¹School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou Guangdong 510631, China
²Department of Mathematics, Hong Kong Baptist University, Hong Kong, China
³Departamento de Matematica - UFPR,Centro Politecnico, CP:19.081, 81531-990, Curitiba, PR, Brazil

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Abstract—In PCA based face recognition, the basis images may contain negative pixels and thus do not facilitate physical interpretation. Recently, the technique of nonnegative matrix Factorization (NMF) has been applied to face recognition: the non-negativity constraint of NMF yields a localized parts-based representation which achieves a recognition rate that is on par with the eigenface approach. In this paper, we propose a new variation of the NMF algorithm that incorporates training information in a supervised learning setting. We integrate an additional term based on Fisher’s Linear Discriminant Analysis into the NMF algorithm and prove that our new update rule can maintain the non-negativity constraint under a mild condition and hence preserve the intuitive meaning for the base vectors and weight vectors while facilitating the supervised learning of within-class and between-class information. We tested our new algorithm on the well-known ORL database, CMU PIE database and FERET database, and the results from experiments are very encouraging compared with traditional techniques including the original NMF, the Eigenface method, the sequential NMF+LDA method and the Fisherface method.

Index Terms—nonnegative matrix factorization, principal component analysis, fisher linear discriminant analysis, eigenface, fisherface

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Cite: Yun Xue, Chong Sze Tong, Jing Yun Yuan, "LDA-based Non-negative Matrix Factorization for Supervised Face Recognition," Journal of Software vol. 9, no. 5, pp. 1294-1301, 2014.