[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

Re: MDS distances

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

----- Original Message ----- From: "Pierre Divenyi" <pdivenyi@xxxxxxxxx>
To: <AUDITORY@xxxxxxxxxxxxxxx>
Sent: Tuesday, June 27, 2006 2:41 PM
Subject: Re: MDS distances


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.


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