The role of eigenvalues in linear feature selection theory

Abstract

The analysis concerns the role of eigenvalues in determining a particular measure of pattern class distinction called the divergence, which is the pairwise average of the expected interclass divergence derived from Hajek's two-class divergence. Decel and Quirein (1973) showed that there always exists a k x n real matrix B such that the transformation determined by B maximizes divergence in k-dimensional space, and that B can be written as a product involving an orthogonal n x n matrix U. In the present paper it is shown that divergence measure of pattern class distinction does not depend on the eigenvalues of U.