Binomial Matrix Factorization for Discrete Collaborative Filtering

Matrix factorization (MF) models have proved efficient and well scalable for collaborative filtering (CF) problems. Many researchers also present the probabilistic interpretation of MF. They usually assume that the factor vectors of users and items are from normal distributions, and so are the ratings when the user and item factors are given. Then they can derive the exact MF algorithm by finding a MAP estimate of the model parameters. In this paper we suggest a new probabilistic perspective on MF for discrete CF problems. We assume that all ratings are from binomial distributions with different preference parameters instead of the original normal distributions. The new interpretation is more reasonable for discrete CF problems since they only allow several legal discrete rating values. We also present two effective algorithms to learn the new model and make predictions. They are applied to the Netflix Prize data set and acquire considerably better accuracy than those of MF.