Solving Undersampled Problem of LDA Using Gram-Schmidt Orthogonalization Procedure in Difference Space

Abstract

In this paper, we propose an efficient and effective method to solve undersampled problem of linear discriminant analysis (LDA) by performing orthogonalization procedure only once in the difference space. Since in the proposed method, the optimal discriminant vectors are immediately obtained by performing orthogonalization procedure once on difference vectors, the efficiency is improved greatly compared with the existing methods. In terms of performance of classification, the proposed method is equivalent to existing LDA methods since these methods search optimal discriminative vectors of LDA in range space of total scatter matrix St and null space of within-class scatter matrix Sw. However, in terms of real-time performance, the proposed method is superior to the existing methods. The effectiveness of the proposed method is verified in the experiments on three standard face databases.