Direct Minimization of Error Rates in Multivariate Classification

Abstract

We propose a computer intensive method for linear dimension reduction which minimizes the classification error directly. Simulated annealing (Bohachevsky et al. 1986) as a modern optimization technique is used to solve this problem effectively. This approach easily allows to incorporate user requests by means of penalty terms. Simulations demonstrate the superiority of optimal classification to classical discriminant analysis (McLachlan 1992). Special emphasis is put on the case when discriminant analysis collapses.