# Sparse Additive Matrix Factorization for Robust PCA and Its Generalization

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Shinichi Nakajima,
Masashi Sugiyama,
S. Derin Babacan
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Proceedings of the Asian Conference on Machine Learning, PMLR 25:301-316, 2012.

#### Abstract

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 unified 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 artificial data and the foreground/background video separation.

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