Currently, many techniques exist for feature selection purposes which are related but, unfortunately, in an indeterminable way to the probability of misclassification. In this paper a procedure is presented which yields an upper bound (to any degree tightness) on the probability of misclassification in sample Gaussian maximum likelihood classification between each pair of categories in p-dimensional space. The technique permits features to be selected so that the optimal q (q <= p) features have the property that no other subset of q features yield a smaller value to the upper bound on the probability of misclassification.
A computer-assessable transformation is utilized which permits a multiple integral over the misclassification region in p-dimensional space to be approximated, to any degree of accuracy, by the product of p iterated integrals, each over univariate space, and each of which may be obtained by a simple table-look-up procedure. Quite often, transformations are used without consideration of loss of information~ however, the one utilized in this procedure results in no loss of information and leaves the standard likelihood ratio invariant in value.
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