Distributed Collaborative Filtering and Adaptive User-to-User - PowerPoint PPT Presentation

Distributed Collaborative Filtering and Adaptive User-to-User Correlation Francesco Ricci Faculty of Computer Science Free University of Bozen-Bolzano, Italy Joint work with Shlomo Berkovsky (CIRSO), Tsvi Kuflik (University of Haifa), and Linas Baltrunas (University of Bozen)

Content � Introduction to recommender systems and collaborative filtering � Motivations: � Decentralized collaborative filtering � Improve accuracy by partitioning ratings and re- aggregating information � Domain-based rating partitioning � Importing user modelling information � Computing inter-domain correlations � Evaluation � Extension: adapting the similarity metric to the prediction problem 2

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Recom m ender System s � In everyday life w e rely on recom m endations from other people either by word of mouth, recommendation letters, movie and book reviews printed in newspapers … � In a typical recommender system people provide recom m endations as inputs, w hich the system then aggregates and directs to appropriate recipients � Aggregation of recommendations � Match the recommendations with those searching for recommendations [Resnick and Varian, 1997] 4

Exam ples Am azon.com – looks in the user past buying history, � and recommends product bought by a user with similar buying behavior Tripadvisor.com - Quoting product reviews of a � community of users Myproductadvisor.com – make questions about � searched benefits (product features) to reduce the number of candidate products Yahoo.com – “Today’s Picks” highlight ten destinations � that are highly-relevant to individual users, based on recent online activity and preferences. iTunes Genius – recommend albums similar to those � found in your library Sm arter Kids – self selection of a user profile – � classification of products in user profiles. 5

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Items 13 Matrix of ratings Users

Collaborative-Based Filtering A collection of n user u i and a collection of m products p j � A n × m matrix of ratings v ij , with v ij = ? if user i did not rate � product j Prediction for user i and product j is computed as � ∑ = + − * ( ) v v K u v v ij i ≠ ik kj k ? v kj Where, v i is the average rating of user i , K is a normalization � factor such that the sum of u ik is 1, and ∑ − − ( )( ) v v v v ij i kj k Similarity of = j u ∑ ∑ users i and k ik − − 2 2 ( ) ( ) v v v v ij i kj k j j Where the sum (and averages) is over j s.t. v ij and v kj are � not “?”. [Breese et al., 1998] 14

Exam ple p j u 5 v 5 = 4 4 v i = 3.2 u i ? u 8 v 8 = 3.5 3 u 9 5 v 9 = 3 Users’ similarities: u i5 = 0.5, u i8 = 0.5, u i9 = 0.8 ∑ = + − * ( ) v v K u v v ≠ ij i ik kj k ? v kj v* ij = 3.2 + 1/(0.5+0.5+0.8) * [0.5 (4 -4) + 0.5 (3 – 3.5) + 0.8 (5 -3) = 3.2 + 1/1.8 * [0 - 0.25 + 1.6] = 3.2 + 0.75 = 3.95 15

Distributed Scenario q=<user = i> recommend j Target Recommender Sys. reply from a remote system q=<user = i, item = j, target = t> � User identifiers � User models � User identifiers and their similarities � Rating prediction for j Remote Recommender Sys. Remote Recommender Sys. Remote Recommender Sys. 16

Related W orks B. N. Miller, J. A. Konstan, J. Riedl, “ PocketLens: � Toward a Personal Recommender System ”, 2004 R. Burke, Hybrid web recommender systems . In � The Adaptive Web , page 377-408. Springer Berlin / Heidelberg, 2007. K. Yu, X. Xu, M. Ester, H. P. Kriegel, Feature � Weighting and Instance Selection for Collaborative Filtering: An Information-Theoretic Approach , in Knowledge Information Systems, vol. 5(2), 2003. J. Freyne, B. Smyth, Communities, � Collaboration and Cooperation in Personalized Web Search , in proc. of the ITWP Workshop, Edinburgh, UK, 2005. 17

I nform ation processing in CF 1 . Sim ilarity com putation: assessing the similarity of all the users to the active user, i.e., the user for whom a recommendation is searched 2 . Neighborhood form ation: selecting the K most similar users to the active user 3 . Com puting the active user rating prediction: for a target item whose rating is unknown 1. weight the ratings - on the target item - of the K most similar users, found at (2) according to the user-to-user similarity computed at (1) 2. the predicted rating is the weighted average. 18

W hat inform ation can be exchanged � UMs ( rating vectors ) stored by the remote systems � Lists of the neighborhood candidates computed by the remote systems � Degrees of sim ilarity between the active user and the other users, computed over the data stored by the remote systems � Complete predictions generated by the remote systems. 19

Assum ptions � Users can be identified uniquely in all the domains � I tem s can be identified uniquely in all domains � Target dom ain sends a request to remote domains specifying q= < i, j, t> � i is the identifier of the active user � j is the target item identifier (possibly null) � t is the target domain. � Different distributed prediction methods are characterized by "w hat the rem ote dom ains reply". 20

Rating Matrix and Dom ains � Given the assumptions: there is a "centralized" (aggregated) model of the distributed scenario � V is the overall rating matrix � V a , V b , V c , are rating sub matrices for three domains R a , R b , R c V c V b V a v 11 v 12 v 13 … v 1m v 21 v 22 v 23 … v 2m v 31 v 32 v 33 … v 3m V = v n1 v n2 v n3 … v nm 21

Prediction Methods - Rem ote Replies Local Prediction: the remote systems { R d } d ∈ D do not return any � data Centralized Prediction: All the ratings managed by { R d } d ∈ D are � sent back - we assume that all the domains are related and D is the full set of domains Distributed Peer I dentification: The identifiers of users that all � the remote systems { R d } d ∈ D consider as “similar” to the target user i are sent back Distributed Neighborhood Form ation: The identifiers of the � users that all the remote systems { R d } d ∈ D consider as “similar” to the target user i, together w ith their sim ilarities to the target user i - similarities are computed by the remote system using only the ratings in V d Distributed Prediction: The rating predictions for item j � computed by the remote systems { R d } d ∈ D using the ratings contained in V d , d ∈ D are sent back. 22

Distributed Peer I dentification � The identifiers of K users that all the remote systems { R d } d ∈ D consider as “similar” to the target user i are sent back � D is the set of all rem ote dom ains � In our experiments a domain is identified by a tag (a genre) � The target domain m erge the received peers and make a prediction using the local data (ratings only in the target domain). � Remote systems provide knowledge as an inform ed selection of users . 23

Distributed Peer I dentification � V a is the target domain � V b and V c are remote domains (containing some ratings of the target user) V c V b V a target domain v 11 v 12 v 13 … v 1m V b peer v 21 v 22 v 23 … v 2m v 31 v 32 v 33 … v 3m V b peer V c peer V = v n1 v n2 v n3 … v nm target user 24

Distributed Neighborhood Form ation The identifiers of some users that the remote systems � { R d } d ∈ D consider as “similar” to the target user i, together w ith their sim ilarities to the target user i - similarities are computed by the remote system using only the ratings in V d The similarity of a neighbor user l with the target user i is a � weighted average ∑ ( , ) ( , ) cor d t sim i l d ∈ = d D ( , ) sim i l ∑ ( , ) cor d t ∈ d D where D is the set of all the domains (including t), t is the � target domain and � cor(d,t) is the I nter-Dom ain Correlation measure between domains. 25

I nter-Dom ain Correlations � Content-based m ethod � Mining the textual descriptions of the items in the domains from external data sources to obtain tf-idf description (vector v ) of each domain � Computing cosine correlation of the domain representations ⋅ v v = = 1 2 ( , ) ( , ) cor content d d sim v v 1 2 1 2 ∗ || || || || v v 1 2 � Rating-based m ethod � Average correlation of the items in the domains ( J d ) = ≠ ∈ ∈ ( , ) { ( , ) : , , } cor d d AVG sim j k j k j J k J 1 2 ratings d d 1 2 26

Distributed Prediction � The rating predictions for item j computed by the remote systems { R d } d ∈ D using the ratings contained in V d , d ∈ D are sent back to the target domain R t � Upon receiving the set of predictions, R t aggregates all the predictions ( including the local one ) into a single value by averaging the predictions � We do not use here the Inter-Domain Correlation. 27