Weighted Fisher Non-negative Matrix Factorization for Face Recognition

In this paper, we extend the Fisher nonnegative matrix factorization (FNMF) to weighted FNMF (WFNMF). The goal of this technique is to improve the performance of FNMF-based face recognition method under varying expressions, varying illumination, and especially for the case of partial occlusions. An objective function is defined by incorporating weighting into the cost of FNMF decomposition in order to emphasize parts of the data matrix to be approximated. Weighted iterative scheme is derived from FNMF algorithm by incorporating weights into the FNMF update rules. In particular, when applied to face recognition, WFNMF employed a face-centered weighting function in order that as many discriminate features as possible at the center of faces are extracted. Experimental results are presented to compare WFNMF with the FNMF, LNMF, NMF and PCA methods for face recognition, which demonstrates advantages of WFNMF.