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I am wondering how and/or why the Mahalanobis distance is different from using the Euclidean distance on standardized variables?

Ben
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    Perhaps the explanation at https://stats.stackexchange.com/questions/62092/bottom-to-top-explanation-of-the-mahalanobis-distance/62147#62147 will make the distinction clear. – whuber Jun 30 '19 at 19:02
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    Both are euclidean distances computed on the reshaped (transformed) data cloud. The reshaping is different, though. Standardization squeezes/stretches along the variable axes and that does not change correlation magnitude. Mahalanobis squeezes/stretches along the principal axes and that makes correlation zero (sphering of the cloud). – ttnphns Jun 30 '19 at 20:18
  • @ttnphns That's interesting. Is it valid to say that Mahalanobis distance constructs its own axes or even orthogonal system? – Ben Jul 01 '19 at 06:50
  • In a sense yes. Wikipedia on Mahalanobis explains what is going geometrically. – ttnphns Jul 01 '19 at 07:12

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