Abstract: Aiming at the problem that matrix factorization based collaborative filtering recommender systems perform low accuracy in prediction and recommendation,a improved matrix factorization method and collaborative filtering recom-mender system were proposed.Firstly,the rating matrix is factorized into two non-negative matrices,and the rating results are normalized to show probabilistic meaning.Then,variational inference is used to compute the distribution of the real posterior distribution of Bayesian model.Lastly,the user groups with the same preference are searched and the preferences of each user are predicted.Besides,a recommendation result decision algorithm with low computational complexity and low storage overhead was designed based on the sparsity of the user vectors.Three public datasets based experimental results show that the proposed algorithm has better performance than other algorithms in prediction accuracy and recommendation effect.

Key words: Collaborative filtering,Bayesian probabilistic model,Variational inference,Matrix factorization,Rating matrix