Feature extraction using fuzzy maximum margin criterion

In pattern recognition, feature extraction techniques are widely employed to reduce the dimensionality of date. In this paper, a novel feature extraction criterion, fuzzy maximum margin criterion (FMMC), is proposed by means of the maximum margin criterion (MMC) and fuzzy set theory. More specifically, the between-class and within-class fuzzy scatter matrices are redefined by incorporating the membership degrees of samples which relates the samples distribution information; then the feature extraction criterion maximized the average margin between classes after dimensionality reduction is applied. Furthermore, we utilize the generalized singular value decomposition (GSVD) to the criterion, which make the algorithm more effective; for nonlinear separated problems, we extend the kernel extension of FMMC with positive definite kernels. The effective of the novel criterion for linear and nonlinear separated problems is illustrated by experiments.