Dynamic Clustering of Partial Preference Relations by Mian Qin Bachelor of Science, Beijing Technology and Business University, 2002 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Computer Science In the Graduate Academic Unit of Computer Science Supervisors: Michael W. Fleming, Ph. D., Computer Science Scott Buffett, Ph. D., Computer Science Examining Board: Huajie Zhang, Ph. D., Computer Science, Chair Kenneth Kent, Ph. D., Computer Science Richard Tervo, Ph. D., Electrical and Computer Engineering This thesis is accepted Dean of Graduate Studies THE UNIVERSITY OF NEW BRUNSWICK September, 2007 ©Mian Qin, 2007 Library and Archives Bibliotheque et 1*1 Canada Archives Canada Published Heritage Direction du Branch Patrimoine de Pedition 395 Wellington Street 395, rue Wellington Ottawa ON K1A 0N4 Ottawa ON K1A 0N4 Canada Canada Your file Votre reference ISBN: 978-0-494-63749-4 Our file Notre reference ISBN: 978-0-494-63749-4 NOTICE: AVIS: The author has granted a non­ L'auteur a accorde une licence non exclusive exclusive license allowing Library and permettant a la Bibliotheque et Archives Archives Canada to reproduce, Canada de reproduire, publier, archiver, publish, archive, preserve, conserve, sauvegarder, conserver, transmettre au public communicate to the public by par telecommunication ou par I'lnternet, preter, telecommunication or on the Internet, distribuer et vendre des theses partout dans le loan, distribute and sell theses monde, a des fins commerciales ou autres, sur worldwide, for commercial or non­ support microforme, papier, electronique et/ou commercial purposes, in microform, autres formats. paper, electronic and/or any other formats. The author retains copyright L'auteur conserve la propriete du droit d'auteur ownership and moral rights in this et des droits moraux qui protege cette these. Ni thesis. Neither the thesis nor la these ni des extra its substantiels de celle-ci substantial extracts from it may be ne doivent etre imprimes ou autrement printed or otherwise reproduced reproduits sans son autorisation. without the author's permission. In compliance with the Canadian Conformement a la loi canadienne sur la Privacy Act some supporting forms protection de la vie privee, quelques may have been removed from this formulaires secondaires ont ete enleves de thesis. cette these. While these forms may be included Bien que ces formulaires aient inclus dans in the document page count, their la pagination, il n'y aura aucun contenu removal does not represent any loss manquant. of content from the thesis. 1*1 Canada Abstract In electronic commerce (EC), negotiation can be performed to determine fair exchanges between trading partners. In order to negotiate autonomously on behalf of a user, an intelligent agent must obtain as much information as possible about the user's preferences over possible outcomes, but without asking the user an unreasonable number of questions. This thesis explores the idea of clustering partial preference relations as a means for predicting a user's preferences. Previously unknown preferences for a user can be predicted by observing those of similar users in the same cluster. Three techniques for clustering and predicting preferences are developed based on the Y- means clustering method, and a number of experiments are conducted. The MovieLens data set, normally used to test recommendation systems, is adapted for this domain and used to provide experiments with real subjects. Results show that one particular method, which predicts which of two outcomes is preferred by analyzing the confidence in average estimated utilities for users in the same cluster, is accurate 70-75% of the time when cluster data are sufficient for making a prediction (about 67% of the time). Another method, while maintaining a slightly lower prediction rate, is shown to be accurate 72-82% of the time, depending on the number of known preferences for clustered users. Statistical tests show that these results are significant. n Acknowledgements I would like to express my sincere gratitude to my supervisors Dr. Scott Buffett and Dr. Michael W. Fleming. Without their invaluable supervision, patience and support throughout the thesis research, I would not have overcome the difficulty that I encountered. Especially, when I wrote my thesis, they gave me encouragement, lots of good ideas, and sound advice to help me achieve my goal. I also extend my gratitude to the members of my academic committee: Dr. Huajie Zhang, Dr. Kenneth Kent and Dr. Richard Tervo. Thanks also go to the financial support from Faculty of Computer Science at University of New Brunswick, and Natural Sciences and Engineering Research Council (NSERC). Last but not least, I would like to thank my parents Jiachun Qin and Xuemei Kong and my husband Yonglin Ren, for their love and support. Ill Table of Contents Abstract ii Acknowledgements iii Table of Contents iv List of Tables vii List of Figures ix Chapter 1 Introduction 1 Chapter 2 Background 4 2.1 Automated Negotiation 4 2.1.1 Introduction 4 2.1.2 Mechanisms 5 2.1.3 Application of Automated Negotiation 7 2.2 Utility Theory 8 2.2.1 Preference Relations 8 2.2.2 Utility and Utility Functions 10 2.3 Preference Elicitation 13 2.4 Clustering 15 2.4.1 Introduction 15 2.4.2 Clustering Techniques 16 2.4.3 Applications of Clustering 18 2.5 Existing Methods for Inferring Preferences 19 2.5.1 Conditional Preference Networks 19 2.5.2 Conditional Outcome Preference Networks (COP-nets) 21 iv 2.5.3 Minimax Regret 22 Chapter 3 Clustering Partial Preference Relations 23 3.1 Motivation 23 3.2 Partial Preferences 24 3.2.1 Complete Preference Relations and Partial Preference Relations 24 3.2.2 Conditional Outcome Preference Networks 26 3.3 Distance Measurement 32 3.3.1 Probabilistic Distance 32 3.3.1.1 Probabilistic Distance on Complete Preference Relations 33 3.3.1.2 Probabilistic Distance on Partial Preference Relations 33 3.3.2 Distance Computation with COP-nets 35 3.4 Y-means Clustering Method for Partial Preference Relations 39 Chapter 4 Inferring Preferences 43 4.1 Direct Inference Based on Clustering 45 4.2 Pre-processing Inference Based on Clustering 47 4.3 Post-processing Inference Based on Clustering 49 4.4 A Simple Example 50 Chapter 5 Implementation 60 5.1 Input and Output 60 5.2 Algorithm for Direct Inference Based on Clustering 62 5.3 Algorithm for Pre-processing Inference Based on Clustering 65 5.4 Algorithm for Post-processing Inference Based on Clustering 66 Chapter 6 Experimentation 68 6.1 Experimental Goals 68 v 6.2 Experimentation Methods 69 6.2.1 Experimentation Method One 69 6.2.1.1 Experimental Data 69 6.2.1.2 Experimental Design 71 6.2.2 Experimentation Method Two 77 6.2.2.1 Experimental Data 77 6.3 Analysis of Results 80 6.3.1 Analysis of Experiment Method One 80 6.3.2 Analysis of Experiment Method Two 84 Chapter 7 Conclusions and Future Work 89 7.1 Conclusions 89 7.2 Future Work 91 Bibliography 93 Curriculum Vitae VI List of Tables Table 3.1 Node representation for Figure 3.4 29 Table 4.1 Three methods for inferring preferences 44 Table 4.2 Users and their preferences 51 Table 4.3 A new user and his preferences 52 Table 4.4 The vectors for each user 54 Table 4.5 The vector for the new user 54 Table 4.6 Clusters formed by the Y-means clustering method 55 Table 4.7 The centers for clusters 55 Table 4.8 Clusters formed by a specified criterion 56 Table 4.9 Sub-clusters from cluster 1 56 Table 4.10 Sub-clusters from cluster 2 56 Table 4.11 Sub-clusters from cluster 3 57 Table 4.12 The centers for each sub-clusters 57 Table 4.13 Sub-clusters formed by a specified criterion 58 Table 4.14 Small clusters from Sub-cluster 1 58 Table 4.15 Small clusters from Sub-cluster 2 58 Table 4.16 Small clusters from Sub-cluster 3 59 Table 4.17 The centers for clusters 59 Table 6.1 Movies and Their Ratings 75 Table 6.2 Possible ranks of the movies 76 Table 6.3 Performance of the Direct Inference Based on Clustering method 80 vii Table 6.4 Performance of the Pre-processing Inference Based on Clustering method 82 Table 6.5 Performance of the Post-processing Inference Based on Clustering method 83 Table 6.6 Performance of the Direct Inference Based on Clustering method 85 Table 6.7 Performance of the Pre-processing Inference Based on Clustering method 85 Table 6.8 Performance of the Post-processing Inference Based on Clustering method 86 vin List of Figures Figure 2.1 An example of a CP-network 21 Figure 3.1 An example of complete preference relations 24 Figure 3.2 An example of partial preference relations 25 Figure 3.3 An example of redundant edges 27 Figure 3.4 An example of COP-nets 30 Figure 3.5 A COP-net for computing utilities 32 Figure 3.6 Two partial preference relations 35 Figure 3.7 Flow chart for calculating distances 36 Figure 3.8 The COP-nets for P, and P2 38 Figure 4.1 Flow chart of the Direct Inference Based on Clustering 46 Figure 4.2 Flow Chart of the Pre-processing Inference Based on Clustering method 48 Figure 4.3 Flow Chart of the Post-processing Inference Based on Clustering method 51 Figure 4.4 The COP-net for w, 53 Figure 6.1 Performance of three techniques 84 Figure 6.2 Performance of three techniques 87 IX Chapter 1 Introduction With the rapid development of networks and the Internet, a new mode of business has emerged: electronic commerce (EC).