<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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