Odell and Decell and Coberly have given necessary and sufficient conditions for calculating the matrix of smallest dimension that will preserve the original Bayes classification regions when all population parameters are known. Tubbs et al have given a solution to the problem of finding the smallest Bayes classification-region-preserving dimension whenever the population parameters are unknown. This paper presents another solution to the problem and then compares the two solutions to the classical Wilks’ method and two other recent methods using a Monte Carlo simulation. The SVD linear feature selection method paroposed by Tubbs et al. performs the best over each of the configurations used in this Monte Carlo simulation study.

--Authors’ Abstract

The superiority of the SVD method over the Principal Components (PC) method is quite marginal. The following data are taken from the authors’ summary table of results:

:9I where M is the Method using known means and covariance matrices, PCC is the Probability of Correct Classification, and SD is the Standard Deviation. In view of the truly insignificant difference between the SVD and PC methods, the only interesting comparison would be based on the relative costs of the two methods. This information is lacking in the article.

--M. Nadler, Blacksburg, VA