文章基本信息

标题：Linear Dimension Reduction for Multiple Heteroscedastic Multivariate Normal Populations
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作者：Songthip T. Ounpraseuth 1 , Phil D. Young 2 , Johanna S. van Zyl 2 , Tyler W. Nelson 2 , Dean M. Young
期刊名称：Open Journal of Statistics
印刷版ISSN：2161-718X
电子版ISSN：2161-7198
出版年度：2015
卷号：05
期号：04
页码：311-333
DOI：10.4236/ojs.2015.54033
语种：English
出版社：Scientific Research Publishing
摘要：For the case where all multivariate normal parameters are known, we derive a new linear dimension reduction (LDR) method to determine a low-dimensional subspace that preserves or nearly preserves the original feature-space separation of the individual populations and the Bayes probability of misclassification. We also give necessary and sufficient conditions which provide the smallest reduced dimension that essentially retains the Bayes probability of misclassification from the original full-dimensional space in the reduced space. Moreover, our new LDR procedure requires no computationally expensive optimization procedure. Finally, for the case where parameters are unknown, we devise a LDR method based on our new theorem and compare our LDR method with three competing LDR methods using Monte Carlo simulations and a parametric bootstrap based on real data.
关键词：Linear Transformation; Bayes Classification; Feature Extraction; Probability of Misclassification