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Olin Perry Norton

Joined: 13 May 2005
Posts: 58 Posted: Tue Feb 21, 2006 3:12 pm    Post subject: Re: Pattern Recognition In Statistics First, a question: How does the Ohio lottery pick their
numbers? Does air blow numbered ping pong balls
out of a large box, or does a computer choose random
numbers, or what?

I'm very skeptical of what you're trying to do. The people who
run the Ohio lottery aren't stupid. If they use a computer to
generate random numbers, there are good (pseudo) random
number generators, which have no discernable patterns to their
output -- at least nothing that one would detect in a relatively
small sample. If they use an analog random number generator
such as numbered balls, a roulette wheel, etc. don't you think
they weighed the balls or balanced the wheel, and then tested
it a number of times to see if some numbers were more likely
to be chosen than others?

I think that the human brain is programmed to find patterns --
so much so that we tend to see patterns even when they aren't
really there (e.g., finding shapes in clouds that resemble animals,
the book "Subliminal Seduction," and a great deal of stock market
analysis.) Hence the need for hypothesis testing.

Now, it is possible that people who buy lottery tickets tend to
favor certain "lucky" numbers, such as 3, 7, etc., so that if one
bought tickets containing the numbers that most people avoid,
you might obtain an edge. But, this isn't a new idea, so I doubt
if you could get enough of an advantage to make buying lottery
tickets worthwhile.

Olin Perry Norton

P.S. Pierre Asselin -- replace invalid with edu and send me an email. brian a m stuckless
science forum Guru

Joined: 31 Aug 2005
Posts: 2024 Posted: Sun Mar 05, 2006 10:04 am    Post subject: Re: help me with this. Quote: "Ken" wrote in message If we have a glass of water at exactly 300 K and another one at exactly 290 K in a room at 295 K, which glass of water will reach 295 K first? why?

\$\$ Volume/(Cube Area)=Edge/3.
\$\$ You MEASURE the following (..BEFORE begining the calculation):
\$\$ 1. The volume/(SURFACE area) of the room, water A and water B.
\$\$ 2. The iNside and OUTside temperatures of the room, and A & B.
\$\$ 3. The SPECiFiC-heat-CAPACiTY of the iNside & OUTside AMBiENT.
\$\$ 4. The RATE of heat-GAiN & the RATE of heat-LOSS, of the room.
\$\$
\$\$ Then with THiS you can calculate if A or B reaches 295K FiRST.
\$\$ [An ANSWER depends on the RATE-of-thermal-CHANGE in the room].
\$\$
\$\$ Brian A M Stuckless.
Re: help me with this. David W. Cantrell
science forum Guru

Joined: 02 May 2005
Posts: 352 Posted: Sun Mar 05, 2006 5:53 pm    Post subject: Re: Dividing an ellipse into equal parts Quote: Or to be more precise, dividing the circumference of an ellipse into equal parts.

OK, I'll help.

 Quote: I'm trying to move items around an ellipse as part of an animation. If I move round the ellipse in constant angular movements from the centre, then the item moves faster when near to the centre of the ellipse and slower round the ends.

True.

 Quote: (If my ellipse is 2w wide and 2h high, and the angle from the centre is a, then I get the co-ordinates by x = w sin a and y = h cos a).

The parameter a above does _not_ represent "the angle from the centre".
Don't feel bad. That's a common misconception. (But I'm surprised that none
of the other respondents mentioned the error.)

 Quote: So, I want to move around the ellipse in constant steps around the circumference. I know the width (2w) and height (2h) of the ellipse, can calculate the foci (+f and -f), and have calculated the circumference (c) successfully.

Did you do that using the complete elliptic integral of the second kind?

And later "tallsteve" <google@sumogoldfish.com> wrote:
 Quote: For arguments sake, say the ellipse is 300 wide by 200 high. This gives a circumference of 793.27. I want to move an item around the ellipse in equal steps, so that it's speed is constant. So if my animation is 24 frames per second, and I want to take one second to get round, I need to move the item round the circumference by 793 / 24 or roughly 33 units each time.

Correct.

IMO, what you need to be able to do is invert the incomplete elliptic
integral of the second kind, inverting with respect to its amplitude z (not
its parameter m). N.B. Since there are differing conventions, to avoid
confusion, let's agree here to use the convention used at
<http://functions.wolfram.com/EllipticIntegrals/EllipticE2/>.

Your computer system might have an implementation of that inverse; if so,
everything would be simple. But it's unlikely that it has such an
implementation. Since you just need a fairly crude approximation, using
just a few terms of a series for that inverse should be satisfactory. I'll
work out an example for you below. But first, you might want to look at two

"Inverting elliptic integrals" sci.math.research

"n equally spaced points around the ellipse's perimeter" sci.math

Now for the example, using the data you gave above. You already know that
your ellipse can be parametrized as x = 150 sin(t), y = 100 cos(t) and that
its perimeter is 793.27. You want 24 points on the ellipse so that the
lengths of the elliptic arcs between consecutive pairs of points are
approximately the same.

It's very convenient that you chose 24; it's divisible by 4. Let me suggest
that you _always_ use a number divisible by 4. Doing so simplifies things.
So in your example, we just need to divide the part of the ellipse in the
first quadrant into six arcs of approximately equal length.

I shall also assume, for greatest convenience, that we start with t = 0,
that is, that we begin at an end of the minor axis.

Here is part of a Mathematica notebook. I hope it's more-or-less
self-explanatory; if not, don't hesitate to ask questions.

In= a = 150; b = 100; param = 1 - (b/a)^2;
quarterperimeter = a*EllipticE[param]

Out:= 150*EllipticE[5/9]

In= distance = %/6

Out:= 25*EllipticE[5/9]

In= N[%]

Out:= 33.0529991443554

thereby confirming your "roughly 33 units".

In= Normal[InverseSeries[Series[EllipticE[z, m], {z, 0, 14}], d]]

Out:= d + (d^3*m)/6 + (1/120)*d^5*(-4*m + 13*m^2) +
(d^7*(16*m - 284*m^2 + 493*m^3))/5040 +
(d^9*(-64*m + 4944*m^2 - 31224*m^3 + 37369*m^4))/362880 +
(d^11*(256*m - 81088*m^2 + 1406832*m^3 - 5165224*m^4 + 4732249*m^5))/
39916800 + (d^13*(-1024*m + 1306880*m^2 - 56084992*m^3 + 474297712*m^4 -
1212651548*m^5 + 901188997*m^6))/6227020800

The result above gives an approximation of the needed inverse.

In= InvE[d_, m_] := d + (d^3*m)/6 + (1/120)*d^5*(-4*m + 13*m^2) +
(d^7*(16*m - 284*m^2 + 493*m^3))/5040 +
(d^9*(-64*m + 4944*m^2 - 31224*m^3 + 37369*m^4))/362880 +
(d^11*(256*m - 81088*m^2 + 1406832*m^3 - 5165224*m^4 + 4732249*m^5))/
39916800 + (1/6227020800)*(d^13*(-1024*m + 1306880*m^2 - 56084992*m^3 +
474297712*m^4 - 1212651548*m^5 + 901188997*m^6));

In= N[Table[{a*Sin[t], b*Cos[t]} /. t -> InvE[d, param],
{d, 0, quarterperimeter/a, quarterperimeter/(6*a)}]]

Out:= {{0., 100.},
{32.93229464625545, 97.56015573157862},
{65.09394815658442, 90.09323050999978},
{95.44895809488033, 77.14199432389246},
{122.25147255789417, 57.94471486752196},
{142.21788527772756, 31.79149506904233},
{149.99996319648417, 0.07005094462200027}}

So we got a list of 7 points. You wouldn't really want to use the last one;
instead, you'd use exactly (150, 0). I showed the last point simply so that
you'd see how far off the approximation was there. Of course, to get the
rest of the 24 points, in the other quadrants, just use symmetry.

David W. Cantrell David W. Cantrell
science forum Guru

Joined: 02 May 2005
Posts: 352 Posted: Sun Mar 05, 2006 5:53 pm    Post subject: Re: Dividing an ellipse into equal parts Quote: Or to be more precise, dividing the circumference of an ellipse into equal parts.

OK, I'll help.

 Quote: I'm trying to move items around an ellipse as part of an animation. If I move round the ellipse in constant angular movements from the centre, then the item moves faster when near to the centre of the ellipse and slower round the ends.

True.

 Quote: (If my ellipse is 2w wide and 2h high, and the angle from the centre is a, then I get the co-ordinates by x = w sin a and y = h cos a).

The parameter a above does _not_ represent "the angle from the centre".
Don't feel bad. That's a common misconception. (But I'm surprised that none
of the other respondents mentioned the error.)

 Quote: So, I want to move around the ellipse in constant steps around the circumference. I know the width (2w) and height (2h) of the ellipse, can calculate the foci (+f and -f), and have calculated the circumference (c) successfully.

Did you do that using the complete elliptic integral of the second kind?

And later "tallsteve" <google@sumogoldfish.com> wrote:
 Quote: For arguments sake, say the ellipse is 300 wide by 200 high. This gives a circumference of 793.27. I want to move an item around the ellipse in equal steps, so that it's speed is constant. So if my animation is 24 frames per second, and I want to take one second to get round, I need to move the item round the circumference by 793 / 24 or roughly 33 units each time.

Correct.

IMO, what you need to be able to do is invert the incomplete elliptic
integral of the second kind, inverting with respect to its amplitude z (not
its parameter m). N.B. Since there are differing conventions, to avoid
confusion, let's agree here to use the convention used at
<http://functions.wolfram.com/EllipticIntegrals/EllipticE2/>.

Your computer system might have an implementation of that inverse; if so,
everything would be simple. But it's unlikely that it has such an
implementation. Since you just need a fairly crude approximation, using
just a few terms of a series for that inverse should be satisfactory. I'll
work out an example for you below. But first, you might want to look at two

"Inverting elliptic integrals" sci.math.research

"n equally spaced points around the ellipse's perimeter" sci.math

Now for the example, using the data you gave above. You already know that
your ellipse can be parametrized as x = 150 sin(t), y = 100 cos(t) and that
its perimeter is 793.27. You want 24 points on the ellipse so that the
lengths of the elliptic arcs between consecutive pairs of points are
approximately the same.

It's very convenient that you chose 24; it's divisible by 4. Let me suggest
that you _always_ use a number divisible by 4. Doing so simplifies things.
So in your example, we just need to divide the part of the ellipse in the
first quadrant into six arcs of approximately equal length.

I shall also assume, for greatest convenience, that we start with t = 0,
that is, that we begin at an end of the minor axis.

Here is part of a Mathematica notebook. I hope it's more-or-less
self-explanatory; if not, don't hesitate to ask questions.

In= a = 150; b = 100; param = 1 - (b/a)^2;
quarterperimeter = a*EllipticE[param]

Out:= 150*EllipticE[5/9]

In= distance = %/6

Out:= 25*EllipticE[5/9]

In= N[%]

Out:= 33.0529991443554

thereby confirming your "roughly 33 units".

In= Normal[InverseSeries[Series[EllipticE[z, m], {z, 0, 14}], d]]

Out:= d + (d^3*m)/6 + (1/120)*d^5*(-4*m + 13*m^2) +
(d^7*(16*m - 284*m^2 + 493*m^3))/5040 +
(d^9*(-64*m + 4944*m^2 - 31224*m^3 + 37369*m^4))/362880 +
(d^11*(256*m - 81088*m^2 + 1406832*m^3 - 5165224*m^4 + 4732249*m^5))/
39916800 + (d^13*(-1024*m + 1306880*m^2 - 56084992*m^3 + 474297712*m^4 -
1212651548*m^5 + 901188997*m^6))/6227020800

The result above gives an approximation of the needed inverse.

In= InvE[d_, m_] := d + (d^3*m)/6 + (1/120)*d^5*(-4*m + 13*m^2) +
(d^7*(16*m - 284*m^2 + 493*m^3))/5040 +
(d^9*(-64*m + 4944*m^2 - 31224*m^3 + 37369*m^4))/362880 +
(d^11*(256*m - 81088*m^2 + 1406832*m^3 - 5165224*m^4 + 4732249*m^5))/
39916800 + (1/6227020800)*(d^13*(-1024*m + 1306880*m^2 - 56084992*m^3 +
474297712*m^4 - 1212651548*m^5 + 901188997*m^6));

In= N[Table[{a*Sin[t], b*Cos[t]} /. t -> InvE[d, param],
{d, 0, quarterperimeter/a, quarterperimeter/(6*a)}]]

Out:= {{0., 100.},
{32.93229464625545, 97.56015573157862},
{65.09394815658442, 90.09323050999978},
{95.44895809488033, 77.14199432389246},
{122.25147255789417, 57.94471486752196},
{142.21788527772756, 31.79149506904233},
{149.99996319648417, 0.07005094462200027}}

So we got a list of 7 points. You wouldn't really want to use the last one;
instead, you'd use exactly (150, 0). I showed the last point simply so that
you'd see how far off the approximation was there. Of course, to get the
rest of the 24 points, in the other quadrants, just use symmetry.

David W. Cantrell Zdenìk Hurák
science forum beginner

Joined: 06 Mar 2006
Posts: 4 Posted: Mon Mar 06, 2006 10:36 am    Post subject: Re: polynomial factoring and round off errors Jeremy, what you describe is definitely the basic trouble with polynomials: computing coefficients of a polynomial from its roots and back... See, for instance, the comprehensive textbook: N.J.Higham. Accuracy and stability of numerical algorithms (2nd ed.) SIAM, 2002. or the celebrated J.H.Wilkinson. Rounding errors in algebraic processes. Prentice-Hall, 1963. However, not all is lost. Even though I did not understand fully the motivation for what you are doing, I guess it must have something to do with tasks known as spectral factorization and stable-unstable factorization, right? For these, a lot more efficient and reliable tools exist. Factoring a polynomial into trivial factors, keeping the stable factors only, that is, those inside the units circle, and inverting those unstable can be done more efficiently using FFT, or Riccati equation solvers, or using Newton method. Calculating the roots can be totally avoided. Should you be interested, I am ready to give you more info. Best regards, Zdenek jeremyscerri@gmail.com
science forum beginner

Joined: 05 Mar 2006
Posts: 6 Posted: Tue Mar 07, 2006 6:04 pm    Post subject: Re: polynomial factoring and round off errors This is some more detail on my work. this site has some images to let you in on my problem http://www.ramsete.com/aurora/saw/roomsim.html i am measuring the characteristics of a room impulse response which is basically a mesaurment of direct and reflected paths between a microphone and a speaker. This will result in a signal as shown on the above site. Depending on the duration of the echoes and the sampling rate i will end up with at least around 1000 to 2000 (or even more) numbers which represent the intensity of the sound at the sampling time. Now to cancel out this echo from music or speech received at the microphone i have to invert this impulse response and convolve with the received signal. The inversion process will be unstable and diverge if it has zeros outside the unti circle. now i need to perform some experiments whereby a) i try removing the zeros outside or b) better reflecting the outside zeros inside unti circle, this last method does not change the magnitude spectrum and apparently this change is not percieved by the humnan ear. Hence if you have any method which avoids calculation of roots but still manages to obtain a) or b) i would appreciate your help. the closest method i found which avoids factoring and reconstruction is mentioned here, http://ccrma.stanford.edu/~jos/filters/Creating_Minimum_Phase_Filters.html i have tried it and it seems to work altough i did not follow the mathematics yet. thanks jeremy Zdenìk Hurák
science forum beginner

Joined: 06 Mar 2006
Posts: 4 Posted: Wed Mar 08, 2006 2:14 pm    Post subject: Re: polynomial factoring and round off errors Jeremy,

what you need in (a) is called plus-minus (or stable-unstable) factorization
of a polynomial and what you need in (b) and is called spectral
factorization in control theory (well, not directly this task but something
very closely related). The latter task being somewhat more common. Search
for papers and book chapters for "spectral factorization". The list of
literature is vast. You can perhaps check
http://dsp.vscht.cz/konference_matlab/matlab03/hromcik2.pdf for a sketch of
one approach and some other references.

My close colleagues are involved in development of a commercial code called
Polynomial Toolbox <http://www.polyx.com> for Matlab, that includes a
reliable tool for this task. I suggest that you send me some polynomial and
we will try to perform both tasks.

Best regards,
Zdenek

jeremyscerri@gmail.com wrote:

 Quote: This is some more detail on my work. this site has some images to let you in on my problem http://www.ramsete.com/aurora/saw/roomsim.html i am measuring the characteristics of a room impulse response which is basically a mesaurment of direct and reflected paths between a microphone and a speaker. This will result in a signal as shown on the above site. Depending on the duration of the echoes and the sampling rate i will end up with at least around 1000 to 2000 (or even more) numbers which represent the intensity of the sound at the sampling time. Now to cancel out this echo from music or speech received at the microphone i have to invert this impulse response and convolve with the received signal. The inversion process will be unstable and diverge if it has zeros outside the unti circle. now i need to perform some experiments whereby a) i try removing the zeros outside or b) better reflecting the outside zeros inside unti circle, this last method does not change the magnitude spectrum and apparently this change is not percieved by the humnan ear. Hence if you have any method which avoids calculation of roots but still manages to obtain a) or b) i would appreciate your help. the closest method i found which avoids factoring and reconstruction is mentioned here, http://ccrma.stanford.edu/~jos/filters/Creating_Minimum_Phase_Filters.html i have tried it and it seems to work altough i did not follow the mathematics yet. thanks jeremy Toni Lassila
science forum Guru Wannabe

Joined: 04 May 2005
Posts: 135 Posted: Mon Mar 20, 2006 11:34 am    Post subject: Re: Choosing a matrix library for image processing. Blitz++,MTL or others? On 19 Mar 2006 19:05:33 -0800, "Guch Wu" <guchnotes@gmail.com> wrote:

 Quote: I'll swictch from Matlab to C++. So I want to find a matrix library of C++, Whitch can process images conveniently as Matlab does. I've googled, and found that Blitz++ and MTL are popular and powerful. I want to know whitch of them fit for image processing better. Or have other choices? Any suggestion whill be appreciated.

How about asking in the proper newsgroup? Anon.
science forum beginner

Joined: 25 Apr 2005
Posts: 11 Posted: Mon Mar 20, 2006 6:28 pm    Post subject: Re: Question about SVD when # rows < # col Phil Sherrod wrote:
 Quote: I'm using the "R" system to prototype a statistical procedure and also working in C++ using an implementation of SVM from Wilkinson and Reinsch: "Handbook of Automatic Computation" I have a case where I am trying to apply SVD (Singular Value Decomposition) to a matrix that has fewer rows than columns. The "R" svm() function seems to be able to handle this case, but my C++ routine disallows # rows < # columns. Is there a general way to handle this type of SVM problem? I saw a reference that suggested adding rows with all zeros to the bottom of the matrix, that that doesn't seem to get the same results as "R". What is the general method for performing SVM when the matrix has fewer rows than columns? Try ?svd, or help(svm, package=e1071) for references that give

algorithms that R uses.

Bob

--
Bob O'Hara
Department of Mathematics and Statistics
P.O. Box 68 (Gustaf Hällströmin katu 2b)
FIN-00014 University of Helsinki
Finland

Telephone: +358-9-191 51479
Mobile: +358 50 599 0540
Fax: +358-9-191 51400
WWW: http://www.RNI.Helsinki.FI/~boh/
Journal of Negative Results - EEB: www.jnr-eeb.org giuseppe
science forum beginner

Joined: 12 May 2005
Posts: 5 Posted: Thu Mar 23, 2006 8:57 am    Post subject: Re: Reducible Matrices But how we can test quicly (maybe with some algebra operation) that the matrix is block-matrix? G Peter Spellucci
science forum Guru

Joined: 29 Apr 2005
Posts: 702 Posted: Thu Mar 23, 2006 10:34 am    Post subject: Re: Reducible Matrices In article <12539431.1143104250908.JavaMail.jakarta@nitrogen.mathforum.org>,
giuseppe <gdemarco@unisa.it> writes:
 Quote: But how we can test quicly (maybe with some algebra operation) that the matrix is block-matrix? G

?????? any matrix is a block matrix of one by one blocks.
what you meant is the test of reducibility via the associated directed graph?
see for example
Ortega&Rheinboldt, "iterative solution of nonlinear equations in several
variables", 2.3.5
hth
peter Reef Fish
science forum Guru Wannabe

Joined: 28 Apr 2005
Posts: 200 Posted: Fri Mar 31, 2006 7:20 am    Post subject: Re: multidimensional scaling clustering bird wrote:
 Quote: 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.

It's not a projection problem. It is the representation of n objects
with given dissimilarity matrix of pairwise dissimilarity measures
by n points in a Euclidean p space such that the pairwise
distances of the points in Euclidean p space best "fits" the
original dissimilarities.

The "badness of fit" is called the "stress".

 Quote: Can someone please instruct me how I can use the configuration to compute the patterns in the lower-dimensional space?

Most multidimensional programs allows you to specify the range of
dimensions p you wish to fit!

However, if you're starting with someone else's recovered configuration
in 4 dimensions say, and want to find the best fitting configuration in

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.

 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.

-- Bob. bird
science forum beginner

Joined: 11 Jun 2005
Posts: 14 Posted: Sun Apr 02, 2006 7:22 pm    Post subject: Re: multidimensional scaling clustering 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? Art Kendall
science forum beginner

Joined: 16 Jun 2005
Posts: 9 Posted: Mon Apr 03, 2006 12:29 pm    Post subject: Re: multidimensional scaling clustering 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:
 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). 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? Reef Fish
science forum Guru Wannabe

Joined: 28 Apr 2005
Posts: 200 Posted: Mon Apr 03, 2006 4:13 pm    Post subject: Re: multidimensional scaling clustering Art Kendall wrote:
 Quote: Doug Carroll and colleagues at Bell labs created extensions to the single matrix MDS (e.g., Joe Kruskal).

I knew all those people well, since I was a member of CSNAB for 20
years
until I finally gave up on the lack of progress in clustering
theory/methods
after Program Chaired the Federation of International Classification
Societies (7 nations, including CSNAB) in 1989, as well as having
been the Program Chairman of two previous Annual Meetings of CSNA.

Since I haven't been in touch with most of the people in those areas
the past 15 years, I phone Doug Caroll directly this morning to hear
from
the horse's mouth what he had done.

He had indeed worked on "cluster-scale" a hybrid model, work still
unpublished, in some network areas in which both scaling and
clustering work had been done, in search of a more "parsimonious"
representation of both.

I questioned why he did not do MDS and "clustering" separately,
because those two methods are INCOMPATIBLE in their goals, as
I mentioned to the OP inquirer "bird". Doug had no good answer
for it. I'll post a separate post to explain WHY those two mothods
are INCOMPETIBLE, in GOAL or METHOD, and why trying to do
both all at once under some "hybrid" model can only make it worse
for both, for ALL the problems and solutions in MDS and clustering
I've seen, in about 3 decades -- and that's quite a few! :-)

In any event. "bird" has not even made a good start toward "first
base", and has quite a bid of homework to do before he can even
ask any sensible question relating to those subjects.

Thus, referring him to Class-L seems to be as inappropriate as
referring a grade-school student to ask a simple arithmetic
question such as "what does 2 + 3 mean or why it is equal to 5"
in sci.math.

However, the Class-L listserv LIST, which started about the time I
stopped my CSNA association, is potentially useful to get some
conversation/discussion on some technical ideas on clustering and
other areas considered in CSNA.

It's VERY light in traffic, and Doug said he "never" read it (quoted
him) when I asked him about a webpage archive version that
most LISTSERV mailing lists have (which make it much easier
to read, in content and in threads). Doug had in fact posted in
it 4 or 5 times since 2000. But I see a conspicuous absence of
those in the know about EITHER subject in that LIST, such as

Bob Sokal (or ANY of the Clustering heavy weights, except Jim
Rohlf). Joe Kruskal (or ANY of the MDS heavy-weights), or
Phipps Arabie (former editor of CLASS; former Prez of CSNAB;
former Prez of Psychometrika; etc.).

Since the LIST is maintained in SUNY, I suspect Jim Rohlf is the
person who either maintains it or is quite familiar with it.

 Quote: George xxxx developed a method that found clusters and dimensions on the same run.

In Cluster Analysis? Doesn't sound like Doug's co-author on his hybrid

stuff. Besides, a "proper and ueful" cluster solution does NOT depend
on the representation (or even existence) in any dimension, but it
does depend heavily on the clustering "criterion" which produce many
DIFFERENT solutions on different criteria -- which is one of the
reasons
an ominbus "hybrid" solution necessarily FAIL for its failure to
consider the existence of clusters of different TYPES, on a single
highly distorted representation of points in a Euclidean space.

-- Bob.

 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. 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?  Display posts from previous: All Posts1 Day7 Days2 Weeks1 Month3 Months6 Months1 Year Oldest FirstNewest First
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