MDS with different matrices
Torsten Franz
as a basis for Multidimensional Scaling I use different matrices: a
distance matrix and a correlation matrix (Spearman). The results are
different, too. Why? I use STATISTICA.
Torsten
James X. Li
Do you expect the same result for different input? !
James X. Li
Torsten Franz
question was: why are the results different? Because the matrices are
different? Is the answer so simple? And which conclusions I have to draw
for the interpretation of the MDS?
Torsten
Rich Ulrich
I tried to do MDS on correlations, 15 years ago when I
was trying to figure out if MDS was worth anything, and
I never figured out how I was supposed to reverse the
correlations in order to have a 'distance' metric that would
work. Did you have some concrete advice from somewhere?
Since the results I could get on correlations did not look
nearly as meaningful to me as what Factor Analysis
gave me, I decided to forget about MDS.
I googled for
< "Multidimensional scaling" FAQ > and two of the first 4 hits
were to my own FAQ -- that is not encouraging.
< "Multidimensional scaling" tutorial > gave a better looking
set of references.
Has somebody cared enough about MDS to update the
computer programs? It's long been my impression that
'marketing' was using MDS. From google, it also seems
like MDS sometimes is included in the tools of data mining.
--
Rich Ulrich, wpi...@pitt.edu
http://www.pitt.edu/~wpilib/index.html
"Taxes are the price we pay for civilization." Justice Holmes.
James X. Li
> I never figured out how I was supposed to reverse the
> correlations in order to have a 'distance' metric that would
> work. Did you have some concrete advice from somewhere?
>
> Since the results I could get on correlations did not look
> nearly as meaningful to me as what Factor Analysis
> gave me, I decided to forget about MDS.
>
MDS is not intended as a modeling method that helps you to establish
analytical relationships. It is more a visualization tool for preliminary
data analysis. It can help you, for instance, to answer
questions like: Are there any clear clusters in a dataset?
Does a data point have many similar data points in a dataset?
Are there many isolated outliers in a dataset?
You can probably answer these questions with statististics, but with MDS
it is more direct and visual. The value and strength of MDS is its mapping
feature which visualizes abstract high dimensional data.
> Has somebody cared enough about MDS to update the
> computer programs? It's long been my impression that
> 'marketing' was using MDS. From google, it also seems
> like MDS sometimes is included in the tools of data mining.
That's right, MDS is more appropriated for areas where
conventional analytical modeling have failed.
For self-promotion purpose please see our software VisuMap at
http://www.visumap.net which combines traditional MDS, PCA,
clustering method with modern navigation user interface. VisuMap
basically turns any numerical table ( or any distance matrix) into map.
cheers,
James X. Li
Torsten Franz
> whatever/ did you use to convert correlations to distances?
> The other part of my reason for asking was my suspicion
> that you hadn't noticed that conversion is needed. Or, Did
> the computer program offer options for default treatment?
> You still haven't settled that suspicion.
As far as I understand my software (STATISTICA) generats the matrices
directly from the raw data. I do not understand why I've to convert
correlations to distances. But I do not look behind the software, so
maybe I've used procedures which are not assumable.
> Hybrid distances? nominal with Interval? Seems awkward,
> at best, to do it or to describe it, whatever MDS is offering.
At the end I used only ordinal variables: I've ranked the nominal
variables after their frequencies of values.
Torsten
Rich Ulrich
<Torsten...@mailbox.tu-dresden.de> wrote:
me > >
> > I was asking, partly from technical curiosity, What algorithm/ or
> > whatever/ did you use to convert correlations to distances?
> > The other part of my reason for asking was my suspicion
> > that you hadn't noticed that conversion is needed. Or, Did
> > the computer program offer options for default treatment?
> > You still haven't settled that suspicion.
TF >
> As far as I understand my software (STATISTICA) generats the matrices
> directly from the raw data. I do not understand why I've to convert
> correlations to distances. But I do not look behind the software, so
> maybe I've used procedures which are not assumable.
From a website on Statistica, it looks like the program is
willing to analyze correlations. Maybe it assumes there
is only one way worth pursuing, for transforming r's to
distances, but there were no details on the page I read.
me > >
> > Hybrid distances? nominal with Interval? Seems awkward,
> > at best, to do it or to describe it, whatever MDS is offering.
TF >
> At the end I used only ordinal variables: I've ranked the nominal
> variables after their frequencies of values.
Now *that* seems difficult to justify, unless the
dimension is 'how conventional is the response' --
I have seen one scale where that is intended. I
suppose you could do that when referring to attitudes,
but I have only seen it once.
Greg Heath
news:<1qhkjvcovt80s7rfb...@4ax.com>...
> On Wed, 13 Aug 2003 10:13:47 +0200, Torsten Franz
> <Torsten...@mailbox.tu-dresden.de> wrote:
>
> > > Do you expect the same result for different input? !
> > Definitely not, although the underlying data set is the same. My
> > question was: why are the results different? Because the matrices are
> > different? Is the answer so simple? And which conclusions I have to draw
> > for the interpretation of the MDS?
> >
>
> I tried to do MDS on correlations, 15 years ago when I
> was trying to figure out if MDS was worth anything, and
> I never figured out how I was supposed to reverse the
> correlations in order to have a 'distance' metric that would
> work. Did you have some concrete advice from somewhere?
Try adding the coauthor name "Young" to your Google search.
If you interpret a correlation coefficient as the cosine
of an angle, a, you can represent the data in terms of
points on a unit 3-dim sphere. When the angle between two
position vectors emanating from the sphere center is a,
the distance between the points is 2*sin(a/2).
Hope this helps.
Greg
Aleks Jakulin
"Rich Ulrich" <wpi...@pitt.edu> wrote:
> Has somebody cared enough about MDS to update the
> computer programs? It's long been my impression that
> 'marketing' was using MDS. From google, it also seems
> like MDS sometimes is included in the tools of data mining.
MDS has become slightly outdated, but there has been some good work into
the same direction recently, primarily in the direction of locally linear
embedding. The problem with MDS is globality: in most stress functions
short dissimilarities are approximated with a similar precision as large
dissimilarities. In reality, what a human analyst expects from MDS is more
a structure alike clustering: one that would identify groups of similar
objects.
The 'old' solution was Shepard's non-metric MDS. NMDS attempts to modify
the dissimilarity matrix so that the distance rankings are maintained,
rather than metric deviations. For example, we are not interested in the
exact distances between A, B and C, but we do want distance A-B to be
greater than A-C if C is more dissimilar from A than is B. It does not work
well in practice, unfortunately. Today, new methods have emerged. For
example, locally linear embedding instead only evaluates the distances from
an object to K of its nearest neighbors. This yields nice results.
Good starting points for further exploration are
http://www.cs.toronto.edu/~roweis/lle/
http://basis.stanford.edu/carrie-web/
Aleks
Eugene D. Gallagher
Forrest Young still distributes the Fortran code and Dos executable of
Alscal, the descendent of KYST, the Bell Labs NMDS program. MDS, for
some reason, is often used as an acronym for NMDS. I follow those who
restrict MDS to Shepard's metric scaling, which is identical to Gower's
Principal coordinates analysis.
http://forrest.psych.unc.edu/
MDS still has huge advantages, if you have access to the case by
variables matrix. There are a variety of transformations that can be
used to transform the data matrix prior to doing the metric scaling.
Pierre Legendre & I wrote a paper in 2001 that describes a number of
these transformations. Pierre provides code on his web page for mac & pc
for doing the transformations and PCA's, and I provide the Matlab 4 &
Matlab 6 code for doing the same:
http://www.es.umb.edu/edgwebp.htm#LegGallMat6
Strictly speaking the MDS model (not the MDS model) can have problems
with non-metric distances, producing negative eigenvalues. Legendre &
Legendre (1998) Numerical Ecology, 2nd ed. review 3 solutions to this
problem, and their algorithms are programmed in Pierre & my programs.
Often it is not the ordination of the cases that is important but
explaining why the cases take the positions they do in low-dimension
space. The Gabriel Euclidean distance biplot and correlation biplot are
important tools for interpreting the low-dimension ordination. Gower's
book 'biplots' is the best overall description of the process.
MDS has also been revived by the use of constrained ordination
techinques. Canonical correspondence analysis can impose conditions that
either the distances among cases in low-dimension space must be linear
functions of a set of external explanatory variables, or uncorrelated
with a set of covariates (partial canonical correspondence analysis).
When preserving Euclidean distances, as in the MDS model, the technique
is called redundancy analysis. Both redundancy analysis and canonical
correspondence analysis (not to be confused with canonical correlation
analysis) are available in the CANOCO package. Using algorithms
presented by ter Braak or by Legendre & Legendre, the basic CANOCO or
redundancy analysis models can be programmed in languages such as Matlab.
BTW, you can perform an MDS, aka Gower Principal coordinates
analysis, on a correlation matrix after converting it to a distance
matrix. This distance matrix will not be Euclidean, so anticipate
negative eigenvalues. The standard NMDS programs have an option to
specify whether the matrix entered is a distance or similarity matrix.
Gene Gallagher
Niko Tiliopoulos
> Has somebody cared enough about MDS to update the
> computer programs? It's long been my impression that
> 'marketing' was using MDS. From google, it also seems
> like MDS sometimes is included in the tools of data mining.
Try this site
It offers a very good MDS windows program developed by Prof. T. Coxon
and co. I have used it (as a beta tester) and it is rather friendly. I
can run almost any possible MDS model available today.
Best
Niko Tiliopoulos
Niko Tiliopoulos
>
> http://www.newmdsx.com/
>
> It offers a very good MDS windows program developed by Prof. T. Coxon
> and co. I have used it (as a beta tester) and it is rather friendly. I
> can run almost any possible MDS model available today.
>
> Best
>
> Niko Tiliopoulos
ERRATUM!
I beg pardon. In the previous message the sentence "I can run
almost... " should have said "IT can run almost... ". I cannot I am
afraid.
Best
Niko Tiliopoulos