Dynamic matrix factorization with social influence

Matrix factorization is a key component of collaborative filtering-based recommendation systems because it allows us to complete sparse user-by-item ratings matrices under a low-rank assumption that encodes the belief that similar users give similar ratings and that similar items garner similar ratings. This paradigm has had immeasurable practical success, but it is not the complete story for understanding and inferring the preferences of people. First, peoples' preferences and their observable manifestations as ratings evolve over time along general patterns of trajectories. Second, an individual person's preferences evolve over time through influence of their social connections. In this paper, we develop a unified process model for both types of dynamics within a state space approach, together with an efficient optimization scheme for estimation within that model. The model combines elements from recent developments in dynamic matrix factorization, opinion dynamics and social learning, and trust-based recommendation. The estimation builds upon recent advances in numerical nonlinear optimization. Empirical results on a large-scale data set from the Epinions website demonstrate consistent reduction in root mean squared error by consideration of the two types of dynamics.