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On Minimizing the Probability of Misclassification for Linear Feature Selection
L. F. Guseman, Jr., B. Charles Peters, Jr. and Homer F. Walker
The Annals of Statistics
Vol. 3, No. 3 (May, 1975), pp. 661-668
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/2958434
Page Count: 8
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We describe an approach to linear feature selection for n-dimensional normally distributed observation vectors which belong to one of m populations. More specifically, we consider the problem of finding a rank k k × n matrix B which minimizes the probability of misclassification with respect to the k-dimensional transformed density functions when a Bayes optimal (maximum likelihood) classification scheme is used. Theoretical results are presented which, for the case k = 1, give rise to a numerically tractable expression for the variation in the probability of misclassification with respect to B. The use of this exression in a computational procedure for obtaining a B which minimizes the probability of misclassification in the case of two populations is discussed.
The Annals of Statistics © 1975 Institute of Mathematical Statistics