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bird
science forum beginner
Joined: 11 Jun 2005
Posts: 14
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 Posted: Thu Mar 30, 2006 11:16 pm Post subject:
multidimensional scaling clustering
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I am learning the multidimensional scaling clustering methods
in a hurry. I can understand how they compute the final
configuration, which is attained when a stress is minimized.
It is supposed to contain the information to project patterns from
a high-dimensional space to a lower-dimensional space.
Can someone please instruct me how I can use the configuration
to compute the patterns in the lower-dimensional space?
how clusters are computed thereafter?
Thank you very much. |
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bird
science forum beginner
Joined: 11 Jun 2005
Posts: 14
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| Posted: Fri Mar 31, 2006 12:44 am Post subject:
Re: multidimensional scaling clustering
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"Reef Fish" <Large_Nassau_Grouper@Yahoo.com> wrote:
| Quote: | bird wrote:
Euclidean 2 dimension say, you can (in most programs) input either
the Euclidean coordinates to compute the distance matrix in 4
dimensions or use the distance matrix in the output of 4 dimensions
as the input for a scaling in 2 dimensions.
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I see the final configuration is in 2 dimensional space in your case. It is
a
good representation of some patterns in an original 6 dimensional space.
then what can we do to use this final configuration? If I have 10 patterns
as a 10 by 6 matrix in the original space, can I get its representation in
the 2 dimensional space, I mean something like a 10 by 2 matrix?
| Quote: |
how clusters are computed thereafter?
The two methods are incompatible in the sense that multidimensional
scaling is more concerned with the interpretable patterns in the
recovered configuration, such as the axes in Factor Analysis or
Principal Components Analysis.
Cluster analysis, while it can use the same input dissimilarity matrix
as multidimensional scaling, is concerned ONLY with the phenomon
of "clustering" or grouping of the objects.
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I am learning these methods from a book "Algorithms for Clustering Data"
by Anil K. Jain et al. Why can not I use them to cluster patterns?
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Greg Heath
science forum beginner
Joined: 24 Feb 2005
Posts: 14
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| Posted: Sat Apr 01, 2006 11:22 pm Post subject:
Re: multidimensional scaling clustering
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bird wrote:
| Quote: | "Reef Fish" <Large_Nassau_Grouper@Yahoo.com> wrote:
bird wrote:
Euclidean 2 dimension say, you can (in most programs) input either
the Euclidean coordinates to compute the distance matrix in 4
dimensions or use the distance matrix in the output of 4 dimensions
as the input for a scaling in 2 dimensions.
I see the final configuration is in 2 dimensional space in your case. It is
a
good representation of some patterns in an original 6 dimensional space.
then what can we do to use this final configuration? If I have 10 patterns
as a 10 by 6 matrix in the original space, can I get its representation in
the 2 dimensional space, I mean something like a 10 by 2 matrix?
how clusters are computed thereafter?
The two methods are incompatible in the sense that multidimensional
scaling is more concerned with the interpretable patterns in the
recovered configuration, such as the axes in Factor Analysis or
Principal Components Analysis.
Cluster analysis, while it can use the same input dissimilarity matrix
as multidimensional scaling, is concerned ONLY with the phenomon
of "clustering" or grouping of the objects.
I am learning these methods from a book "Algorithms for Clustering Data"
by Anil K. Jain et al. Why can not I use them to cluster patterns?
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It is better to cluster first. Then apply MDS to the cluster centers.
Hope this helps.
Greg |
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Reef Fish
science forum Guru Wannabe
Joined: 28 Apr 2005
Posts: 200
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| Posted: Sun Apr 02, 2006 4:01 am Post subject:
Re: multidimensional scaling clustering
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bird wrote:
| Quote: | "Reef Fish" <Large_Nassau_Grouper@Yahoo.com> wrote:
bird wrote:
Euclidean 2 dimension say, you can (in most programs) input either
the Euclidean coordinates to compute the distance matrix in 4
dimensions or use the distance matrix in the output of 4 dimensions
as the input for a scaling in 2 dimensions.
I see the final configuration is in 2 dimensional space in your case. It is
a
good representation of some patterns in an original 6 dimensional space.
then what can we do to use this final configuration? If I have 10 patterns
as a 10 by 6 matrix in the original space, can I get its representation in
the 2 dimensional space, I mean something like a 10 by 2 matrix?
|
In Multidimensional Scaling (MDS), you have n "objects" and an n x n
matrix of pairwise distances (or dissimilarities or similarities) as
input.
The END result is to represent these n objects in a Euclidean p-space
of n points.
If you have only 10 objects, MDS in 6 dimensions would not be
meaningful because you would be fitting with 60 free parameters
(the coordinates in 6 dimensions), when you DATA consists of only
n(n-1)/2 or 45 distances. Thus, you'll always get a perfect fit
(zero stress) while the recovered configuration would not mean
anything.
See Forest Young's intro article for MDS in
http://forrest.psych.unc.edu/teaching/p208a/mds/mds.html
| Quote: | how clusters are computed thereafter?
The two methods are incompatible in the sense that multidimensional
scaling is more concerned with the interpretable patterns in the
recovered configuration, such as the axes in Factor Analysis or
Principal Components Analysis.
Cluster analysis, while it can use the same input dissimilarity matrix
as multidimensional scaling, is concerned ONLY with the phenomon
of "clustering" or grouping of the objects.
I am learning these methods from a book "Algorithms for Clustering Data"
by Anil K. Jain et al. Why can not I use them to cluster patterns?
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Jain's book is about clustering ALGORITHMS. It has nothing to do
with MDS.
It appears you need a general introduction to both of these methods
FIRST. Try reading the multivariate analysis textbook by Johnson
and Wichern.
http://tinyurl.com/gc7xh
-- Bob. |
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Reef Fish
science forum Guru Wannabe
Joined: 28 Apr 2005
Posts: 200
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| Posted: Sun Apr 02, 2006 4:05 am Post subject:
Re: multidimensional scaling clustering
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Greg Heath wrote:
| Quote: | bird wrote:
"Reef Fish" <Large_Nassau_Grouper@Yahoo.com> wrote:
bird wrote:
Euclidean 2 dimension say, you can (in most programs) input either
the Euclidean coordinates to compute the distance matrix in 4
dimensions or use the distance matrix in the output of 4 dimensions
as the input for a scaling in 2 dimensions.
I see the final configuration is in 2 dimensional space in your case. It is
a
good representation of some patterns in an original 6 dimensional space.
then what can we do to use this final configuration? If I have 10 patterns
as a 10 by 6 matrix in the original space, can I get its representation in
the 2 dimensional space, I mean something like a 10 by 2 matrix?
how clusters are computed thereafter?
The two methods are incompatible in the sense that multidimensional
scaling is more concerned with the interpretable patterns in the
recovered configuration, such as the axes in Factor Analysis or
Principal Components Analysis.
Cluster analysis, while it can use the same input dissimilarity matrix
as multidimensional scaling, is concerned ONLY with the phenomon
of "clustering" or grouping of the objects.
I am learning these methods from a book "Algorithms for Clustering Data"
by Anil K. Jain et al. Why can not I use them to cluster patterns?
It is better to cluster first. Then apply MDS to the cluster centers.
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Greg, this is still another piece of your nonsense!
A cluster analysis may result in NO cluster centers! You suggestion
is nonsense even if there are cluster centers. You are as ignorant
about these two methods (MDS and Clustering) as you are about
the detection of multicollinearity in a multiple regression problem.
-- Bob. |
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Reef Fish
science forum Guru Wannabe
Joined: 28 Apr 2005
Posts: 200
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| Posted: Sun Apr 02, 2006 10:01 pm Post subject:
Re: multidimensional scaling clustering
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bird wrote:
| Quote: | Thank you for your help. I read some books and I think I see
some of your points now. I have just one more question.
Suppose I have n objects, each has m features, then I actually
have a matrix A(nxm).
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To use MDS, you must first decide what distance or similarity
measure you want to use to obtain the D(n x n) matrix of pairwise
distances between the n objects.
| Quote: | I want to use MDS to reduce the features
to a p dimensional space, that's say I want a matrix B(nxp).
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Then you tell the MDS program to give you a solution in Euclidean
p-space. The Euclidean p-space is NOT even necessarily a
reduction of the original m
| Quote: | The final configuration attained by MDS is actually a transformation
T(mxp) telling me how to transform A to B. Is it right?
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No, it is not a transformation in usual sense of A T = B where T is
a transformation matrix such as what's done in Principal Components
or Factor Analysis.
Once you defined the n x n input matrix D, all of the original data
A(n, m) is gone, except for the number of objects n. MDS
reconstructs an entirely new set of Euclidean coordinates in p-space,
so that the recovered n x n matrix of Dhat closely matches the
original D(n x n).
| Quote: | Since it is a nonliear transformation, does B equal A x T?
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No. It is an entirely different kind of "transformation" if you call
it that.
It is the creation of a set of points in Euclidean p-space to match
the original matrix of dissimilarities (which may be directly measured
dissimilarites in an unknown dimension m). The input matrix can
even be asymmetrical. But the output matrix of distances will always
be symmetrical.
-- Bob.. |
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bird
science forum beginner
Joined: 11 Jun 2005
Posts: 14
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| Posted: Tue Apr 04, 2006 1:57 pm Post subject:
Re: multidimensional scaling clustering
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Ark,
Thank you so much for your help. I will keep looking
the links you provide. Thank you again.
-Kevin
"Art Kendall" <Arthur.Kendall@verizon.net> wrote:
| Quote: | Doug Carroll and colleagues at Bell labs created extensions to the
single matrix MDS (e.g., Joe Kruskal).
George xxxx developed a method that found clusters and dimensions on the
same run.
The Classification Society Of North America is for people from all kinds
of disciplines who are interested in MDS, clustering, etc. Biologists,
Psychologists, statisticians, astronomers, zoologists, computer and
information scientists, etc.
If you go to
http://www.classification-society.org/csna/csna.html
to learn about the society
click < mailing list > on the bottom left of the page or go to
http://www.classification-society.org/csna/lists.html#class-l
to learn about class-l
This would be a good place to pose your questions.
Art
Art@DrKendall.org
Social Research Consultants
bird wrote:
Thank you for your help. I read some books and I think I see
some of your points now. I have just one more question.
Suppose I have n objects, each has m features, then I actually
have a matrix A(nxm). I want to use MDS to reduce the features
to a p dimensional space, that's say I want a matrix B(nxp).
The final configuration attained by MDS is actually a transformation
T(mxp) telling me how to transform A to B. Is it right? Since
it is a nonliear transformation, does B equal A x T?
|
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Reef Fish
science forum Guru Wannabe
Joined: 28 Apr 2005
Posts: 200
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| Posted: Wed Apr 05, 2006 4:24 am Post subject:
The best way to access the CLASS-L archives. But ...
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Art Kendall wrote:
| Quote: |
The Classification Society Of North America is for people from all kinds
of disciplines who are interested in MDS, clustering, etc. Biologists,
Psychologists, statisticians, astronomers, zoologists, computer and
information scientists, etc.
http://www.classification-society.org/csna/lists.html#class-l
to learn about class-l
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Within it, you'll find:
#> You may read the archives of the CLASS-L at the mail archive.
#> There are separate archives for
#> 1988-2000 and
#> 2000-present.
The 2000-present archives is virtually unususable because it has
a completely UNORGAINZED list of threads since 2000.
After about 6 rounds of e-mail exchange with Jim Rohlf asking him if
he was aware of the existence of a LISTSERV archives for CLASS-L,
he seemed unaware of it. But after I told him that the new
LISTSERV 14.5 has an excellent archiving support for listserv lists,
such as CLASS-L, I finally got the key reply from Jim earlier today,
"We are also using listserv 14.5. Our management webpage is at
https://lists.sunysb.edu
Within THAT link, THIS is by far the best way to browse, read, or
post in CLASS-L:
https://lists.sunysb.edu/archives/class-L.html
When you access that page, you'll get:
------------------------------------------------------------
Archives of CLASS-L@LISTS.SUNYSB.EDU
Classification, clustering, and phylogeny estimation
Search the archives
Post to the list
Join or leave the list (or change settings)
Manage the list (list owners only)
March 2006
February 2006
January 2006
etc
------------------------------------------------------------
and the monthly listing of THREADED posts goes back to Feb, 2000.
Notice you can search the archives using keywords, post to the list
or join or leave the list, all without using your email!
So, this is the link you should use (unless you prefer the clumsy
e-mail and unorganized approach):
=================================
https://lists.sunysb.edu/archives/class-l.html
=================================
| Quote: | This would be a good place to pose your questions.
|
Art. I don't think so  for these reasons:
1. The list is virtually moribund. There were a total of 19 posts
in 2006,
(8 in January; 5 in February; 6 in March; and none in April),
less
than the average of an active LIST in a single day!
2. The worst part of it is that of the 19 posts, 17 of them were
announcements!
The one follow-up in January was a correction of the IFCS posted
The one follow-up in February was an unrelated announcement
itself.
3. Here's a couple of questions with answers, that will explain my
remark to Art's posted comment:
AK> This would be a good place to pose your questions.
Q1: How many questions were asked in 2006? (Answer: 0)
Q2: When was the last two times Art Kendall asked a question
in Class-L? Did he get an answer or discussion?
(Answer: Oct 2005; July 2005. No and no.)
-- Bob. |
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