Graphical tools for quadratic discriminant analysis

被引:26
作者
Pardoe, Iain [1 ]
Yin, Xiangrong
Cook, R. Dennis
机构
[1] Univ Oregon, Lundquist Coll Business, Dept Decis Sci, Eugene, OR 97403 USA
[2] Univ Georgia, Dept Stat, Athens, GA 30605 USA
[3] Univ Minnesota, Sch Stat, Minneapolis, MN 55455 USA
基金
美国国家科学基金会;
关键词
canonical variates; classification; dimension reduction; linear discrimmant analysis; quadratic discriminant analysis; sliced average variance estimation;
D O I
10.1198/004017007000000074
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
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.
引用
收藏
页码:172 / 183
页数:12
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