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Re: MDS distances

I'm currently doing MDS only on music but i think on my experience your output has a quite high dimensionality. What is the stress value you get out of it? Usually this is the measure to test your dimensions in literature. If the stress is between 0.1 and 0.15 the dimensions found are sufficient. I tried different matlab implementation of MDS and i am not sure they are really good. For my experience ALSCAL is a good free alternative and i can send a link to you if you need.
Try to freeze the number of dimensions (3:10) and  see how goes the stress value trend and then choose the best compromise.

Alberto Novello
Philips Research

Philips High Tech
WO 88 
prof. Holstlaan 4
5600 AA 

> Dear Jim,
> I think the motivation behind your MDS question is a very interesting one.
> To me it seems that there are two likely possibilities.
> -one is that "auditory dissimilarity" is truly quite high-dimensional, so
> Matlab did not manage to project the data into a low dimensional space
> because it simply cannot be done, and even reducing the dimensionality just
> a little bit from 10 to 8 leads to appreciable distoritions (i.e. "error"),
> -the other (which seems to be the possibility you are asking about) is that
> Matlab's algorithm doesn't work properly. However, you could quite easily
> "sanity check" Matlab's algorithm: Just draw ten points randomly on
> (2-dimensional) graph paper, measure their pairwise distances, and feed
> those into the Matlab MDS algorithm. If Matlab does its job right it should
> give you a 2 D solution with errors no larger than the measurement errors
> you would expect from holding your ruler up to the points on your paper. In
> fact, it should be easily be possible to "virtualize" and automate his sort
> of sanity check by letting random numbers generate points in space of any
> dimensionality you choose and work out relative pairwise distances using
> Pythagoras. Once you have automated code that does this you could run
> hundreds of sanity checks like that you should know pretty quickly how far
> you can trust Matlab's algorithm. And I hope you will let us know the
> answer. I, for one, would not be too surprised if it turned out that sounds
> could sound dissimilar on at least 8 "different dimensions".
> Best wishes,
> Jan
> On 15/06/06, beaucham <beaucham@xxxxxxxxxxxxxxxxxxxxxx> wrote:
> >
> > We ran an MDS calculation (using MatLab) on a 10x10 distance
> > matrix based on dissimilarity judgements between all pairs of
> > 10 sounds, and obtained an 8-dimension solution, which gives
> > the coordinates of the sounds in 8-D space. The distances
> > between the positions of the sounds are supposed to match
> > the original distances. In fact, we get an rms error of 8%
> > and a max error of 30%.
> >
> > Is this typical? Is MatLab's program accurate? Is there a way
> > to improve on the MDS results?
> >
> > Jim Beauchamp
> > Univ. of Illinois Urbana-Champaign
> > jwbeauch@xxxxxxxx
> >
> >
> -- 
> Dr Jan Schnupp
> University of Oxford
> Dept. of Physiology, Anatomy and Genetics
> Sherrington Building - Parks Road
> Oxford OX1 3PT - UK
> +44-1865-272513
> www.oxfordhearing.com