Direct minimization of error rates in multivariate classification

We propose a computer intensive method for linear dimension reduction that minimizes the classification error directly. Simulated annealing (Bohachevsky et al. 1986), a modern optimization technique, is used to solve this problem effectively. This approach easily allows user preferences to be incorporated by means of penalty terms. Simulations and a real world example demonstrate the superiority of this optimal classification to classical discriminant analysis (McLachlan 1992). Special emphasis is given to the case when discriminant analysis collapses.