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May, 1975 On Minimizing the Probability of Misclassification for Linear Feature Selection
L. F. Guseman Jr., B. Charles Peters Jr., Homer F. Walker
Ann. Statist. 3(3): 661-668 (May, 1975). DOI: 10.1214/aos/1176343128

Abstract

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 $k k \times n$ 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 $\mathbf{B}$. The use of this exression in a computational procedure for obtaining a $\mathbf{B}$ which minimizes the probability of misclassification in the case of two populations is discussed.

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L. F. Guseman Jr.. B. Charles Peters Jr.. Homer F. Walker. "On Minimizing the Probability of Misclassification for Linear Feature Selection." Ann. Statist. 3 (3) 661 - 668, May, 1975. https://doi.org/10.1214/aos/1176343128

Information

Published: May, 1975
First available in Project Euclid: 12 April 2007

zbMATH: 0303.62048
MathSciNet: MR370937
Digital Object Identifier: 10.1214/aos/1176343128

Subjects:
Primary: 62H30
Secondary: 62C10

Rights: Copyright © 1975 Institute of Mathematical Statistics

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Vol.3 • No. 3 • May, 1975
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