A clustering algorithm to find groups with homogeneous preferences J. Díez, J.J. del Coz, O. Luaces, A. Bahamonde Centro de Inteligencia Artificial. Universidad de Oviedo at Gijón Workshop on Implicit Measures of User Interests and Preferences

To find groups with homogeneous preferences Centro de Inteligencia Artificial. Univ. Oviedo at Gijón. Spain 2 People tend to rate their preferences in a relative way Which middle circle do you think is larger? The framework to learn preferences

To find groups with homogeneous preferences Centro de Inteligencia Artificial. Univ. Oviedo at Gijón. Spain 3 o Regression is not a good idea o We will use training sets of preference judgments pairs of vectors (v, u) where someone expresses that he or she prefers v to u The framework to learn people’s preferences Me {v i > u i : i  I Me } SVM linear f Me f Me is a linear ranking function: f(v i ) > f(u i ) whenever v i is preferable to u i

To find groups with homogeneous preferences Centro de Inteligencia Artificial. Univ. Oviedo at Gijón. Spain 4 The framework to learn people’s preferences Me {v i > u i : i  I Me } SVM linear f Me How useful is this ranking function f Me ? reliable, general, … Accuracy, generalization error # Training examples # Attributes

To find groups with homogeneous preferences Centro de Inteligencia Artificial. Univ. Oviedo at Gijón. Spain 5 To improve ranking functions, we present a new algorithm for clustering preference criteria The problem addressed P1 {v i 1 > u i 1 } f1f1 P2 {v i 2 > u i 2 } P3 {v i 3 > u i 3 } f2f2 f3f3 P4 {v i 4 > u i 4 } f4f4 f 2U3 if f 2U3 is better than f 2 and f 3 f 2U3

To find groups with homogeneous preferences Centro de Inteligencia Artificial. Univ. Oviedo at Gijón. Spain 6 Applications oInformation retrieval Optimizing Search Engines Using Clickthrough Data [Joachims, 2002] oPersonalized recommenders Adaptive Route Advisor [Fiechter, Rogers, 2000] oAnalysis of sensory data Used to test the quality (or the acceptability) of market products Panels of experts and consumers

To find groups with homogeneous preferences Centro de Inteligencia Artificial. Univ. Oviedo at Gijón. Spain 7 Baseline approaches P1 {object 1  rating 1 } P2 {object 2  rating 2 } P3 {object 3  rating 3 } P4 {object 4  rating 4 } If rating i  rating j then merge Pi with Pj Where  uses correlation or cosine

To find groups with homogeneous preferences Centro de Inteligencia Artificial. Univ. Oviedo at Gijón. Spain 8 Weaknesses of baseline approaches Correlation or cosine were devised for prediction purposes in collaborative filtering, and they are not easily extendable to clustering: oNot all people have seen the same objects oTwo samples of preferences of the same person would not be considered homogeneous oRating is not a good idea

To find groups with homogeneous preferences Centro de Inteligencia Artificial. Univ. Oviedo at Gijón. Spain 9 Our approach: a clustering algorithm Ranking functions are linear maps: f(x) =w·x Then weight vectors w codify the rationale for these preferences Therefore, we will try to merge data sets with similar (cosine) ranking functions (= weight vectors) The merge will be accepted if the join ranking function improves the quality of individual functions

To find groups with homogeneous preferences Centro de Inteligencia Artificial. Univ. Oviedo at Gijón. Spain 10 Our approach: a clustering algorithm A set of clusters ClusterPreferencesCriteria (a list of preference judgments (PJ i : i = 1,…, N)) { Clusters =  ; for each i = 1 to N { w i = Learn a ranking hyperplane from (PJ i ); Clusters = Clusters U {(PJ i, w i )}; } repeat { let (PJ 1, w 1 ) and (PJ 2, w 2 ) be the clusters with most similar w 1 and w 2 ; w = Learn a ranking hyperplane from (PJ 1 U PJ 2 ); if (quality of w >= (quality of w 1 + quality of w 2 )) then replace the clusters (PJ 1, w 1 ) and (PJ 2, w 2 ) by (PJ 1 U PJ 2, w) in Clusters; } until (no new merges can be tested); return Clusters; }

To find groups with homogeneous preferences Centro de Inteligencia Artificial. Univ. Oviedo at Gijón. Spain 11 To estimate quality of ranking functions The quality of the ranking functions depends on: oAccuracy, generalization errors oNumber of Training examples oNumber of Attributes

To find groups with homogeneous preferences Centro de Inteligencia Artificial. Univ. Oviedo at Gijón. Spain 12 To estimate quality of ranking functions If we have enough training data: odivide them in train (itself) and verification sets o compute the confidence interval of the probability of error when we apply each ranking function to the corresponding verification set: [L, R] oquality is 1-R the estimated proportion of successful generalization errors in the pessimistic case

To find groups with homogeneous preferences Centro de Inteligencia Artificial. Univ. Oviedo at Gijón. Spain 13 To estimate quality of ranking functions If we don’t have too many training data: oXi-alpha estimator [Joachims, 2000] (texts) oCross-validation oOther

To find groups with homogeneous preferences Centro de Inteligencia Artificial. Univ. Oviedo at Gijón. Spain 14 Experimental results oPeople: the 100 spectators with more ratings oObjects: the ratings of 504 movies (60% train, 20% verification, 20% test) given by other 89 spectators 808 spectators Training sets: preference judgments We used a collection of preference judgments taken from EachMovie to simulate reasonable situations in the study of preferences of groups of people

To find groups with homogeneous preferences Centro de Inteligencia Artificial. Univ. Oviedo at Gijón. Spain 15 Experimental results

A clustering algorithm to find groups with homogeneous preferences J. Díez, J.J. del Coz, O. Luaces, A. Bahamonde Centro de Inteligencia Artificial. Universidad de Oviedo at Gijón Workshop on Implicit Measures of User Interests and Preferences