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*To*: AUDITORY@xxxxxxxxxxxxxxx*Subject*: Re: MDS distances*From*: "Bruno L. Giordano" <bruno.giordano@xxxxxxxxxxxxxxx>*Date*: Tue, 27 Jun 2006 14:56:18 -0400*Comments*: To: Pierre Divenyi <pdivenyi@EBIRE.ORG>*Delivery-date*: Tue Jun 27 15:05:48 2006*References*: <200606151846.k5FIkE1G021309@manfred.music.uiuc.edu> <9c1a4ffb0606210211y40a45568wb428d93267e66b4@mail.gmail.com> <4499175D.6010303@imag.fr> <DD117415-D827-4597-BCE4-9CA2CECB0BC7@ieee.org> <4ce21ddc0606271110w336acfa9pcd24aae97bc0956c@mail.gmail.com> <6.2.3.4.2.20060627113406.02918a70@ebire.org>*Reply-to*: "Bruno L. Giordano" <bruno.giordano@xxxxxxxxxxxxxxx>*Sender*: AUDITORY Research in Auditory Perception <AUDITORY@xxxxxxxxxxxxxxx>

weighted MDS models, which compute a subject-specific weight for each of the dimensions, give solutions which are not rotation-invariant.

Bruno

To: <AUDITORY@xxxxxxxxxxxxxxx>

Sent: Tuesday, June 27, 2006 2:41 PM

Subject: Re: MDS distances

Jean-Francois,

As to PCA (and factor analysis), interpreting the components (factors) runs into the same problem: any rotation will end up with a different set and a different story. One way out of the mess is to impose one particular rotation criterion (I used to use varimax), so at least you know how the loading matrix came to existence. But even that does not obviate the need for imagination. I used to say that without an artistic background, or bend, one should stay away from interpreting loading matrices.

Pierre

One should not try to interpret the "meaning" of MDS dimensions, since any rotation of an MDS solution is a completely equivalent solution. Hence, looking at the vectors components of an MDS solution has no sense unless you find a way to fix some dimensions in a meaningful way. That's why different MDS algorithms can lead to different (valid) solutions given the same initial similarity matrix. If your goal is to find the "intrinsic" dimensions of sound data, my opinion is that it would be preferable to use state-of-the-art dimensionality reduction algorithms (Isomap, LLE, non-local techniques, or even PCA), on a set of points obtained from MDS with no loss in higher dimension.

-- Jean-François Paiement Research Assistant IDIAP Research Institute Martigny, Switzerland paiement@xxxxxxxx

**References**:**MDS distances***From:*beaucham

**Re: MDS distances***From:*Jan Schnupp

**Re: MDS distances***From:*Olivier Tache

**Re: MDS distances***From:*Malcolm Slaney

**Re: MDS distances***From:*Jean-François Paiement

**Re: MDS distances***From:*Pierre Divenyi

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