A model-based collaborative filtering method for bounded support data

Collaborative filtering (CF) is an important technique used in some recommendation systems. The task of CF is to estimate the persons´ preferences (e.g., ratings) or to predict the preferences for the future, based on some already known persons´ preferences. In general, the model-based CF performs better than the memory-based CF, especially for highly sparse data. In this paper, we present a new model-based CF method for bounded support data, which takes into account the facts that the ratings are usually in a limited interval. A nonnegative matrix factorization (NMF) model is applied to investigate and learn the patterns hidden in the observed data matrix. Each rating value is assumed to be beta distributed and we assign the gamma prior to the parameters in a beta distribution for the purpose of Bayesian estimation. With variation inference framework and some lower bound approximations, an analytically tractable solution can be obtained for the proposed NMF model. By comparing with several existing low-rank matrix approximation methods, the good performance of the proposed method is demonstrated.