<div dir="ltr"><div><div>Hi Dorian, hi Scott,<br><br></div>first of all, thanks for the
question and the answer! I was thinking about the same as well, and the
answer I got by now basically was "it's the math". Your answer is quite
interesting in the perspective that in theory it could be different,
right? So, if I understood this right, one could for example have as
many ICs as one has supposed sources in the beamformer for source
reconstruction plus some amount for artifacts and noise? But this would
actually be less useful than having fewer ICs which "sum up" the small
sources to bigger cortical patches, which are actually what we want to
investigate (plus it would probably be a mathematical disaster and not
applicable in acceptable runtime...)? If so this is quite interesting,
because by now I thought, the closer one looks, the better. But at least
concerning EEG, looking closer diffuses the actual signal in a way that
it's not anymore of useful information to us... or at least of
different information, which we're not looking for.<br><br></div><div>Cheers,<br></div>Marius</div><div class="gmail_extra"><br><div class="gmail_quote">2015-11-18 20:00 GMT+01:00 Scott Makeig <span dir="ltr"><<a href="mailto:smakeig@ucsd.edu" target="_blank">smakeig@ucsd.edu</a>></span>:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr">Dorian -<div><br></div><div>Finding the same number of sources as channels makes ICA into a linear change of basis problem -- this makes the math simpler and reduces the number of assumptions involved in applying the analysis. </div><div><br></div><div>We know, of course, that strictly speaking, small-scale potential variations in cortex alone are vastly more variegated than the number of scalp channels -- but most of these variations will be cancelled out through common volume conductance and summation at the scalp electrodes (i.e., through destructive phase interference, positive-going and negative-going potentials at any time point tending to cancel each other in their summation at each scalp electrode channel). </div><div><br></div><div>EEG signals are thus dominated by (i.e,. chiefly sum) larger signals arising from locally synchronous 'patches' of cortical activity whose signals, summed across the disparate patch source activity, thus act as the effective (brain) sources of scalp EEG signals. In practice, ICA is of interest for brain EEG data analysis because it separates out signals from these patches (Delorme et al., 2012 PLoS ONE; Akalin Acar et al, Neuroimage, 2015).</div><div><br></div><div>Scott Makeig</div></div><div class="gmail_extra"><br><div class="gmail_quote">On Tue, Nov 10, 2015 at 2:11 AM, Dorian Grelli <span dir="ltr"><<a href="mailto:dorian.grelli@gmail.com" target="_blank">dorian.grelli@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr">Hi guys,<div>I've another questions about ICA. This is more theretical. I am wondering why, after running ICA, we get as many indipendent components as we have channells. I studied a bit of ICA theory in the tutorials ("for dummies" and "not for dummies" that I found on the Internet) but, unfortunately, my background is quite far from math and matrixes and it's difficult for me to digest every detail. I think I get a bit of the theory but the point above is still unclear. Could you help me?</div><div><br></div><div>Cheers,</div><div><br></div><div>Dorian</div></div>
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