List-wise probabilistic matrix factorization for recommendation

• We improve the model of probabilistic matrix factorization, and propose ListPMF.
• The log-posterior over the predicted preference order is maximized in ListPMF.
• Two kinds of permutation probability are used in ListPMF.
• Compared with other methods, ListPMF gets more satisfying results.

Matrix factorization based recommendation methods gain great success due to their efficiency and accuracy. But optimizing the objective function in conventional matrix factorization based recommendation methods, which is the sum-of-square of factorization errors with regularization terms, does not ensure that the obtained recommendation results are consistent with the preference orders of the users. To address this problem, in this paper, we improve the model of probabilistic matrix factorization (PMF) and propose list-wise probabilistic matrix factorization (ListPMF). In ListPMF, we take the preference orders of the users indicated by observed ratings as a whole instance, and we maximize the log-posterior over the predicted preference order with the observed preference orders. By this way, the proposed method is able to get recommendation results more consistent with the user preferences. The proposed method is computationally efficient and can be applied to very large dataset. Experimental results on two real world datasets show that our method outperforms most of the compared state-of-the-art approaches.