Dear All,
Thanks for valuable information. Just one more question! Could somebody explain to me the difference/similarity among Mahalanobis distance, Hotelling's T-square and PCA ? I believe that Hotelling's T-square is the sum of squares of the principal component scores if all components are extracted as the number of input variables. It seems to me that the Mahalanobis distance is the same as the Hotelling's T-square.
The relationship is not between Mahalanobis distance (D^2) and PCA, but rather between Mahalanobis distance and discriminant analysis. PCA decomposes the total variance, without regard for any kind of group structure, while DA decomposes the total among-group variance (with respect to within-group variance). The principal-component and discriminant functions need not coincide, and in fact can be quite different, depending on the nature of the group differences. Mahalanobis distance is one of the "triumvirate" of complementary procedures: D^2 measures the difference between groups, MANOVA tests whether that difference is statistically significant, and DA provides an ordination of the groups and describes the nature of the difference in terms of the original variables. Just as the t-test is the two-group special case of ANOVA, Hotelling's T^2 is the two-group case of the more general MANOVA.
I appreciate any helps and references. Happy holidays to all.
Sangdon Lee, Ph.D, GM Tech Center, MI, USA. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
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