Nonnegative matrix factorization with bounded total variational regularization for face recognition

Authors:
Haiqing Yin;Hongwei Liu
Affiliations:
Department of Applied Mathematics, Xidian University, Xi'an 710071, China;Department of Applied Mathematics, Xidian University, Xi'an 710071, China
Venue:
Pattern Recognition Letters
Year:
2010

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Abstract

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.