Robust probabilistic tensor analysis for time-variant collaborative filtering

The input data of collaborative filtering, also known as recommendation system, are usually sparse and noisy. In addition, in many cases the data are time-variant and have obvious periodic property. In this paper, we take the two characteristics into account. To utilize the time-variant and periodic properties, we describe the data as a three-order tensor and then formulate the collaborative filtering as a problem of probabilistic tensor decomposition with a time-periodical constraint. The robustness is achieved by employing Tsallis divergence to describe the objective function and q-EM algorithm to find the optimal solution. The proposed method is demonstrated on movie recommendation. Experimental results on two Netflix and Movielens databases show the superiority of the proposed method.