Total variation norm-based nonnegative matrix factorization for identifying discriminant representation of image patterns

The low-rank approximation technique of nonnegative matrix factorization (NMF) is emerging recently for finding parts-based structure of nonnegative data based on minimizing least-square error (L2L2 norm). However, it has been observed that the proper norm for image processing is the total variation norm (TVN) other than the L2L2 norm, and image denoising methods applying TVN can preserve clearer local features, such as edges and texture than L2L2 norm. In this paper, we propose a robust TVN-based NMF algorithm for identifying discriminant representation of image patterns. We provide update rule in optimality search process and prove mathematically convergence of the iteration. Experimental results show that the proposed TVNMF is more effective to describe local discriminant representation of image patterns than NMF.