Statistical Estimation of Discriminant Space using Various Projection Indices

Abstract

Projection pursuit is a method for finding interesting projections of high-dimensional multivariate data. Typically interesting projections are found by numerical maximizing some measure of non-normality of projected data (so-called projection index) over projection direction. The problem is to select the index for pro jection pursuit. In this article we compare performance of fi ve projection indices: projection indices based on !2, 2, Kolmogorov-Smirnov goodness-of- fit measures, entropy index and Friedman's index. It is supposed that observed random variable satisfi es a multidimensional Gaussian mixture model.

Keywords

• Gaussian mixture model
• discriminant space
• projection pursuit
• projection index