The algorithm presented in this paper is a direct approach to the problem of determining a linear discriminant function which minimizes total classification error in a two-class training set. Discriminant function coefficients are determined by a search technique which is based on two theorems derived from convexity theory. The number of iterative steps in the search sequence has a theoretical upper bound which is strictly less than the number required for full enumeration, and applications of the algorithm to experimental data have established its tractability under nontrivial conditions. Although the training set patterns are initially assumed to be in general position, this restriction is essentially eliminated by an extension of the algorithm which is briefly discussed.
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