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PushTrust: An Efficient Recommendation Algorithm by
Leveraging Trust and Distrust Relations
Rana Forsati, Iman Barjasteh, Farzan Masrour, Abdol-Hossein Esfahanian, Hayder Radha
Michigan State University
RecSys’15
Outline
• Some background
• Problem statement
• Our Algorithm
• Results
2
Recommender Systems
Recommend items to users to maximize some objective(s)
Latent feature models (e.g., matrix factorization): The current most successful technique as demonstrated in KDD Cup and Netflix competition
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Latent Feature Models
Intuition: ratings are deeply influenced by a set of non-obvious features specific to the domainGoal: Extract latent features from existing ratings for future (unknown) predictions
Items:
Users:
Partially observed rating matrix:
4
Latent Features Models…
How to find latent features for users and items?
Assume there are k latent features for rating
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Matrix Factorization
Solve the following optimization problem:
Model each user/item as a vector of features (learned from data)
: observed ratings
Training error onobserved ratings
Regularization toavoid overfitting
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Huge number of unrated movies
Handling cold-start usersor items
• Cold-start users: new users who have rated only a few items
• Cold-start items: new items without ratings
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Sparsity of rating matrixExample: Epinions only 0.02%of matrix is observed.
Challenges
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Side Information about Items
Rating Matrix
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Goal: exploit other sources of information to cope with these challenges
Side Information about Items
Side Information about Users
Side Information
Side Information about Ratings
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■ Trust/Distrust Relations between users
Social Recommender Systems
Spatial Recommender Systems
■ Attribute of users such as location, age,….
Side Information about Users
Social Networking Services
(e.g., Facebook, Twitter)
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Social Information and Data Sparsity
Adding side information to resolve sparsity and cold-start problems.
Our focus: trust/distrust relations between users
How to effectively exploit social relations of users in recommendation to boost the accuracy?
Growth of social networks
Trust = agreement on ratings [Guo et al., 2014] Opinion Aware
Recommendation
Systems
Distrust = disagreement on ratings [Forsati et al., 2014]
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Matrix Factorization &
PushTrust Algorithm
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• Trust can be considered as a transitive relation and can propogate.
• Distrust is not transitive.
• Distrust propagates only one step [Guha et al., 2004]
• Distrust can not be considered as negative of trust.
Trust versus Distrust
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Social Regularization with Trust and Distrust
Rating Matrix Trust Network Distrust Network
Memory based methods: distrust is used to either filter out ordebug propagated trust network [Victor et al., 2011]
Factorization based methods: regularization by ranking of latentfeatures [Forsati et al., 2014]
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Social Regularization with Trust and Distrust
Trust+Distrust enhanced MF: the latent features of trusted usersare closer and distrusted users are more distant
trust network
Distrust networkusers arranged based on
similarity of their latent features14
Social Regularization with Trust and Distrust
where
Regularization with Social Ranking
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Issues with RankingComputationally expensive: in large social graphs,optimization cost features can increase cubically in thenumber of users .
Only consider the trusted and distrusted friends andignores the neutral (users with no relation) users.
The neutral friends might appear before the trust friends and be negatively influential!
Not scalable to large social networks!
The top portion of ranked list might include distrusted friendsdue to nature of pairwise ranking model
The latent features might affected by distusted friends who appear at top of the ranked list!
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PushTrust
A more complete approach:- the trustees are PUSHEDto the top of list as much as possible.
- The foes are PUSHED to the bottom of list as much as possible.
- The neutral friends are PUSHED to the middle of list.
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Rewrite the social-regularized matrix factorization
Here is social regularization of latentfeatures of individual users.
PushTrust: A Convex Formulation
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Put neutral friendsabove distrusted ones
Put trusted friendsabove neutral ones
Put trusted friendsabove distrusted ones
where is indicator function.non-convex indicator
function
PushTrust: A Convex Formulation: latent features of trusted friends
: latent features of neutral friends
: latent features of distrusted friends
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Indicator function:
Convex Loss Function
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Hinge loss:
Convex Loss Function
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Rewrite the social regularized matrix factorization
where
PushTrust Objective
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Optimization Procedure
The problem is non-convex jointly in both U and V.
Solution: The standard gradient descent method
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1. Updating U while keeping V fixed:
Set , where
Optimization Procedure
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2. Updating V while keeping V fixed:
Set , where
Optimization Procedure
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• Conventional:The neutral friends of users are also incorporated in ranking the latent features.
• Computational: The number of constraints increasesquadratically
Key Features
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Experiments
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Experimental Evaluation
Two evaluation metrics:
Mean Absolute Error:
Root Mean Squared Error:
where is the set of rating that should be predicted.
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The Epinions Dataset
The only social rating networkdataset publicly available.
User trust and distrust informationis included in this dataset
The social network in Epinions is directed
UsersUsers ItemsItems RatingsRatings Trust Relations
Trust Relations
Distrust RelationsDistrust
Relations
QuantityQuantity 121,240 685,621 12,721,437 481,799 96,823
80% of the rating data was selected as the training set with 20% as the test data.
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Baseline Algorithms &Experimental Design
■ MF:Matrix Factorization■ MF-T:Matrix Factorization with Trust information■ MF-D: Matrix Factorization with Distrust information■ MF-DT:Matrix Factorization with Trust and Distrust■ PushTrust: The proposed algorithm
0.
0.25
0.5
0.75
1.
5 10
MA
E
Latent vector dimensions
PushTrustMFMF-TMF-DMF-DT
0.0.10.20.30.40.50.60.70.80.91.1.11.21.3
5 10
RM
SE
Latent vector dimensions
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Experiment on handling cold-start users
To evaluate different algorithms: select 30%, 20%, and 10%of the users, to be cold-startusers. For cold-start users, no rating is included in the training data consider all ratings made bycold-startusers as testing data.
0.750.8125
0.8750.9375
1
10% 20% 30%Cold-start users
MAE
MF MF-TMF-D MF-TDPushTrust
11.18751.375
1.56251.75
10% 20% 30%Cold-start users
RMSE
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Thank You for you attention!
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Questions?32
