Fast calculation for fisher criteria in small sample size problem

LDA is popularly used in the pattern recognition field. Unfortunately LDA always confronts the small sample size problem (S3), which leads the within-class scatter matrix to be singular. In this case, PCA is always used for dimensional reduction to solve the problem in practice. This paper analyzes that when the small sample size problem happens, the PCA processing is not only to play the role of solving the S3 problem but also can be used to induce a fast calculation algorithm for solving the fisher criteria. This paper will show that calculating the eigenvectors of within-class scatter matrix after dimensional reduction can solve the optimal projection for fisher criteria.