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Dear Max,<br>
<br>
just my small input concerning your question "How could frequencies
that do not exist in the input be created by the ICA?" <br>
<br>
Take a 2 channel, 2 source artificial scenario, wherein source 2
contains a positive component that is negative in source 1, say with
respective weights +1 and -1 in observation 1. It can easily be seen
that in the observation 1 that component (frequency component if you
want -- I use component to not interfere with what is called a
source, a source here can consist out of multiple components) will
not be visible, whereas if one excludes either one of the sources in
the reconstruction the component does become visible (either
positively or negatively). These "components" are not always
physiologically realistic, but they do form a valid "mathematical"
decomposition. <br>
<br>
Now, you might wonder why this is more often the case with frequency
components than it is with temporal components? This is because the
temporal waveform of such components resemble gaussian noise
(temporal structure not taken into account) and will thus be
invisible to the ICA algorithm. This can be explained as the source
and the source + gaussian component having the same behaviour when
submitted to an ICA algorithm.<br>
<br>
There exist some works that do, e.g., posterior wavelet aided
cleaning of the sources (e.g., <a
href="http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5713804&tag=1">http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5713804&tag=1</a>),
or some works that try to get a best trade-off between temporal and
spectral independence (see, e.g., <a
href="http://si.utia.cas.cz/pubs/TNN08.pdf">http://si.utia.cas.cz/pubs/TNN08.pdf</a>).
Another hybrid approach used in ECG data may be found in <a
href="http://personales.gan.upv.es/jjrieta/pub_whole.htm">http://personales.gan.upv.es/jjrieta/pub_whole.htm</a>
(see Castells, F., Rieta, J. J., Millet, J. and Zarzoso, V.
"Spatiotemporal Blind Source Separation Approach to Atrial Activity
Estimation in Atrial Tachyarrhythmias", IEEE Transactions on
Biomedical Engineering, vol. 52, no. 2, pp. 258-267, Feb. 2005. ).<br>
<br>
Good luck,<br>
<br>
Ronald<br>
<br>
Le 07/09/2011 19:26, Maximilien Chaumon a écrit :
<blockquote
cite="mid:CAFU3-hGuY2BjB+8svZ_A51bkAm2boSbD3sg-nSki-NfJrmsEQw@mail.gmail.com"
type="cite">Hi eeglabbers,<br>
<br>
I am still having issues with ICA returning extremely similar (but
not identical) topographies. The gui (although I run a version
updated a few days ago) does not popup any suggestion to reduce
the rank. I only get this warning (Warning: fixing rank
computation inconsistency (68 vs 69) most likely because running
under Linux 64-bit MatlabAttempting to convert data matrix to
double precision for more accurate ICA results.) I still get 69
components in the end.<br>
<br>
Here's some more info:<br>
the rank of the data is 68. The svd drops abruptly close to zero
at the last value. I have 69 electrodes (64 heancap +
3EOG+2mastoids). I guess there's a gel bridge somewhere. Although
correlations between all electrodes don't reach .95.<br>
When I let the ICA run with default options, I still get <a
moz-do-not-send="true"
href="http://oszilla.hgs.hu-berlin.de/public/2P3like_components.png">these
two components</a> (always 'P3 like' components, this was
reproduced in other subjects). Their frequency profiles are too
good to be true, with low noise and a peak at 10Hz, another one
around 20Hz, see the figure. I would leave them alone if they were
not spoiling all my data: As I remove the components, when I click
this 'singles' button, which shows me the trial by trial time
course. I get what is shown on the right of the <a
moz-do-not-send="true"
href="http://oszilla.hgs.hu-berlin.de/public/2P3like_components.png">figure</a>.
High frequency bursts appearing every now and then, usually at
times where there is high variability across channels.<br>
Removing both components resolves the issue, but I loose a rather
important part of the data.<br>
Here is the <a moz-do-not-send="true"
href="http://oszilla.hgs.hu-berlin.de/public/2P3spectopo.png">spectopo
at 60Hz</a>. There is a strong artefact here. The two components
show a high power at all frequencies.<br>
How could frequencies that do not exist in the input be created by
the ICA? I filter my data, before ICA below 45Hz.<br>
<br>
I tried running fastica, asking for 68 components, no such
artifact appears but the decomposition looks much less nice, at
least with the parameters I've used.<br>
<br>
So in the end, my question is: <br>
How can I run an ICA without trouble if the rank of the data is
not equal to the number of electrodes? How can I identify
potentially gel bridged electrodes?<br>
<br>
Many thanks,<br>
Max<br>
<br>
<br>
<div class="gmail_quote">2011/8/27 Arnaud Delorme <span dir="ltr"><<a
moz-do-not-send="true" href="mailto:arno@ucsd.edu">arno@ucsd.edu</a>></span><br>
<blockquote class="gmail_quote" style="margin:0 0 0
.8ex;border-left:1px #ccc solid;padding-left:1ex;">
<div style="word-wrap:break-word">Regarding the matrix rank,
we have recently realized that the rank function (and other
rank function we had programmed) are not fully reliable
which is probably with Max observes the component he
observes. The runica function should automatically decrease
the rank of the input data matrix. However, sometimes it
does not use the correct rank. We have modified the runica
GUI so that if the matrix is not full rank, it now pops up a
new window suggesting to the user a rank reduced value. This
value may be adjusted by the user based on prior knowledge.
For instance, if you have removed 5 components from the
data, you would reduce the rank by 5 (and overwrite the rank
that is automatically detected if it is not correct).
<div>
<br>
</div>
<div>Arno
<div>
<div class="h5">
<div><br>
<div>
<div>On Aug 23, 2011, at 10:11 PM, John J.B. Allen
wrote:</div>
<br>
<blockquote type="cite">Max
<div><br>
</div>
<div>I have observed that when the data are not
full rank. You can test the rank of your
data by reshaping your epoched data to a 2D
matrix, and running the rank command, like
this:</div>
<div><br>
</div>
<div>rank(reshape(EEG.data,EEG.nbchan,EEG.trials*EEG.pnts))</div>
<div><br>
</div>
<div>When I did this, your rank is 63, but you
have 69 channels, indicating that some
channels are linearly dependent on others. I
think this is the source of your problem, and
if you remove those channels before running
ICA, you should no longer see this issue.</div>
<div><br>
</div>
<div>Best</div>
<div><br>
</div>
<div>John</div>
<div><br>
</div>
<div><br>
</div>
<div><br>
<br>
<div class="gmail_quote">On Tue, Aug 23, 2011
at 07:24, Maximilien Chaumon <span
dir="ltr"><<a moz-do-not-send="true"
href="mailto:maximilien.chaumon@gmail.com"
target="_blank">maximilien.chaumon@gmail.com</a>></span>
wrote:<br>
<blockquote class="gmail_quote"
style="margin:0 0 0 .8ex;border-left:1px
#ccc solid;padding-left:1ex">Hi
eeglabbers,<br>
<br>
I sometimes get ICs with extremely similar
topographies and time courses, like on <a
moz-do-not-send="true"
href="http://oszilla.hgs.hu-berlin.de/public/Similar_ICs.PNG"
target="_blank">this slide</a>.<br>
I know that ICA returns independent
components.<br>
Does that not mean that they should not
look the same?<br>
I know the components are independent in a
statistical sense, which is not the same
as uncorrelated, but still. I'm a bit
surprised. What do these two components
mean if they cancel one another? well, do
they?<br>
<br>
Sorry if my question is naive, but what is
happening?<br>
<br>
The data is <a moz-do-not-send="true"
href="http://oszilla.hgs.hu-berlin.de/public/Similar_ICs.mat"
target="_blank">here</a>.<br>
<br>
Best,<br>
Max<br>
<br>
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<div class="moz-signature">-- <br>
<p><b>Ronald Phlypo</b><br>
<i>Vision and Brain Signal Processing (ViBS) Research Group</i><br>
<i>Universités de Grenoble / CNRS UMR 5216</i><br>
961 Rue de la Houille Blanche<br>
BP 46<br>
38402 Saint Martin d'Hères<br>
FRANCE</p>
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tel: +33 (0)4 76 82 62 47<br>
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