Abstract:Users who rate few will have features that are close to the prior mean once the probabilistic matrix factorization(PMF) model has been fitted, which leads to the predictions close to the movie average ratings. Constrained probabilistic matrix factorization(CPMF) algorithm has not fully considered about the holistic diversity among different rating systems and the inherent attributes that different users and products hold within the datasets. To solve the problems above, the user and product bias and global average are combined with constrained probabilistic matrix factorization to build a new matrix factorization algorithm. The algorithm brings in the constrains to restrain the user bias among users of similar action while evaluating different rating systems with global average and representing the attributes of different users and products with biases to increase the prediction accuracy. The results of experiments on two real datasets indicate that the prediction accuracy of the algorithm has been improved compared to PMF and CPMF.