Logistic discriminant analysis

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 showed that the ONDA was closely related to Bayesian decision theory (the posterior probabilities). Also Otsu pointed out that LDA could be regarded as a linear approximation of the ONDA through the linear approximations of the Bayesian posterior probabilities. Based on this theory, we propose a novel nonlinear discriminant analysis named logistic discriminant analysis (LgDA) in which the 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.