Robust Local Coordinate Non-negative Matrix Factorization via Maximum Correntropy Criteria

Abstract

Non-negative matric factorization (NMF) decomposes a given data matrix X into the product of two lower dimensional non-negative matrices U and V. It has been widely applied in pattern recognition and computer vision because of its simplicity and effectiveness. However, existing NMF methods often fail to learn the sparse representation on high-dimensional dataset, especially when some examples are heavily corrupted. In this paper, we propose a robust local coordinate NMF method (RLCNMF) by using the maximum correntropy criteria to overcome such deficiency. Particularly, RLCNMF induces sparse coefficients by imposing the local coordinate constraint over both factors. To solve RLCNMF, we developed a multiplicative update rules and theoretically proved its convergence. Experimental results on popular image datasets verify the effectiveness of RLCNMF comparing with the representative methods.