Fuzzy maximum scatter discriminant analysis with kernel methods

A novel nonlinear feature extraction method with fuzzy set theory, called KFMSD (kernel based fuzzy maximum scatter difference), is proposed. The proposed method first maps the input data into a potentially much higher dimensional feature space by virtue of nonlinear kernel trick, and thus, the problem of nonlinear feature extraction is overcome. Then, the fuzzy maximum scatter difference is performed on the feature space; therefore, not only the singularity problem of the within-class scatter matrix due to small sample size problem occurred in classical Fisher discriminant analysis is avoided, but also the overlapping (outlier) samples' distribution information is incorporated in the redefinition of corresponding scatter matrices, which is important for classification. The experiment results on the FERET face database and Yale face database show that the proposed method can work well.