A note on optimum linear feature extraction for gaussian populations with equal covariances and equal a priori probabilities |
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Authors: | B C Peters Jr J L Solomon |
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Institution: | 1. TF32/Earth Observations , Johnson Space Center , Houston, Texas, 77058;2. Department of Mathematics , Mississippi State University , Mississippi State, MS, 39762 |
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Abstract: | We consider the linear feature selection problem of obtaining a nonzero 1 × n matrix B which minimizes the probability of misclassification based on the Bayes decision rule applied to the random variable Y = BX, where X is a random n-vector arising from one of m Gaussian populations with equal covariances and equal apriori probabilities. It is shown that the optimal B satisfies a fixed point equation B = F(B) which can be solved by successive substitution. |
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Keywords: | feature selection classification multivariate normal populations local contraction fixed point |
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