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A Modified Algorithm for Generalized Discriminant Analysis

wenming_zheng{at}seu.edu.cn, Engineering Research Center of Information Processing and Application, Southest University, Nanjing, Jiangsu 210096, People's Republic of China

Li Zhao

zhaoli{at}seu.edu.cn, Engineering Research Center of Information Processing and Application, Southest University, Nanjing, Jiangsu 210096, People's Republic of China

Cairong Zou

cairong{at}seu.edu.cn, Engineering Research Center of Information Processing and Application, Southest University, Nanjing, Jiangsu 210096, People's Republic of China

Generalized discriminant analysis (GDA) is an extension of the classical linear discriminant analysis (LDA) from linear domain to a nonlinear domain via the kernel trick. However, in the previous algorithm of GDA, the solutions may suffer from the degenerate eigenvalue problem (i.e., several eigenvectors with the same eigenvalue), which makes them not optimal in terms of the discriminant ability. In this letter, we propose a modified algorithm for GDA (MGDA) to solve this problem. The MGDA method aims to remove the degeneracy of GDA and find the optimal discriminant solutions, which maximize the between-class scatter in the subspace spanned by the degenerate eigenvectors of GDA. Theoretical analysis and experimental results on the ORL face database show that the MGDA method achieves better performance than the GDA method.

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				W. Zheng Class-incremental generalized discriminant analysis. Neural Comput., April 1, 2006; 18(4): 979 - 1006. [Abstract] [Full Text] [PDF]