Modified Generalized Discriminant Analysis Using Orthogonalization in Feature Space and Difference Space

Abstract

In this paper we propose a more efficient and effective algorithm of generalized discriminant analysis (GDA) by performing Gram-Schmidt orthogonalization procedure in feature space only once on difference vectors. The proposed method is substantially equivalent to class-incremental GDA [W. Zheng, ?class-Incremental generalized discriminant analysis?, neural computation 18, 979-1006 (2006)], since both methods search the essentially equivalent nonlinear optimal discriminative vectors in the range space of total scatter matrix and the null space of within-class scatter matrix. But since there is no need to compute the class mean in the proposed method as needed in class-incremental GDA, the computational cost is reduced greatly in the proposed method. The experiments on two standard face databases verified the effectiveness of the proposed method.