| 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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