Discriminant Kernels derived from the optimum nonlinear discriminant analysis

Abstract

Linear discriminant analysis (LDA) is one of the well known methods to extract the best features for multi-class discrimination. Recently Kernel discriminant analysis (KDA) has been successfully applied in many applications. KDA is one of the nonlinear extensions of LDA and construct nonlinear discriminant mapping by using kernel functions. But the kernel function is usually defined a priori and it is not known what the optimum kernel function for nonlinear discriminant analysis is. Also the class information is not usually introduced to define the kernel functions. In this paper the optimum kernel function in terms of the discriminant criterion is derived by investigating the optimum discriminant mapping constructed by the optimum nonlinear discriminant analysis (ONDA).