Finding Relevant Linear Manifolds in Classification by Gaussian Mixtures

Abstract

In this article, we present a strategy for producing low-dimensional projections that maximally separate the classes in Gaussian Mixture Model classification. The most revealing linear manifolds are those along which the classes are maximally separable. Here we consider a particular probability product kernel as a measure of similarity or affinity between the class-conditional distributions. It takes an appealing closed analytical form in the case of Gaussian mixture components. The performance of the proposed strategy has been evaluated on real data.

Keywords:

• Bayes error
• Dimension reduction
• Expected likelihood kernel
• Gaussian mixture models

Mathematics Subject Classification:

• Primary 62Hxx
• Secondary 62H30