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From: Alex Zak <zak.alex@gmail.com>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Distance between two distributions
Date: Mon, 2 Feb 2009 12:56:08 -0800 (PST)
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On Jan 31, 12:44=A0am, Greg Heath <he...@alumni.brown.edu> wrote:
> On Jan 31, 12:00=A0am, Greg Heath <he...@alumni.brown.edu> wrote:
>
> > On Jan 30, 4:26 pm,AlexZak<zak.a...@gmail.com> wrote:
>
> > > What is the best criteria to measure distance between two independent
> > > normal distributions using Matlab??
>
> > > Thanks.
>
> > 1. Mahalanobis distance for linear classifiers is proportional to
>
> > (m2-m1)' * inv( (C1 + C2)/2 ) * (m2-m1)
>
> > 2. Bhattycharya (Bhattacharya?) distance for linear and quadratic
> > classifiers is proportional to
>
> > (m2-m1)' * ( ( inv(C1) + inv(C2) )/2 ) * (m2-m1)
>
> BZZT!
>
> Sorry, that is proportional to a term in the quadratic classifier
> discriminant.
>
> Seehttp://en.wikipedia.org/wiki/Bhattacharyya_coefficient
>
> which yields
>
> (1/8) * (m2-m1)' * inv( (C1 + C2)/2 ) * (m2-m1)
>
> + (1/2) * ln( det(C) / sqrt( det(C1) * det(C2) )
>
> > See Devijver and Kittler (1981?) for a comprehensive discussion of
> > separability measures.
>