Subject: Re: MDS distances From: "Bruno L. Giordano" <bruno.giordano@xxxxxxxx> Date: Tue, 27 Jun 2006 14:56:18 -0400Dear 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. Bruno ----- Original Message ----- From: "Pierre Divenyi" <pdivenyi@xxxxxxxx> To: <AUDITORY@xxxxxxxx> 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 > >