2009 IEEE International Conference on
Systems, Man, and Cybernetics |
Abstract
Linear discriminant analysis (LDA) is one of the well known methods to extract the best features for the multi-class discrimination. Otsu derived the optimal nonlinear discriminant analysis (ONDA) by assuming the underlying probabilities and shown that the ONDA closely relates to Bayesian decision theory (a posteriori probabilities). Also Otsu pointed out that LDA can be regarded as the linear approximation of the ONDA through the linear approximations of the Bayesian a posterior probabilities. Based on these theory, we propose a novel nonlinear discriminant analysis named logistic discriminant analysis (LgDA) in which the Bayesian a posterior probabilities are estimated by multi-nominal logistic regression (MLR). The experimental results are shown by comparing the discriminant spaces constructed by LgDA and LDA for the standard repository datasets.