A non negative matrix factorization for collaborative filtering recommender systems based on a Bayesian probabilistic model

In this paper we present a novel technique for predicting the tastes of users in recommender systems based on collaborative filtering. Our technique is based on factorizing the rating matrix into two non negative matrices whose components lie within the range [0, 1] with an understandable probabilistic meaning. Thanks to this decomposition we can accurately predict the ratings of users, find out some groups of users with the same tastes, as well as justify and understand the recommendations our technique provides.