Fast Non-Negative Matrix Factorizations for Face Recognition

Abstract

Non-negative Matrix Factorization (NMF), as a promising image-data representation approach, encounters the problems of slow convergence and weak classification ability. To overcome these limitations, this paper, based on different error measurements, proposes two kinds of NMF algorithms with fast gradient descent and high discriminant performance. It is shown that the proposed Fast NMF (FNMF) methods have larger step sizes than those of traditional NMFs. Moreover, the traditional NMFs are the special cases of our methods. To further enhance the discriminative power of non-negative features, we exploit our previous block NMF technique and obtain Block FNMF (BFNMF) algorithms, which are supervised decomposition approaches with some good properties, such as the highly sparse features and orthogonal features from different classes. In experiments, both convergence on non-negative decomposition and performance on face recognition (FR) are considered for evaluations. Compared with traditional NMF algorithms and some state-of-the-art methods, experimental results indicate the effective and superior performance of the proposed NMF methods.