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SummaryWe 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 my 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.

Direct Minimization of Error Rates in Multivariate Classification