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IanMike
Posts:
102
Registered:
12/4/04


Re: LU decomposition and Mahalanobis distance
Posted:
Jul 3, 2006 2:44 PM


"Gordon Sande" <g.sande@worldnet.att.net> wrote in message news:2006070313042216807gsande@worldnetattnet...
> If you have a symmetric positive definite matrix (a covarince matrix > fits the requirements) then you should use a (Cholesky) LL^t > decomposition. > LU is for when there is either no symmetry or it is not positive definite.
To add to that: if you are calculating lots of Mahanalobis distances, you can use L^{1} to map your entire data set. Then Euclidean distance in the new space is equivalent to Mahanalobis distance in the old one.
I wouldn't worry about numerical accuracy in calculating an inverse of a 100x100 covariance matrix. Unless you have fantastic amount of data, the covariance matrix will be so poorly estimated that this will swamp any rounding errors. Regularizing the estimate is much more to the point.
Graham



