Robust sparse tensor decomposition by probabilistic latent semantic analysis

Movie recommendation system is becoming more and more popular in recent years. As a result, it is becoming increasingly important to develop machine learning algorithm on partially-observed matrix to predict users' preferences on missing data. Motivated by the user ratings prediction problem, we propose a novel robust tensor probabilistic latent semantic analysis (RT-pLSA) algorithm that not only takes time variable into account, but also uses the periodic property of data in time attribute. Different from the previous algorithms of predicting missing values on two-dimensional sparse matrix, we formulize the prediction problem as a probabilistic tensor factorization problem with periodicity constraint on time coordinate. Furthermore, we apply the Tsallis divergence error measure in the context of RT-pLSA tensor decomposition that is able to robustly predict the latent variable in the presence of noise. Our experimental results on two benchmark movie rating dataset: Netflix and Movielens, show a good predictive accuracy of the model.