[Eeglablist] indipendent component analisys

Scott Makeig smakeig at ucsd.edu
Wed Nov 18 11:00:11 PST 2015

Dorian -

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.

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).

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).

Scott Makeig

On Tue, Nov 10, 2015 at 2:11 AM, Dorian Grelli <dorian.grelli at gmail.com>

> Hi guys,
> 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?
> Cheers,
> Dorian
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Scott Makeig, Research Scientist and Director, Swartz Center for
Computational Neuroscience, Institute for Neural Computation, University of
California San Diego, La Jolla CA 92093-0961, http://sccn.ucsd.edu/~scott
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