Re: MDS distances

[Pierre Divenyi <pdivenyi@xxxxxxxxx>]

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