  Social recommender systems exploit users' social relationships to improve the
recommendation accuracy. Intuitively, a user tends to trust different subsets
of her social friends, regarding with different scenarios. Therefore, the main
challenge of social recommendation is to exploit the optimal social dependency
between users for a specific recommendation task. In this paper, we propose a
novel recommendation method, named probabilistic relational matrix
factorization (PRMF), which aims to learn the optimal social dependency between
users to improve the recommendation accuracy, with or without users' social
relationships. Specifically, in PRMF, the latent features of users are assumed
to follow a matrix variate normal (MVN) distribution. The positive and negative
dependency between users are modeled by the row precision matrix of the MVN
distribution. Moreover, we have also proposed an efficient alternating
algorithm to solve the optimization problem of PRMF. The experimental results
on real datasets demonstrate that the proposed PRMF method outperforms
state-of-the-art social recommendation approaches, in terms of root mean square
error (RMSE) and mean absolute error (MAE).
