ICA based artifact correction and phase-locking

[Markus Werkle-Bergner]

Hi Christian, hi Stefan,

I thank both of you for your helpful comments. I now know better about
the possible problems, but I also see that it may be worth a try. I will
keep you posted about the progress via the discussion list as soon as
new problems arise ;-)

Thank you and best regards,
Markus

Christian Hesse schrieb:
> 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 <mailto:c.hesse at fcdonders.ru.nl>
> Web: www.fcdonders.ru.nl <http://www.fcdonders.ru.nl>
> ----------------------------------------------------------------------
>
>
>
>


--
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Markus Werkle-Bergner, Dipl. Psych.
Predoctoral Research Fellow

Center for Lifespan Psychology
Max Planck Institute for Human Development
Lentzeallee 94, Room 211, D-14195 Berlin, Germany.
Phone: +49(0)30-82406-447       Fax: +49(0)30-8249939
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