Optimum Nonlinear Discriminant Analysis and Discriminant Kernel Support Vector Machine

抄録

Kernel discriminant analysis (KDA) is the mainstream approach of nonlinear discriminant analysis (NDA). Since it uses the kernel trick, KDA does not consider its nonlinear discriminant mapping explicitly. In this paper, another NDA approach where the nonlinear discriminant mapping is analytically given is developed. This study is based on the theory of optimal nonlinear discriminant analysis (ONDA) of which the nonlinear mapping is exactly expressed by using the Bayesian posterior probability. This theory indicates that various NDA can be derived by estimating the Bayesian posterior probability in ONDA with various estimation methods. Also, ONDA brings an insight about novel kernel functions, called discriminant kernel (DK), which is defined by also using the posterior probabilities. In this paper, several NDA and DK derived from ONDA with several posterior probability estimators are developed and evaluated. Given fine estimation methods of the Bayesian posterior probability, they give good discriminant spaces for visualization or classification.