On the Effects of Dimension in Discriminant Analysis for Unequal Covariance Populations

Abstract

This paper is a continuation of earlier work (Van Ness and Simpson [9]) studying the high dimensionality problem in discriminant analysis. Frequently one has potentially many possible variables (dimensions) to be measured on each object but is limited to a fixed training data size. For particular populations, we give here the change in probability of correct classilication caused by adding dimensions. This gives insight into how many variables one should use for fixed training data sizes, especially when dealing with the populations of these studies. We consider six basic discriminant analysis algorithms. Graphs are provided which compare the relative performance of the algorithms in high dimensions.

KEYWORDS:

• Discriminant analysis
• Pattern recognition
• Linear discriminant analysis
• Quadratic discriminanl analysis
• Nonparametric discriminant analysis
• Variable selection