Mahalanobis distance

From: Vasileios Zografos (noone_at_nowhere.net)
Date: 11/15/04 

Date: Mon, 15 Nov 2004 17:00:47 +0000

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?

Thank you
V.Z.

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