Nonparametric discriminant analysis via recursive optimization of Patrick-Fisher distance

A method for the linear discrimination of two classes is presented. It searches for the discriminant direction which maximizes the Patrick-Fisher (PF) distance between the projected class-conditional densities. It is a nonparametric method, in the sense that the densities are estimated from the data. Since the PF distance is a highly nonlinear function, we propose a recursive optimization procedure for searching the directions corresponding to several large local maxima of the PF distance. Its novelty lies in the 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 and a medical data analysis indicate the potential of the method to find the sequence of directions with significant class separations.