instants. But that is it. Apart from this promising beginning, the languages of situation calculus and the modal languages based on Kripke’s and Prior’s work have always stayed far removed from each other. We think this is at least partly due to historical reasons. First of all, Prior’s writing is notoriously difficult. Secondly, in the late 60’s first order modal logic was a hot topic but the debate centered around all its philosophical problems. At that time hardly anyone saw it as a useful language for doing knowledge representation, with McCarthy and Hayes as notable exceptions. In fact, Prior is an exception too; he saw that modal logic could be used for a general (dynamic) theory of information. Another important reason was the inadequate expressive power of the available modal languages for the purposes McCarthy and Hayes had in mind. Since the late 60’s, this situation has changed considerably. First and foremost, we know now that actions can be naturally represented in dynamic logic, a branch of modal logic.1 Secondly, nowadays modal logic has become a respectable member in the field of knowledge representation, be it under the name of description logic.2 Finally, the 90’s saw the emergence of a branch of modal logic called hybrid logic which took up, or sometimes reinvented, many of Prior’s ideas. E.g., seemingly unaware of Prior, Passy and Tinchev [15] argue for the introduction of names for states in dynamic logic. Hybrid logic adds to modal logic explicit reference to states, a mechanism to bind variables to states (the modal–logical term for situation), and a holds operator @i φ, allowing one to express that a formula φ holds at a state named i. The purpose of this paper is to introduce hybrid logic to the artificial intelligence community. We will do this by showing that hybrid logic is very well suited to express what is normally formulated in the situation calculus. We have chosen for a comparison with the very first situation calculus language, from [14]. Our prime reason for choosing [14], apart from the fact that it started the field, is that one can feel their struggle with the first order language they are using. They have to introduce λ–abstraction, and all the time they introduce abbreviations to make their formulas look intuitive. These abbreviations foreshadowed a number of later technical developments in modal logic (e.g., van Benthem’s celebrated standard translation into first order logic). In fact, we see McCarthy and Hayes as forerunners of the use of modal logic as a knowledge representation language and would not be surprized if they had used hybridized first order modal logic to state the situation calculus if only the right ingredients had been available when they wrote their article. The rest of this paper is structured as follows. We start with with a brief introduction to hybrid logic. In the main part of the paper we show how to express typical situation calculus statements in hybrid logic. Here we gently introduce the notions of hybrid logic and show their use in examples. Rigorous definitions of its syntax and semantics are provided in the appendix. We end with a discussion of the presented work. 1

2

Dynamic logic originates with V. Pratt [16]. The recent monograph [10] contains many applications of dynamic logic to computer science. The rendering of a version of the situation calculus in GOLOG by Levesque, Pirri and Reiter [12] is also based on dynamic logic. Description logic [5,8] evolved out of Brachman and Schmolze’s knowledge representation language KL–ONE [6]. There are now a number of very fast DL provers for very expressive (exptime complete) languages, e.g., DLP and Racer, cf., the DL web page http://dl.kr.org/.

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2

255

H ybrid Logic

The rapidly growing field of hybrid logic, although rooted in the philosophical logic of Prior, is now being recognized as a tool in the field of knowledge representation. Hybrid logic has close connections with the field of description logic (cf., the page http://dl.kr.org/ or [8]). At present, several description logic theorem provers are being adjusted to handle the full nominals of hybrid logic. These provers handle propositional hybrid fragments with an exponential time worst case complexity with surprising efficiency. The proof and model theory of propositional hybrid logic is by now understood very well [3,2]. Recent unpublished work on first order hybrid logic indicates it has enormous advantages over first order modal logic. For instance, a complete analytic tableau system exists which also yields interpolants. One of the strong indications that something is missing in the usual formulation of first order modal logic is its failure of the interpolation property [9]. The computational and applied logic group at the University of Amsterdam is currently implementing a resolution–based theorem prover for hybrid logic. Carlos Areces maintains a web page devoted to hybrid logic at http://www.hylo.net. There have been a number of hybrid logic (HyLo) workshops. The next will be held as a LICS–affiliated workshop during the summer of 2002.

3

Situation Calculus as H ybrid Logic, First Steps

In this section we argue that hybrid logic is an excellently suited formalism to speak about situations and fluents. We do this by reviewing the key examples in [14] and reformulate them in hybrid logic. The hybrid language will be introduced informally and step by step. A rigorous formal definition of the resulting quantified hybrid logic can be found in the Appendix. McCarthy and Hayes seem very much willing to suppress the situation argument in their formulas, just as in first order modal logic. This shows in all example formulas in section 2 of [14]. They find it unnatural (and going against natural language practice) to add an extra argument to each predicate symbol for the situation. For example “John loves Mary” has to be expressed as love(j, m, s) where s refers to a situation. For this reason they introduce “abbreviations” in which this extra argument is suppressed. (We write this between quotes as the syntactical status of these formulas is not always clear.) Still they cannot do this in all cases because they sometimes need to refer to situations explicitly. They note the similarity with Prior’s nominals: The use of situation variables is analogous to the use of time-instants in the calculi of world-states which Prior [17] calls U -T calculi. [14, p.480]

We will now show that the modern treatment of Prior’s ideas which has become known under the name of hybrid logic provides exactly the linguistic elements that McCarthy and Hayes seemed to be searching for. The two most important semantic constructs in the situation calculus are the situation and the fluent. A situation is the complete state of the universe at an instant of time. A fluent is a function whose domain is the set of situations. Propositional fluents are fluents

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whose range is the set of truth values {true, false}. Situational fluents are those whose range is the set of situations itself. We start with considering propositional fluents. The key idea of situation calculus is that the meaning of every expression is a fluent. If we equate situations with the possible worlds from Kripke semantics, following the suggestion in [14, p.495], then sentences in quantified modal logic express propositional fluents. For example, the meaning of the sentence “John walks” is traditionally given as the set of possible worlds in which the sentence “John walks” is true. This set of course uniquely determines a propositional fluent. Key idea of modal logic: Every first order modal logical sentence expresses a propositional fluent. It does so without referring explicitly to situations. In fact in traditional modal logic one can not refer to the situations (more traditionally called “worlds”) in the models. Also in quantified hybrid logic (QHL) every sentence expresses a propositional fluent. But in addition one can refer to situations and indicate that a formula holds at a certain situation. Names for situations and a holds operator. But McCarthy and Hayes need more expressive power than quantified modal logic has to offer. They want to be able to express “At situation s, ‘John walks’ holds”.3 This is not possible in quantified modal logic because it contains no machinery to refer to possible worlds. This is where Prior’s ideas and their modern treatment in the form of hybrid logic come into action. For the moment, add a second sort of variables, called nominals, to the language of first order logic. Every nominal is a formula, and nominals can be freely combined to form new formulas. In addition, whenever i is a nominal and φ is a formula, then also @i φ (pronounce: at i, φ) is a formula. The function of nominals is to name situations. The meaning of a nominal i—an atomic formula in hybrid logic—in a model will be the propositional fluent which is true only for the unique situation that is named by i in the model. @i φ adds a holds–operator to first order logic: @i φ states that the formula φ holds at the situation named i. Thus the meaning of @i φ is the constant propositional fluent which sends every situation to true if φ holds at the situation named i, and every situation to false otherwise. Let’s consider the first example from [14, p.478]. McCarthy and Hayes want to “assert about a situation s that person p is in place x and that it is raining in place x.” This is expressed by at(p, x, s) ∧ raining(x, s). Not being satisfied with this notation they give two other possible equivalent notations: [at(p, x) ∧ raining(x)](s) [λs .at(p, x, s ) ∧ raining(x, s )](s).

(1) (2)

In QHL all these are expressible by different formulas without lambda abstraction. The fluent λs .at(p, x, s ) ∧ raining(x, s ) is simply expressed in QHL by at(p, x) ∧ raining(x). The formulas (1) and (2) are then expressed by @s (at(p, x) ∧ raining(x)), an almost literal translation of the statement in natural language. Finally the original 3

The holds operator plays an important role in a number of knowledge representation formalisms, for instance in Allen’s work on events and intervals [1] and in Kowalski’s event calculus [11].

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formulation is expressed by distributing @s over the conjunction as in @s at(p, x) ∧ @s raining(x). Theories and definitions. There is a second reason why McCarthy and Hayes want explicit reference to situations. To express laws of nature, definitions or other information which is supposed to be true in all situations, you have to universally quantify over situations. They give the example of a kind of transitivity for the predicate in(x,y,s) which expresses that x is in the location in situation s: ∀x∀y∀z∀s.(in(x, y, s) ∧ in(y, z, s) → in(x, z, s)) ∀x∀y∀z∀.(in(x, y) ∧ in(y, z) → in(x, z)).

(3) (4)

In the second statement the situation argument is suppressed and ∀. is meant to implicitly quantify over all situations. In modal terminology ∀. functions as a universal modality. In description logic a special status is given to statements which are supposed to be true in all situations. They are placed in, what is called, the T–Box (for Theory Box). This is the natural place to collect definitions and other laws which hold universally. We adopt this T–Box machinery and express (3) and (4) simply by putting the QHL sentence (5) in the T–Box. (5) ∀x∀y∀z(in(x, y) ∧ in(y, z) → in(x, z)) Note that this is almost literally the formulation (4) which is preferred in [14], except that the unappealing empty quantifier is replaced by the T–Box. Prior’s temporal operators. In section 2 of [14], Prior’s temporal operator F is introduced in the situation calculus. Here it becomes clear that the used formalism is not suited: only with explicit λ–abstraction can one make a simple causality assertion. F(π, s) means that “the situation s will be followed (after an unspecified time) by a situation that satisfies the fluent π”. To describe the temporal aspect of situations, McCarthy and Hayes postulate a function time from the set of situations to a set of time–points. The last set comes with the usual (linear) earlier than ordering. Now (6) is the formalization of the assertion that “if a person is out in the rain, he will get wet”. ∀x∀p∀s[raining(x, s) ∧ at(p, x, s) ∧ outside(p, s) → F(λs .wet(p, s ), s)].

(6)

This is also too much for McCarthy and Hayes and they quickly suppress explicit mention of situations, yielding ∀x∀p∀.[raining(x) ∧ at(p, x) ∧ outside(p) → F(wet(p))].

(7)

If we delete the empty quantifier ∀. in (7) and put the result in the T–Box, we get the formalization in temporal QHL. In temporal QHL, Prior’s temporal operators F and P are added to the language: whenever φ is a formula, also Fφ and Pφ are formulas. Their meaning is evaluated locally in a situation: Fφ is true in a situation s if there exists a situation s such that time(s) < time(s ) and φ is true at s . The meaning of Pφ is defined similarly but with s before s. Thus Fφ is true in a situation s if there exists a situation in the future of s at which φ is true. Pφ expresses the same thing, but with respect to the past.

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Actions. The largest change in the language comes from our treatment of actions as compared to that in [14]. (A related approach is taken by Levesque, Pirri and Reiter [12], cf. also Reiter’s book [18]). We treat actions as in dynamic logic [10] and introduce a modality for every action. McCarthy and Hayes [14] deal with actions through the situational fluent result(p, σ, s). In this, p is a person, σ an action and s a situation. The value of result(p, σ, s) is the situation that results when p carries out σ, starting in s. If the action does not terminate result(p, σ, s) is considered undefined. Note that result(p, σ, s) is a function with the set of situations as its range. Using functions one can only handle deterministic actions. Another drawback of this representation is the use of partial functions. It is unclear what truth value a formula should receive when some of its arguments are undefined. Reiter [18] has similar problems which lead to the introduction of “ghost situations.” Dynamic logic offers a solution for these problems, but pays the price that explicit reference to situations is not possible in the language. As we will see, when this is needed it can be elegantly done in hybrid logic. To simplify matters, we just consider actions and let the actor be implicit. So assume there is a set ACT of primitive actions. Then whenever φ is a formula and α ∈ ACT is an action, also αφ and [α]φ are formulas. αφ is true in a situation s if there exists a situation s which is the result of carrying out α in s and φ is true in s . [α]φ is defined dually, so that φ needs to be true in all situations s which result from carrying out α in s. Thus if α is a deterministic action @s [α]φ expresses that φ is true in the situation result(α, s). McCarthy and Hayes use result to express certain laws of ability of the form @s φ → @s ψ with s = result(σ, s), expressing that if φ holds at s, then ψ is true in the situation which is the result of carrying out σ in s. With action modalities one can make more fine–grained distinctions. @s φ → α expresses that α can be carried out in situation s if φ holds there. @s φ → [α]ψ expresses that if α is carried out in s under the assumption of φ, then ψ is true in every resulting situation (though there need not exist one). Here are two more examples of properties which cannot be expressed in situation calculus (or for that matter, in dynamic logic), but can in the hybrid formalism: @s α expresses that it is possible to carry out action α successfully in situation s; @s [α]Ps expresses that the situation which results after carrying out action α in situation s is later in time than s. In plain words this formula expresses that it takes time to perform α. The combination of actions into strategies is immediate in this approach. Whenever φ is a formula and α1 , . . . , αn ∈ ACT are actions, also α1  · · · αn φ and [α1 ] · · · [αn ]φ are formulas.

4

Discussion and Conclusions

The seminal paper that McCarthy and Hayes [14] published in 1969 marks a watershed in artificial intelligence. Its importance can simply not be underestimated: apart from introducing the situation calculus as one of the main representation languages in artificial intelligence, the paper is most famous for singling out a number of fundamental problems that did set artificial intelligence’s research agenda for years to come. Amongst its most important contributions are its role in the identification of the monotonicity of classical logic as a fundamental problem for intelligent robots; and perhaps it is most famous for introducing the frame problem (an area of unsurpassed activity in artificial intelligence). Both these fundamental problems resulted in important research traditions (see [7] for an

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overview of the field of non-monotonic reasoning, and see [19] for a survey of the frame problem). Nowadays, the ideas of [14] seem to have reached their ultimate success— they are part of the common knowledge and taken for granted by most researchers. Nevertheless, we feel that there are more than historical reasons for re-appraising [14]. A less frequently discussed contribution of the original paper is that it highlighted the connection between the fields of AI and philosophical logic (especially modal logics of belief, knowledge, and tense). This is even more extraordinary considering that the formulation in terms of Kripke semantics of these modal logics were recent developments in the 60s, and at that time part of a rather peripheral area in logic, plagued by deep philosophical problems. However, also modal logic progressed since the 60s and broadened its subject matter. As an illustration, the recent monograph [4] starts with stating that “modal languages are simple yet expressive languages for talking about relational structures”. It is this view, of modal logic as a multi–purpose knowledge representation language, which holds the promise to shed new light on some of the fundamental problems of knowledge representation. Arthur Prior held this view already, now it is being fully developed in the fields of description logic [8] and hybrid logic [3]. The main contribution of this paper is a new quantified hybrid logic with temporal operators and action modalities, tailor-made for expressing the fluents of situation calculus. We have shown that in this quantified hybrid logic, situation calculus formulas can be expressed more natural and concise than the original formulations. Moreover, it comes with additional operators such as a downarrow binder that may enhance its expressive power beyond the original situation calculus. More generally speaking, the aim of this paper was to revive the connection between situation calculus and modal logic. This aim can perhaps best be viewed as an effort to bring back together two research traditions that have worked independently for many years. This may also help to highlight some of the common interests of knowledge representation and modal logic. We can only hope that this inspires further collaboration, and fruitful exchange of ideas between the two communities.

References 1. J.Allen. Maintaining knowledge about temporal intervals. Artificial Intelligence, 26:832–843, 1983. 2. C. Areces, P. Blackburn, and M. Marx. Hybrid logics. Characterization, interpolation and complexity. Journal of Symbolic Logic, 2001. In print. 3. P. Blackburn. Representation, reasoning, and relational structures: a hybrid logic manifesto. Logic Journal of the IGPL, 8(3):339–365, 2000. 4. P. Blackburn, M. de Rijke, and Y. Venema. Modal Logic, volume 53 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge UK, 2001. 5. A. Borgida. Description logics in data management. IEEE Transactions on Knowlede and Data Engineering, 7:671–682, 1995. 6. R. Brachman and J. Schmolze. An overview of the KL–ONE knowledge representation system. Cognitive Science, 9(2):171–216, 1985. 7. G. Brewka, J. Dix, and K. Konolige. Nonmonotonic Reasoning: an overview. Number 73 in CSLI Lecture Notes. CSLI Publications, Stanford CA, 1997. 8. D. Calvanese, G. De Giacomo, D. Nardi, and M. Lenzerini. Reasoning in expressive description logics. In A. Robinson and A. Voronkov, editors, Handbook of Automated Reasoning. Elsevier Science Publishers, 1999.

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9. M. Fitting. Proof Methods for Modal and Intuitionistic Logics. Number 169 in Synthese Library. Reidel, Dordrecht, 1983. 10. D. Harel, D. Kozen, and J. Tiuryn. Dynamic Logic. MIT Press, 2000. 11. R.A. Kowalski and M. J. Sergot. A logic based calculus of events. New Generation Computing, 4:67–95, 1986. 12. H. J. Levesque, F. Pirri, and R. Reiter. Foundations for a calculus of situations. Electronic Transactions on Artificial Intelligence, 2:159–178, 1998. 13. J. McCarthy. Situations, actions, and causal laws. Stanford Artificial Intelligence Project Memo 2, Stanford University, 1963. 14. J. McCarthy and P. J. Hayes. Some philosophical problems from the standpoint of artificial intelligence. In B. Meltzer and D. Michie, editors, Machine Intelligence 4, pages 463–502. Edinburgh University Press, 1969. 15. S. Passy and T. Tinchev. An essay in combinatory dynamic logic. Information and Computation, 93:263–332, 1991. 16. V. Pratt. Models of program logics. In Proceedings of the 20th IEEE symposium on Foundations of Computer Science, pages 115–122, 1979. 17. A. N. Prior. Past, Present and Future. Oxford University Press, 1967. 18. R. Reiter. Knowledge in action: Logical foundations for describing and implementing dynamical systems. Draft version of a book on situation calculus, 1996–2000. 19. M. Shanahan. Solving the Frame Problem: A Mathematical Investigation of the Common Sense Law of Intertia. The MIT Press, Cambridge MA, 1997.

Appendix: Formal Definition of Quantified H ybrid Logic The language of quantified hybrid logic QHL has a set NOM of nominals, a set ACT of action statements, a set FVAR of first order variables, a set CON of first order constants, and predicates of any (including nullary) arity. The terms of the language are the constants from CON plus the first order variables from FVAR. The atomic formulas are all symbols in NOM together with the usual first order atomic formulas generated from the predicate symbols and equality using the terms. Complex formulas are generated from these according to the rules @n φ | ¬φ | φ ∧ ψ | φ ∨ ψ | φ → ψ | ∃xφ | ∀xφ | Fφ | Pφ | αφ | [α]φ Here n ∈ NOM, x ∈ FVAR, and α ∈ ACT. These formulas are interpreted in situation calculus models. Such a model is a structure (S, time, T, 2 5  

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Author Index

Lavraˇc, Nada 44 Leite, Jo˜ ao Alexandre 169, 261, 276 Lopes, Gabriel P. 30, 74 Lynce, Inˆes 363

Aguilar-Ruiz, Jes´ us S. 22 Agustini, Alexandre 30 Alferes, Jos´e J´ ulio 276 Almeida, Pedro De 116 Amado, Nuno 6 Antunes, Lu´ıs 142

Malheiro, Benedita 205 Mamede, Nuno 219 Marques-Silva, Jo˜ ao 363 Martins, Jo˜ ao P. 335 Marx, Maarten 253 Marzal, Eliseo 393, 409 Mayer, Helmut A. 63 Medina, Jes´ us 290 Mexia, Jo˜ ao 74 Mirkin, B. 52 Moura-Pires, Fernando 52

Baptista, Lu´ıs 363 Barahona, Pedro 349 Barber, Federico 379 Blackburn, Patrick 253 Bourne, Rachel A. 155 Brazdil, Pavel 14,88 Broda, Sabine 321 Bueno, Francisco 1 Cachopo, Jo˜ ao P. 335 Cachopo, Ana C. 335 Coelho, Carlos A. 74 Coelho, Helder 142 Cravo, Maria R. 335 Cruz, Jorge 349 Damas, Lu´ıs 321 Dell’Acqua, Pierangello Dhar, Vasant 5 Dignum, Frank 191 Dignum, Virginia 191 Escrig, Maria Teresa

Nascimento, S.

52

Ojeda-Aciego, Manuel 290 Oliveira, Eug´enio 205, 232 Oliveira, Elias 371 Onaind´ıa, Eva 379, 393, 409 169, 183 Pacheco, Julio 298 Pearce, David 306 Pereira, Lu´ıs Moniz 169, 183, 276 Pereira, Rui 14 Petrak, Johann 88 Prasad, Bhanu 401

298

Faria, Jo˜ ao 142 Ferrer-Troyano, Francisco J. Flach, Peter A. 3 Gama, Jo˜ ao 6 Gamallo, Pablo 30 Garc´ıa-Villalba, Javier 96 Garrido, Antonio 379 Gonz´ alez, Jos´e Carlos 96

22

Reis, Joaquim 219 Riquelme, Jos´e C. 22 Rocha, Ana Paula 232

Jennings, Nicholas R. 155 Jovanovski, Victor 44

Sapena, Oscar 393 Schwaiger, Roland 63 Sebastia, Laura 393, 409 Shoop, Karen 155 Silva, Joaquim 74 Silva, Fernando 6 Smith, Barbara M. 371 Soares, Carlos 14, 88

Kamps, Jaap

Tapia, Elizabeth

Hellstr¨ om, Thomas

253

130

96

418

Author Index

Toledo, Francisco 298 Tompits, Hans 306 Torgo, Lu´ıs 104, 116 Trajkovski, Goran 246

Villena, Julio Vojt´ aˇs, Peter Woltran, Stefan

96 290 306