High-order Fisher's discriminant analysis

Abstract

This paper introduces a novel nonlinear extension of Fisher's classical linear discriminant analysis (FDA) known as high-order Fisher's discriminant analysis (HOFDA). The ability of the new method to capture nonlinear relationships stems from its use of an extended polynomial space constructed out of the original features. Furthermore, a genetic algorithm (GA) is used in order to incrementally generate an optimal subset of polynomial features out of an initial pool of minimal discriminants. This procedure yields surprisingly compact discriminants with state of the art recognition rates for the difficult UCI thyroid classification problem.