To whomever it may concern (especially Jim Rohlf and David Dubin),
I sent an email response to this same broadcast email sent out via the
CLASSL system, but addressed it directly to Jim Rohlf, since, for some
reason I misinterpreted this as being an inquiry initiated by him, not
one from someone else (Dirk Meurer, I now see) simply passed on by Jim
as administrator of CLASSL. I had thought at the time that perhaps
David and Mark Rorvig, prior to Rorvig's tragic and untimely death last
year, had put together such a program. While I gather from this message
from David that, instead, Michael Trosset (who was also involved in the same
DIMACS Workshop on MDS Algorithms I mentioned in that earlier email addressed
to Jim) has done so. I would therefore endorse David's recommendation that
this software developed by Trosset be used for this purpose. I personally
think that, in practice, it seldom makes a great difference whether one uses
an MDS procedure that is purely "metric" (as long as you're reasonably careful
to make sure the data are transformed, if necessary, to a form as consistent
as possible with the assumptions that the procedure is based on in
particular,
most likely that they be DISsimilarities which may simply entail reversing
the scale, if data are similarities, by, say, subtracting all values from the
largest similarity value in the matrix, and possibly, if the particular method
assumes RATIO SCALE instead of merely INTERVAL SCALE dissimilarities, that
these
dissimilarity values are transformed so that it is reasonable to assume that a
dissimlarity of zero (0) corresponds to a DISTANCE of zero (0) in the
recovered
multidimensional representation or "nonmetric" (in which the similarities or
dissimilarities are assumed only to be monotonic with the proximities
monotone
nonincreasing or monotone nondecreasing respectively for the two types
sim.'s
or dissim.'s of proximity data). The metric MDS procedures are sufficiently
robust under even fairly severe nonlinearities in the monotonic "distance
function"
transforming proximities into distances in the underlying representation
that the
solutions are usually almost totally indistinguishable (as long as the same
dimensionality is assumed in two analyses, of course), although, as is well
known,
an orthogonal rotation of a twoway MDS solution (based, as almost all MDS
algorithms are, on assumption of Euclidean metric in the underlying space), no
matter HOW obtained, is necessary to bring even what are really identical
solutions
into exact congruence (since Euclidean spaces are defined only up to
similarity
transforms including an orthogonal rotation, as well as translation of
the origin
and, in some cases a possible uniform dilation resulting in multiplication
of all
distances by a positive constant but the latter two types of
transformations are
typically resolved by normalization conventions, so generally do not need to be
considered). In fact, not only are metric solutions (in the same
dimensionality)
usually as good as nonmetric ones, there is considerable empirical and
theoretical
evidence that, for certain types of data, they are in fact BETTER being less
susceptible to various degeneracies and quasidegeneracies that can affect
many
nonmetric MDS analyses, if the data exhibit certain characteristics that
are not at
all unusual in the case of realistic proximity data from various domains.
Best,
Doug Carroll.
At 03:52 PM 11/12/2002 0600, David Dubin wrote:
>Michael Trosset wrote a program for classical metric MDS that Mark Rorvig
>and I used with success on matrices much larger than 400 by 400. But it
>doesn't do nonmetric MDS. The program is written in Fortran and requires the
>ARPACK libraries. I was able to compile with g77 on Linux and Solaris with
>little trouble.
>
>Dave Dubin
>
>Dirk Meurer <[log in to unmask]> writes:
>
> > Dear Listmembers,
> > I would like to do a MDS with a 400X400 square, symetric matrix of
> > (dis)similaritys. Most MDSSoftware is limited to a much smaller amount
> > of variables though. I have been told, that SAS might be able to process
> > the analyis I need, but this is quite inconvenient for me in terms of
> > access to the software, hardwarerequirements etc. Could anybody tell
> > me, if there is a standalone program that can do MDS (preferably
> > nonmetric) with a matrix of that size?
> >
> > Thanks a lot for your help,
> > dirk
> >
> > P.S: My Matrix is not suitable for factor analysis and clustering does
> > not produce the results I need.
> >
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