Sangdon Lee wrote: > 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.
You are correct. T-squared from PCA with all possible components is exactly equal to Mahalanobis distance. If fewer than the maximum number of components are used, then the two quantities would NOT be equal. Reference: Jackson, J.E. (1991) "A User's Guide To Principal Components", John Wiley and Sons, New York. Jackson doesn't specifically refer to Mahalanobis, but his formula 1.7.3 shows the relationship between T-squared and x'Sx which is the Mahalanobis formula. -- Paige Miller Eastman Kodak Company paige dot miller at kodak dot com http://www.kodak.com "It's nothing until I call it!" -- Bill Klem, NL Umpire "When you get the choice to sit it out or dance, I hope you dance" -- Lee Ann Womack . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
