Re: Mahalanobis distance
From: Graham Jones (graham_at_visiv.co.uk)
Date: 11/15/04
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Date: Mon, 15 Nov 2004 21:06:04 +0000
In article <cnanbe$5oi$1@newsg4.svr.pol.co.uk>, Vasileios Zografos
<noone@nowhere.net> writes
>Can someone please clarify for me which is the formula for the Mahalanobis
>distance?
>
>Is it (1) M=(x-m)'(S^-1)(x-m)
>
>or (2) M=[(x-m)'(S^-1)(x-m)]^1/2
>
>where S^-1 the inverse of the covariance matrix and m the mean of the
>cluster.
>
>My guess is that it is (1) because if we do PCA we can derive that
>M=sum(b^2/lamda) where b are the parameters of the PCA and lamda the
>eigenvalues of the eigendecomposition.
>
>
>However, I have seen formula (2) for the Mahalanobis distance, with the
>explanation that for S=identity, the Mahalanobis simplifies to the
>Euclidean distance.
>
>So, which is the right one?
>
As far as I know, (2) is correct. (1) is properly called "Mahalanobis
distance squared". But it is not uncommon to see people forget the
"squared".
-- Graham Jones http://www.visiv.co.uk Emails to graham@visiv.co.uk may be deleted as spam Please add a j just before the @ to ensure delivery
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