Re: MDS distances

[Jan Schnupp <jan@xxxxxxxxxxxxxxxx>]

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