Linear discriminant analysis using sparse matrix transform for face recognition

Abstract

In this paper, we present a sparse matrix transform (SMT) based linear discriminant analysis (LDA) algorithm for high dimensional data. The within-class scatter matrix in LDA is constrained to have an eigen-decomposition that can be represented as an SMT. Then, under maximum likelihood framework, based on greedy minimization strategy, the within-class scatter matrix can be efficiently estimated. Moreover, the estimated within-class scatter matrix is always positive definite and well-conditioned even with limited sample size, which overcomes the singularity problem in traditional LDA algorithm. The proposed method is compared, in terms of recognition rate, to other commonly used LDA methods on ORL and UMIST face databases. Results indicate that the performance of the proposed method is overall superior to those of traditional LDA approaches, such as the Fisherfaces, D-LDA, S-LDA and newLDA methods.