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A Matrix Factorization Technique with Trust Propagation for Recommendation in Social NetworksMohsen Jamali, Martin EsterSimon Fraser UniversityVancouver, Canada
ACM RecSys 2010
Outline
Introduction Matrix Factorization Models
Basic MF Model Social Trust Ensemble Model
The SocialMF Model Data Sets Experiments Conclusions
2Mohsen Jamali, Social Matrix Factorization
Introduction
Need For Recommenders Input Data
A set of users U={u1, …, uN}
A set of items I={i1, …, iM}
The rating matrix R=[ru,i]NxM
Problem Definition: Given user u and target item i Predict the rating ru,i
Collaborative Filtering Approach
3Mohsen Jamali, Social Matrix Factorization
Introduction (cont.)
Social Networks Emerged Recently Independent source of information
Motivation of SN-based RS Social Influence: users adopt the
behavior of their friends Social Rating Network
Social Network Trust Network
Mohsen Jamali, Social Matrix Factorization 4
Recommendation in Social Networks
Memory based approaches for recommendation in social networks [Golbeck, 2005] [Massa et.al.
2007] [Jamali et.al.
2009] [Ziegler, 2005]
Mohsen Jamali, Social Matrix Factorization 5
A Sample Social Rating Network
Matrix Factorization
Model based approach Latent features for users
Latent features for items
• Ratings are scaled to [0,1]• g is logistic function
Mohsen Jamali, Social Matrix Factorization 6
U and V have normal priors
Social Trust Ensemble [2009]
Mohsen Jamali, Social Matrix Factorization 7
Social Trust Ensemble (cont.)
Issues with STE Feature vectors of neighbors should
influence the feature vector of u not his ratings
STE does not handle trust propagation Learning is based on observed ratings
only.
Mohsen Jamali, Social Matrix Factorization 8
The SocialMF Model
Social Influence behavior of a user u is affected by his direct neighbors Nu.
Latent characteristics of a user depend on his neighbors.
Tu,v is the normalized trust value.
Mohsen Jamali, Social Matrix Factorization 9
The SocialMF Model (cont.)
Mohsen Jamali, Social Matrix Factorization 10
The SocialMF Model (cont.)
Mohsen Jamali, Social Matrix Factorization 11
The SocialMF Model (cont.)
Mohsen Jamali, Social Matrix Factorization 12
The SocialMF Model (cont.)
Mohsen Jamali, Social Matrix Factorization 13
The SocialMF Model (cont.)
Mohsen Jamali, Social Matrix Factorization 14
The SocialMF Model (cont.)
Properties of SocialMF Trust Propagation User latent feature learning possible with
existence of the social network▪ No need to fully observed rating for learning▪ Appropriate for cold start users
Mohsen Jamali, Social Matrix Factorization 15
Data Sets
Epinions – public domain Flixster
Flixster.com is a social networking service for movie rating
The crawled data set includes data from Nov 2005 – Nov 2009
Available at http://www.cs.sfu.ca/~sja25/personal/datasets/
Mohsen Jamali, Social Matrix Factorization 16
Data Sets (cont.)
Mohsen Jamali, Social Matrix Factorization 17
General Statistics of Flixster and Epinions
Flixster: 1M users, 47K items 150K users with at least one rating Items: movies 53% cold start
Epinions: 71K users, 108K items Items: DVD Players, Printers, Books,
Cameras,… 51% cold start
Experimental Setups
5-fold cross validation Using RMSE for evaluation Comparison Partners
Basic MF STE CF
Model parameters SocialMF: STE:
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Results for Epinions
Gain over STE: 6.2%. for K=5 and 5.7% for K=10
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CF BaseMF STE SocialMF1
1.021.041.061.08
1.11.121.141.161.18
1.2
k=5k=10R
MS
E
Results for Flixster
SocialMF gain over STE (5%) is 3 times the STE gain over BasicMF (1.5%)
Mohsen Jamali, Social Matrix Factorization 20
CF BaseMF STE SocialMF0.76
0.78
0.8
0.82
0.84
0.86
0.88
0.9
0.92
k=5k=10R
MS
E
Sensitivity Analysis on λT
Mohsen Jamali, Social Matrix Factorization 21
Sensitivity Analysis for Epinions
Sensitivity Analysis on λT
Mohsen Jamali, Social Matrix Factorization 22
Sensitivity Analysis for Flixster
Experiments on Cold Start Users
Mohsen Jamali, Social Matrix Factorization 23
RMSE values on cold start users (K=5)
CF BaseMF STE SocialMF1
1.1
1.2
1.3
1.4
Epinions
Experiments on Cold Start Users
Mohsen Jamali, Social Matrix Factorization 24
RMSE values on cold start users (K=5)
CF BaseMF STE SocialMF0.95
11.051.1
1.151.2
1.25
Flixster
Experiments on Cold Start Users
Mohsen Jamali, Social Matrix Factorization 25
Flixster Epinions
Cold Start Users 0.085 0.115
All Users 0.05 0.062
-1.00%
1.00%
3.00%
5.00%
7.00%
9.00%
11.00%
RMSE Gain of SocialMF over STE
Analysis of Learning Runtime
SocialMF: STE: SocialMF is faster by factor
Mohsen Jamali, Social Matrix Factorization 26
N # of Users
K Latent Feature Size
Avg. ratings per user
Avg. neighbors per user
rt
Conclusion
A model based approach for recommendation in social networks based on matrix factorization
Handling Trust Propagation Appropriate for cold start users Fast Learning phase Improved quality for experiments on
two real life data sets.
Mohsen Jamali, Social Matrix Factorization 27
Mohsen Jamali. Using Trust Networks to Improve Top-N Recommendation
28
Thank you!
