Bayesian Robust Matrix Factorization for Image and Video Processing

Abstract

Matrix factorization is a fundamental problem that is often encountered in many computer vision and machine learning tasks. In recent years, enhancing the robustness of matrix factorization methods has attracted much attention in the research community. To benefit from the strengths of full Bayesian treatment over point estimation, we propose here a full Bayesian approach to robust matrix factorization. For the generative process, the model parameters have conjugate priors and the likelihood (or noise model) takes the form of a Laplace mixture. For Bayesian inference, we devise an efficient sampling algorithm by exploiting a hierarchical view of the Laplace distribution. Besides the basic model, we also propose an extension which assumes that the outliers exhibit spatial or temporal proximity as encountered in many computer vision applications. The proposed methods give competitive experimental results when compared with several state-of-the-art methods on some benchmark image and video processing tasks.