ICA based artifact correction and phase-locking

[Christian Hesse]

Hi Markus,

>> Why do you remove these epochs? Do the signals saturate or is
>> there excessive electrode(-cap) or subject movement in these?
>>
> Yes, that's correct. I remove epochs before any further analysis,
> if I find saturated channels or excessive subject movements.

Seems reasonable to me, then.


>> How many EEG channels do you have, by the way? I need to know in
>> order to continue with the 'slightly longer answer'
>
> I recorded my data from 60 Ag/Ag-Cl electrodes embedded in an
> elastic cap (with BrainAmp amplifiers) positioned according to the
> extended 10/20 system. Additionally, I record EOG with two
> electrodes placed at the outher canthi and one electrode placed
> below the left eye. All channels are referenced to the right
> mastoid during recording, while the left mastoid electrode is
> recorded as an additional active channel (off-line re-refrenced to
> the mean of both mastoids).

Ok, thanks for this extra info. 60 channels is (I think) a good
number in that you are less likely to be affected by the problem of
over-fitting in ICA: this can sometimes happen when there are fewer
source signals which are identifiable by the ICA algorithm (i.e.,
statistically independent signals with non-gaussian marginal
distributions) than sensors. Note that fewer sources than sensors
does not necessarily mean that your data is rank-deficient (you can
easily check this by looking at the singular spectrum of your data
matrix or, equivalently, at the spectrum of eigenvalues of the data
covariance matrix - the former is gives the square root of the
latter) because there is always some form of either "sensor" or
"ambient" noise, which will have a gaussian distribution. The point
is that when ICA has found all the obvious components (non-gaussian
ones) it then tries to decompose the gaussian part of the signal into
non-gaussian parts, and this will lead to so-called "over-fitting",
which also affects the accuracy of the estimates of the "true"
components. Different ICA algorithms behave differently in this case,
some will give you spurious solutions, others will simply not
converge to a solution (because there is none in the ICA sense, and
throw an error of the code is smart enough to spot this). But you
should not really have to worry too much about that; although do
watch out for it: warnings and error messages about mixing or de-
mixing matrix being (close to) singular is a good indication of over-
fitting, and PCA-based dimension reduction of your data as part of
the ICA is then recommended (though not a "magic" solution, either).

When there are fewer channels than sources, you can have the opposite
problem, namely under-fitting. In this situation, there are not
enough components to describe all of the data, and the solution is
then likely to be some sort of compromise, where "true" sources that
are "weak" are spread over several ICs, none of which individually
describes a source. In this case the accuracy of your mixing matrix
estimate will also be "off", but the estimates of the stronger
components are usually pretty robust in this case.

What can also affect the accuracy of the mixing matrix estimate is
the violation of the assumption of statistical independence of the
sources, and this is pretty likely in the case of networks of
neuronal populations displaying oscillatory activity with greater or
lesser coherence because coherent signals (i.e. with a constant phase
relationship other than 90 degrees) are generally not statistically
independent. This need not be a disaster provided that the total
activity of these coherent networks (i.e. in the signal subspace of
coherent sources) is statistically independent of all the artifact
stuff you wish to remove. Then you can go ahead with ICA and remove
artifacts, but you will not necessarily be able to identify/interpret
individual oscillatory components of brain activity. But since you do
your analysis at the sensor level, this does not matter.

Another problem related to ICA and sources of oscillatory activity is
that the amplitude time course of this activity is generally
modulated over time, which in turn can make these sources have
marginal distributions which "look" essentially Gaussian, in which
case the ICA algorithm may again be unable to correctly (or uniquely)
identify the sensor projections associated with such source signals,
EVEN if they are statistically independent, since ICA ONLY works
exactly if the sources are statistically independent AND non-gaussian.

So in summary, I guess my advice to you would be to always use
EXTREME CAUTION when working with ICA :-), but to go ahead with what
you're doing and just make sure you are able to robustly identity all
of your artifacts, and don't spend too much time worrying about which
components reflect brain activity, as this is likely to live in a
subspace so individial topographies give a limited story. I really
don't mean to sound negative, but these problems and limitations
regularly occur in real life ICA-usage, and you need to know that it
is not a "cure" for "bad" data (from an ICA point of view).

Hope this helps,
Christian


----------------------------------------------------------------------
Christian Hesse, PhD, MIEEE

F.C. Donders Centre for Cognitive Neuroimaging
P.O. Box 9101
NL-6500 HB Nijmegen
The Netherlands

Tel.: +31 (0)24 36 68293
Fax: +31 (0)24 36 10989

Email: c.hesse at fcdonders.ru.nl
Web: www.fcdonders.ru.nl
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