SoRec: Social Recommendation Using Probabilistic Matrix Factorization

Hao Ma, Haixuan Yang, Michael R. Lyu, Irwin King (CIKM-08)
In this paper, Hao Ma et al. present an approach that help to deal with very large datasets and users who have made few ratings in recommender systems. Traditional methods (e.g., Pearson Correlation Coefficient and Cosine) assume that two users have rated at least some items in common so that they can compute the similarity of these users. Thus, memory-based and model-based collaborative filtering algorithms fail to find similarities of users who have never rated any items. In daily life, people usually ask their family or friends for recommendations of new movies, songs, books, restaurants or places to visit. Therefore, the authors propose a factor analysis approach based on probabilistic matrix factorization to solve the data sparsity and poor prediction accuracy problems by employing both users’ social network information and rating records.
Different with traditional perspectives that users are independent and identically distributed, the authors of this paper assume that people are tend to be influenced by the people whom they trust. In terms of quality and usefulness, they prefer recommendations from their friends more than those from computer systems. Therefore, both social network and user-item rating information should be considered in order to improve the quality as well as quantity of recommendation. From this perspective, the authors introduced a Social Recommendation framework that integrates social network structure and the user-item rating matrix, based on probabilistic factor analysis. They connect these two different data resources through the shared user latent feature space, that is, the user latent feature space in the social network structure is the same in the user-item rating matrix. based on probabilistic matrix factorization­, the low-rank user latent feature space and item latent feature space are learned in order to make social recommendations.
The core elements of this framework are social network matrix factorization and user-item matrix factorization. Given a social network graph of users and a user-item rating matrix, we can apply this framework to generate a predicted user-item matrix. Firstly, they factorize the social network graph G and user-item matrix A simultaneously and seamlessly using UT Z and UT V, where the shared low-dimensional matrix U denotes the user latent feature space, Z is the factor matrix in the social network graph, and V represents the low-dimensional item latent feature space.
  • Social network graph G: the vertices of the graph represents all the users in a social network and the edges of the graph represents the relations between the users.
  • User-item matrix A: shows the information that how users rate items.

In order to derive three matrix U, V, Z, they fuse both the social network graph and the user-item rating matrix into a consistent and compact feature representation, which reflect the assumption that a user’s social connections will affect this user’s judgement of interest in items. This results in the objective functions with quadratic regularization terms of G, A, U, V, Z. In this function, the authors use the parameter λC to control the effect of the social network, balancing the information from the user-item rating matrix and the user social network.
For the experiments, Hao Ma et al. use Epinions as the data source for their experiments on social recommendation. They compare their algorithm with some state-of-the-art algorithms: Maximum Margin Matrix Factorization, Probabilistic Matrix Factorization, and Constrained Probabilistic Matrix Factorization. They also use different amounts of training data (99%, 80%, 50%, 20%) and MAE metric to test all the algorithms. Moreover, to analyze the impact of the social network, they set different value for λC, ranging from 0.1 to 100. The results show that:
  • The value of λimpacts the recommendation results significantly, which demonstrates that fusing the user-item rating matrix with the user social network greatly improves the recommendation accuracy.
  • Their algorithm generally performs better than other methods, especially when few user ratings are given.
  • Using little social network information can cause overfitting problem, and that the predictive accuracy can be improved by incorporating more social network information.


This paper demonstrates that using social information can help to improve the quality and quantity of recommender systems. Especially, in the cases that users have never rated any items or just joined the system, having their social network information enables the systems to do feasible recommendations. Moreover, this information also helps to provide transparency about recommending items to users; for example, “this item was bought and liked by your mother and your brother”. Although the authors use the “trust” social network for their work, which is difficult to be measured in reality, the proposed framework gives us a better understanding about the importance of social information, and it could be applied for other systems.

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