Linear discriminant analysis for two classes via recursive neural network reduction of the class separation

Abstract

A method for the linear discrimination of two classes is presented. It maximizes the Patrick-Fisher (PF) distance between the projected class-conditional densities. Since the PF distance is a highly nonlinear function, we propose a method, which searches for the directions corresponding to several large local maxima of the PF distance. Its novelty lies in a neural network transformation of the data along a found direction into data with deflated maxima of the PF distance and iteration to obtain the next direction. A simulation study indicates that the method has the potential to find the global maximum of the PF distance.