Principal component analysis (PCA) can be regarded as approximating a data matrix with a low-rank one by imposing sparsity on its singular values, and its robust variant further captures sparse noise. In this paper, we extend such sparse matrix learning methods, and propose a novel unied framework called sparse additive matrix factorization (SAMF). SAMF systematically induces various types of sparsity by the so-called model-induced regularization in the Bayesian framework. We propose an iterative algorithm called the mean update (MU) for the variational Bayesian approximation to SAMF, which gives the global optimal solution for a large subset of parameters in each step. We demonstrate the usefulness of our method on articial data and the foreground/background video separation.
['Shinichi Nakajima', 'Masashi Sugiyama', 'S. Derin Babacan']
Sparse Additive Matrix Factorization for Robust PCA and Its Generalization