[Ifeffit] Determining the correct number of components from PCA

Voegelin, Andreas Andreas.Voegelin at eawag.ch
Thu Aug 27 16:12:12 CDT 2009


Hi Kevin

Maybe the 3rd component is not due to noise but accounts for very small
shifts in energy calibration between scans (considering that the
reconstructed white-line is shifted to higher energies in the
2-component reconstruction). Do you have a reference foil measured with
each scan to exactly align the spectra or some other way to check for
small shifts in energy calibration?

Best regards,

Andreas

-----Original Message-----
From: ifeffit-bounces at millenia.cars.aps.anl.gov
[mailto:ifeffit-bounces at millenia.cars.aps.anl.gov] On Behalf Of Kevin
McPeak
Sent: Donnerstag, 27. August 2009 07:23
To: ifeffit at millenia.cars.aps.anl.gov
Subject: [Ifeffit] Determining the correct number of components from PCA

Hi all,

I have a question about the "best" method to use to decide the correct
number of components in a system based on a PCA.  Myself and a
collaborator took in-situ XANES scans of the formation of ZnO in
aqueous solution. We have a series of scans from this experiment and I
have done a PCA on them using SIXPack. After doing the PCA I unchecked
the components until I could no longer visually reconstruct the series
of scans accurately (by visual determination). Using this visual
method I only need 2 components. But if I go by the minimum of the IND
function (what the SIXPack user guide recommends) I should use three
components.

I have posted the sample/reconstruction plots for 2 and 3 component
reconstructions here (the scan I chose to reconstruct is
representative of the data series):

http://dunx1.irt.drexel.edu/~kmm333/xafs/pca_recon_12.5_90_scan10_2comp.
html
http://dunx1.irt.drexel.edu/~kmm333/xafs/pca_recon_12.5_90_scan10_3comp.
html

The main difference between the two plots is that the 3 component
reconstruction fits the edge region better. Zoom in (hold down the
right mouse button) and you'll see what I'm talking about. That said I
really have my doubts about 3 components being necessary, the visual
differences are so slight that I can't help but think that these
differences are just part of the noise. As for 2 or 3 components being
physically possible, both are feasible give the chemistry involved.

SIXPack does not provide IE or F test, so I plotted the IND results
vs. number of components for all the reactions. Except for the lowest
concentration the IND value reached a minimum at 3 components for all
the reactions. You can see the plot of IND value vs. number of
components here:

http://dunx1.irt.drexel.edu/~kmm333/xafs/pca_ind_results.html

The IND minimum is rather broad. Are there other techniques that I
should be using to determine the number of components from the PCA? I
look forward to your feedback.

Kevin McPeak
kmm333 at drexel.edu
--
PhD Candidate
Chemical Engineering
Drexel University

P.S If you use Firefox or Safari you can zoom in on these plots by
holding down the right mouse button and making a box. Release the
right mouse button to zoom in on that box. Press the left arrow button
to the left of the plot to un-zoom.
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