Sufficient dimension-reduction methods provide effective ways to visualize discriminant analysis problems. For example, Cook and Yin showed that the dimension-reduction method of sliced average variance estimation (SAVE) identifies variates that are equivalent to a quadratic discriminant analysis (QDA) solution. This article makes this connection explicit to motivate the use of SAVE variates in exploratory graphics for discriminant analysis. Classification can then be based on the SAVE variates using a suitable distance measure. If the chosen measure is Mahalanobis distance, then classification is identical to QDA using the original variables. Just as canonical variates provide a useful way to visualize linear discriminant analysis (LDA), so do SAVE variates help visualize QDA. This would appear to be particularly useful given the lack of graphical tools for QDA in current software. Furthermore, whereas LDA and QDA can be sensitive to nonnormality, SAVE is more robust.
Bibliographical noteFunding Information:
The authors are grateful to the associate editor and the referees for helpful comments on earlier versions of this article. This work was supported in part by National Science Foundation grant DMS-04-05360 awarded to R. Dennis Cook.
Copyright 2011 Elsevier B.V., All rights reserved.
- Canonical variAtes
- Dimension reduction
- Linear discriminant analysis
- Quadratic discriminant analysis
- Sliced average variance estimation