Robust kernel discriminant analysis using fuzzy memberships

Linear discriminant analysis (LDA) is a simple but widely used algorithm in the area of pattern recognition. However, it has some shortcomings in that it is sensitive to outliers and limited to linearly separable cases. To solve these problems, in this paper, a non-linear robust variant of LDA, called robust kernel fuzzy discriminant analysis (RKFDA) is proposed. RKFDA uses fuzzy memberships to reduce the effect of outliers and adopts kernel methods to accommodate non-linearly separable cases. There have been other attempts to solve the problems of LDA, including attempts using kernels. However, RKFDA, encompassing previous methods, is the most general one. Furthermore, theoretical analysis and experimental results show that RKFDA is superior to other existing methods in solving the problems.