| Re: Principal Componets Analysis [message #55697] |
Wed, 05 September 2007 07:45 |
wlandsman
Messages: 743
Registered: June 2000
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Senior Member |
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On Sep 3, 8:33 pm, David Fanning <n...@dfanning.com> wrote:
>
> You can find the tutorial here:
>
> http://www.dfanning.com/code_tips/pca.html
>
> Any and all comments welcome.
Well, a minor historical comment about the different PCA
conventions. The pcomp.pro procedure was introduced into IDL in
1996, but prior to that Immanuel Freedman had written a procedure
pca.pro ( http://idlastro.gsfc.nasa.gov/ftp/pro/math/pca.pro) based on
a FORTRAN program by Fionn Murtagh.
When pcomp.pro was introduced, it took me a long time to prove that
pca.pro and pcomp.pro gave the same results Below are the notes I
wrote at the time:
*************************
The intrinsic IDL function PCOMP duplicates most most of the
functionality of PCA, but uses different conventions and
normalizations. Note the following:
(1) PCOMP requires a N_ATTRIB x N_OBJ input array; this is the
transpose of what PCA expects
(2) PCA uses standardized variables for the correlation matrix: the
input vectors are set to a mean of zero and variance of one and
divided by sqrt(n); use the /STANDARIZE keyword to PCOMP for a direct
comparison.
(3) PCA (unlike PCOMP) normalizes the eigenvectors by the square root
of the eigenvalues.
(4) PCA returns cumulative percentages; the VARIANCES keyword of PCOMP
returns the variance in each variable
(5) PCOMP divides the eigenvalues by (1/N_OBJ-1) when the covariance
matrix is used.
***********************
And, yes, I verified that pca.pro also reproduces the results in your
tutorial, but it requires even more adjustment than does pcomp.pro !
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| Re: Principal Componets Analysis [message #55712 is a reply to message #55697] |
Tue, 04 September 2007 09:23  |
David Fanning
Messages: 11724
Registered: August 2001
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Senior Member |
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Jeff N. writes:
> I'm reading through the tutorial, and spotted something you might want
> to fix in your discussion of CORRELATE. It's not true that negative
> values returned from that function are uncorrelated. You actually
> describe the reason why this is true in your tutorial: "a change in
> one vector will predict an opposite change in the other." if one
> vector predicts a change in the other, it's correlated. The negative
> sign just means that the change is an opposite change, like you
> mentioned. How well two variables are correlated depends on the
> magnitude of the number: 0 is not correlated, 1 is perfectly
> correlated (so -1 is perfectly negatively correlated).
Oh, my goodness. I must have been asleep when I wrote that.
One of the problems with working at 3AM. :-(
Fixed now. Thanks.
Cheers,
David
--
David Fanning, Ph.D.
Fanning Software Consulting, Inc.
Coyote's Guide to IDL Programming: http://www.dfanning.com/
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| Re: Principal Componets Analysis [message #55714 is a reply to message #55712] |
Tue, 04 September 2007 09:02 |
Jeff N.
Messages: 120
Registered: April 2005
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Senior Member |
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David,
I'm reading through the tutorial, and spotted something you might want
to fix in your discussion of CORRELATE. It's not true that negative
values returned from that function are uncorrelated. You actually
describe the reason why this is true in your tutorial: "a change in
one vector will predict an opposite change in the other." if one
vector predicts a change in the other, it's correlated. The negative
sign just means that the change is an opposite change, like you
mentioned. How well two variables are correlated depends on the
magnitude of the number: 0 is not correlated, 1 is perfectly
correlated (so -1 is perfectly negatively correlated).
Jeff
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| Re: Principal Componets Analysis [message #55732 is a reply to message #55714] |
Mon, 03 September 2007 18:06 |
David Fanning
Messages: 11724
Registered: August 2001
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Senior Member |
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David Fanning writes:
Principal "Componets" Analysis!? It's probably just as well
that no one is going to find that tutorial. :-(
Cheers,
David
--
David Fanning, Ph.D.
Fanning Software Consulting, Inc.
Coyote's Guide to IDL Programming: http://www.dfanning.com/
Sepore ma de ni thui. ("Perhaps thou speakest truth.")
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