Re: MDS distances

[beaucham <beaucham@xxxxxxxxxxxxxxxxxxxxxx>]

I was surprised to receive four new responses to my query of last
week, when I received several responses, mostly off the list. I 
am also getting some local help. One problem is that I haven't 
been using MatLab directly but rather through an off-campus
colleague who is currently unavailable for questions. However, I 
am now getting some on-campus help, using both MatLab and Systat,
as well as a member of this list, using Statistica. Also, I'm 
boning up on MDS, and I expect to get my hands on MatLab very 
soon.

One thing I found out is that lower dimension MDS coordinates of
a high dimension calculation are not the same as the corresponding
dimension coordinates for a low dimension calculation. I.e., it
doesn't work like orthogonal functions such as Fourier series.
Another thing is the triangular inequality (p(A,C)<=p(A,B)+p(B,C))
of the proximity matrix has to be satisified -- our matrix 
fortunately satisfies that.

The upshot is that other people have run jobs on my data that have
achieved relatively low stresses with linear and monotonic 2-D and
3-D solutions. I'm not entirely satisfied with the results, but
it's getting close. The next step is to discovery aspects of the
stimuli (musical tones) which correlate well with the dimensions
or combinations of dimensions.

For more details on the stimuli, the method of testing, and the
provisional MDS results please look at 

  http://ems.music.uiuc.edu/beaucham/mds/mds.txt

Jim Beauchamp
Univ. of Illinois at Urbana-Champaign
jwbeauch@xxxxxxxx