Nonnegative matrix factorization with bounded total variational regularization for face recognition

Nonnegative matrix factorization (NMF) is a recently developed technique for finding parts-based, linear representations of nonnegative data based on minimizing least square error (L-2 norm). However it has been observed that the proper norm for images is the bounded total variation (TV) norm other than the L-2 norm. The space of functions of bounded TV allows discontinuous solution and plays an important role in image processing. In this paper, we propose a new NMF model with bounded TV regularization for identifying discriminate representation of image patterns. We provide a simple update rule for computing the factorization and give supporting theoretical analysis. Finally, we perform a series of numerical experiments to show evidence of the good behavior of the numerical scheme. Crown Copyright (C) 2010 Published by Elsevier B.V. All rights reserved.