LDA-based Non-negative Matrix Factorization for Supervised Face Recognition

Abstract

In PCA based face recognition, the basis imagesmay contain negative pixels and thus do not facilitatephysical interpretation. Recently, the technique of nonnegativematrix Factorization (NMF) has been applied to face recognition: the non-negativity constraint of NMF yieldsa localized parts-based representation which achieves arecognition 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 basedon Fisher’s Linear Discriminant Analysis into the NMF algorithm and prove that our new update rule can maintainthe non-negativity constraint under a mild condition andhence 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.