FAQFAQ   SearchSearch   MemberlistMemberlist   UsergroupsUsergroups 
 ProfileProfile   PreferencesPreferences   Log in to check your private messagesLog in to check your private messages   Log inLog in 
Forum index » Science and Technology » Math » num-analysis
convergence of QR-algorithm
Post new topic   Reply to topic Page 17 of 19 [276 Posts] View previous topic :: View next topic
Goto page:  Previous  1, 2, 3, ..., 15, 16, 17, 18, 19 Next
Author Message
Olin Perry Norton
science forum addict


Joined: 13 May 2005
Posts: 58

PostPosted: Tue Feb 21, 2006 3:12 pm    Post subject: Re: Pattern Recognition In Statistics Reply with quote

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?

Now, some comments:

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.
Back to top
brian a m stuckless
science forum Guru


Joined: 31 Aug 2005
Posts: 2024

PostPosted: Sun Mar 05, 2006 10:04 am    Post subject: Re: help me with this. Reply with quote

Quote:
"Ken" <krushpin@videotron.ca> 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.
Back to top
David W. Cantrell
science forum Guru


Joined: 02 May 2005
Posts: 352

PostPosted: Sun Mar 05, 2006 5:53 pm    Post subject: Re: Dividing an ellipse into equal parts Reply with quote

"tallsteve" <google@sumogoldfish.com> wrote:
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
previous threads:

"Inverting elliptic integrals" sci.math.research
<http://groups.google.com/group/sci.math.research/browse_frm/thread/6eb1aa7e07b1c382>

"n equally spaced points around the ellipse's perimeter" sci.math
<http://groups.google.com/group/sci.math/browse_frm/thread/10a64db323853322>


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

Out[1]:= 150*EllipticE[5/9]

In[2]= distance = %/6

Out[2]:= 25*EllipticE[5/9]

In[3]= N[%]

Out[3]:= 33.0529991443554

thereby confirming your "roughly 33 units".


In[4]= Normal[InverseSeries[Series[EllipticE[z, m], {z, 0, 14}], d]]

Out[4]:= 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[5]= 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[6]= N[Table[{a*Sin[t], b*Cos[t]} /. t -> InvE[d, param],
{d, 0, quarterperimeter/a, quarterperimeter/(6*a)}]]

Out[6]:= {{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
Back to top
David W. Cantrell
science forum Guru


Joined: 02 May 2005
Posts: 352

PostPosted: Sun Mar 05, 2006 5:53 pm    Post subject: Re: Dividing an ellipse into equal parts Reply with quote

"tallsteve" <google@sumogoldfish.com> wrote:
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
previous threads:

"Inverting elliptic integrals" sci.math.research
<http://groups.google.com/group/sci.math.research/browse_frm/thread/6eb1aa7e07b1c382>

"n equally spaced points around the ellipse's perimeter" sci.math
<http://groups.google.com/group/sci.math/browse_frm/thread/10a64db323853322>


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

Out[1]:= 150*EllipticE[5/9]

In[2]= distance = %/6

Out[2]:= 25*EllipticE[5/9]

In[3]= N[%]

Out[3]:= 33.0529991443554

thereby confirming your "roughly 33 units".


In[4]= Normal[InverseSeries[Series[EllipticE[z, m], {z, 0, 14}], d]]

Out[4]:= 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[5]= 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[6]= N[Table[{a*Sin[t], b*Cos[t]} /. t -> InvE[d, param],
{d, 0, quarterperimeter/a, quarterperimeter/(6*a)}]]

Out[6]:= {{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
Back to top
Zdenžk HurŠk
science forum beginner


Joined: 06 Mar 2006
Posts: 4

PostPosted: Mon Mar 06, 2006 10:36 am    Post subject: Re: polynomial factoring and round off errors Reply with quote

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
Back to top
jeremyscerri@gmail.com
science forum beginner


Joined: 05 Mar 2006
Posts: 6

PostPosted: Tue Mar 07, 2006 6:04 pm    Post subject: Re: polynomial factoring and round off errors Reply with 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
Back to top
Zdenžk HurŠk
science forum beginner


Joined: 06 Mar 2006
Posts: 4

PostPosted: Wed Mar 08, 2006 2:14 pm    Post subject: Re: polynomial factoring and round off errors Reply with quote

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
Back to top
Toni Lassila
science forum Guru Wannabe


Joined: 04 May 2005
Posts: 135

PostPosted: Mon Mar 20, 2006 11:34 am    Post subject: Re: Choosing a matrix library for image processing. Blitz++,MTL or others? Reply with quote

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?
Back to top
Anon.
science forum beginner


Joined: 25 Apr 2005
Posts: 11

PostPosted: Mon Mar 20, 2006 6:28 pm    Post subject: Re: Question about SVD when # rows < # col Reply with quote

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 HšllstrŲmin 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
Back to top
giuseppe
science forum beginner


Joined: 12 May 2005
Posts: 5

PostPosted: Thu Mar 23, 2006 8:57 am    Post subject: Re: Reducible Matrices Reply with quote

But how we can test quicly (maybe with some algebra operation) that the matrix is block-matrix?
G
Back to top
Peter Spellucci
science forum Guru


Joined: 29 Apr 2005
Posts: 702

PostPosted: Thu Mar 23, 2006 10:34 am    Post subject: Re: Reducible Matrices Reply with quote

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
Back to top
Reef Fish
science forum Guru Wannabe


Joined: 28 Apr 2005
Posts: 200

PostPosted: Fri Mar 31, 2006 7:20 am    Post subject: Re: multidimensional scaling clustering Reply with quote

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.
Back to top
bird
science forum beginner


Joined: 11 Jun 2005
Posts: 14

PostPosted: Sun Apr 02, 2006 7:22 pm    Post subject: Re: multidimensional scaling clustering Reply with 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?
Back to top
Art Kendall
science forum beginner


Joined: 16 Jun 2005
Posts: 9

PostPosted: Mon Apr 03, 2006 12:29 pm    Post subject: Re: multidimensional scaling clustering Reply with 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:
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?



Back to top
Reef Fish
science forum Guru Wannabe


Joined: 28 Apr 2005
Posts: 200

PostPosted: Mon Apr 03, 2006 4:13 pm    Post subject: Re: multidimensional scaling clustering Reply with quote

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.

Reader's Digest Version:

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. Smile 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?



Back to top
Google

Back to top
Display posts from previous:   
Post new topic   Reply to topic Page 17 of 19 [276 Posts] Goto page:  Previous  1, 2, 3, ..., 15, 16, 17, 18, 19 Next
View previous topic :: View next topic
The time now is Fri Oct 20, 2017 5:51 pm | All times are GMT
Forum index » Science and Technology » Math » num-analysis
Jump to:  

Similar Topics
Topic Author Forum Replies Last Post
No new posts how to deduce a number validation algorithm? Tim_Mac Math 1 Fri Jul 21, 2006 10:43 am
No new posts uni. convergence bill1158 Math 3 Wed Jul 19, 2006 10:59 am
No new posts convergence of probability measures pkg Math 0 Sat Jul 15, 2006 7:15 pm
No new posts analysis with uniform convergence.. mina_world Math 4 Fri Jul 14, 2006 8:26 am
No new posts Name of algorithm for pairwise comparison ? Paul Nutteing Math 10 Fri Jul 14, 2006 6:55 am

Copyright © 2004-2005 DeniX Solutions SRL
Other DeniX Solutions sites: Electronics forum |  Medicine forum |  Unix/Linux blog |  Unix/Linux documentation |  Unix/Linux forums  |  send newsletters
 


Powered by phpBB © 2001, 2005 phpBB Group
[ Time: 0.0432s ][ Queries: 16 (0.0091s) ][ GZIP on - Debug on ]