IEEE TRANSACTIONS ON SYSTEM, MAN AND CYBERNETICS, PART B 1 Discriminant Subspace Analysis for Face Recognition with Small Number of Training Samples Hui Kong, Xuchun Li, Matthew Turk, and Chandra Kambhamettu Abstract In this paper, a framework of Discriminant Subspace Analysis (DSA) method is proposed to deal with the Small Sample Size (SSS) problem in face recognition area. Firstly, it is rigorously proven that the null space of the total covariance matrix, S t , is useless for recognition. Therefore, a framework of Fisher discriminant analysis in a low-dimensional space is developed by projecting all the samples onto the range space of S t . Two algorithms are proposed in this framework, i.e., Unified Linear Discriminant Analysis (ULDA) and Modified Linear Discriminant Analysis (MLDA). ULDA extracts discriminant information from three subspaces of this low-dimensional space. MLDA adopts a modified Fisher criterion which can avoid the singularity problem in conventional LDA. Experimental results on a large combined database have demonstrated that the proposed ULDA and MLDA can both achieve better performance than the other state-of-the-art subspace based methods in recognition accuracy. Keywords Fisher Linear Discriminant, face recognition, Small Sample Size problem I. Introduction L INEAR Discriminant Analysis [1] is a well-known scheme for feature extraction and dimension reduction. It has been used widely in many applications such as face recognition [3], image retrieval [5], text classification [6], micro-array data classification [7], etc. Classical LDA projects the data onto a lower-dimensional vector space such that the ratio of the between-class scatter to the within-class scatter is maximized, thus achieving maximum discrimination. The optimal projection (transformation) can be readily computed by solving a generalized eigenvalue problem. However, the intrinsic limitation of classical LDA is that its objective function requires the within-class covariance matrix to be nonsingular. For many applications, such as face recognition, all scatter matrices in question can be Hui Kong, Xuchun Li are with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798. E-mail: konghui@pmail.ntu.edu.sg. Matthew Turk is with the Department of Computer Science, University of California, Santa Barbara, CA, U.S.A Chandra Kambhamettu is with the Department of Computer and Information Science, University of Delaware, Newark, DE, USA 19716- 2712