Movie Recommendation via Markovian Factorization of Matrix Processes

The success of the probabilistic matrix factorization (PMF) model has inspired the rapid development of collaborative filtering algorithms, among which timeSVD++ has demonstrated great performance advantage in solving the movie rating prediction problem. Allowing the model to evolve over time, timeSVD++ accounts for “concept drift” in collaborative filtering by heuristically modifying the quadratic optimization problem derived from the PMF model. As such, timeSVD++ no longer carries any probabilistic interpretation. This lack of frameworks makes the generalization of timeSVD++ to other collaborative filtering problems rather difficult. This paper presents a new model family termed Markovian factorization of matrix process (MFMP). On one hand, MFMP models, such as timeSVD++, are capable of capturing the temporal dynamics in the dataset, and on the other hand, they also have clean probabilistic formulations, allowing them to adapt to a wide spectrum of collaborative filtering problems. Two simple example models in this family are introduced for the prediction of movie ratings using time-stamped rating data. The experimental study using MovieLens dataset demonstrates that the two models, although simple and primitive, already have comparable or even better performance than timeSVD++ and a standard tensor factorization model.