Re: Mahalanobis distance
From: Dave Eberly (dNOSPAMeberly_at_usemydomain.com)
Date: 11/16/04
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Date: Tue, 16 Nov 2004 04:07:38 GMT
"Vasileios Zografos" <noone@nowhere.net> wrote in message
news:cnanbe$5oi$1@newsg4.svr.pol.co.uk...
> 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.
This is one of those terms that folks have used correctly
and incorrectly. I have usually seen (1) as the definition,
but as others have pointed out, the units are squared
distance. Naturally, (2) has units of distance, but once
an incorrect usage shows up in the literature, it tends to
be propagated. For the purposes of classification in
statistical pattern recognition, you only compare two
such "distances", so (1) or (2) equally suffice.
This type of ambiguity in nomenclature is right up there
with "Gaussian curvature", which actually has units of
(signed) squared curvature and "norm of a quaternion"
(sometimes length, sometimes squared length).
-- Dave Eberly http://www.magic-software.com
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