TITLE:
Linear Dimension Reduction for Multiple Heteroscedastic Multivariate Normal Populations
AUTHORS:
Songthip T. Ounpraseuth, Phil D. Young, Johanna S. van Zyl, Tyler W. Nelson, Dean M. Young
KEYWORDS:
Linear Transformation, Bayes Classification, Feature Extraction, Probability of Misclassification
JOURNAL NAME:
Open Journal of Statistics,
Vol.5 No.4,
June
24,
2015
ABSTRACT: 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.