Abstract

Matrix factorization underlies a large variety of computer vision ap- plications. It is a particularly challenging problem for large-scale applications and when there exist outliers and missing data. In this paper, we propose a novel probabilistic model called Probabilistic Robust Matrix Factorization (PRMF) to solve this problem. In particular, PRMF is formulated with a Laplace error and a Gaussian prior which correspond to an *1 loss and an *2 regularizer, respec- tively. For model learning, we devise a parallelizable expectation-maximization (EM) algorithm which can potentially be applied to large-scale applications. We also propose an online extension of the algorithm for sequential data to offer fur- ther scalability. Experiments conducted on both synthetic data and some practical computer vision applications show that PRMF is comparable to other state-of- the-art robust matrix factorization methods in terms of accuracy and outperforms them particularly for large data matrices.