  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.
