[Eeglablist] ICA suggests weirdly low rank

[Makoto Miyakoshi]

Hi Eugen,

The misbehavior of ICA when overcomplete decomposition is forced (i.e. you
request rank-n decomposition when data rank is n-1) is more definitive and
catastrophic than observing less accurate dipole modeling (but here you
don't know what you are modeling anyway). See this Wiki article to see an
example of ICA failure :
https://sccn.ucsd.edu/wiki/Makoto's_preprocessing_pipeline#Examples_of_artifact_from_ICA_.28Modified_09.2F08.2F2020.29

An ICA result is invariable to the selection of a reference electrode
because (correct) re-reference does not change the linear property of the
data. If re-reference changes ICA result, including losing one IC after
applying an incorrect average reference, that means your re-referencing
process does not pass the invariability test using ICA (but mean values
across the column vectors of the mixing matrix change, hence you can see
all red or all blue scalp topographies if you do not apply re-reference to
average before ICA, which itself is not a failure but inconvenient in
practice).

Makoto

On Thu, Jun 13, 2024 at 3:41 AM Евгений Машеров <emasherov at yandex.ru> wrote:

> Hi Makoto,
>
> Thanks for the interesting and useful article.
> I encountered the problem of rank deficiency in averaged referenced in
> connection with dipole localization. It turned out that despite getting rid
> of artifacts from ear electrodes, localization accuracy decreased. It seems
> to me that this is due to the fact that the dimension of the signal space
> is reduced from n to n-1, so that 1/n part of the signal information goes
> into the orthogonal subspace and is not available for analyze. Trying to
> eliminate this effect, they tried to replace the average when calculating
> the averaged electrode with the median, which formally restored the rank,
> since the median is equal to the average only on the average. However, the
> desired restoration of accuracy did not happen.
> On older devices with analog averaging, differences in resistor values and
> amplifier characteristics led to the fact that the sum of signals at the
> averaged lead could differ from zero and the rank could not be deficient.
> In a digital implementation, the sum of the signals differs from zero by an
> amount of the order of the error in number representation (10-7 - 10-10).
> It seems to me that to use the ICA it is better to work with the ear
> reference, and after eliminating artifacts, if such a need arises, it can
> be recalculated to the average.
>
> Eugen Masherov
>
> > Hi Eugen,
> >
> > There are three levels of understanding on the issue of average
> reference.
> >
> > Level 1: Why rank -1? I don't understand it.
> > Level 2: a1+a2+a3+...+an=0 is a hallmark of linear dependency. Rank -1
> is a
> > mathematical consequence.
> > Level 3: Rank -1 is a result of not including the initial reference
> > electrode in calculating the average potential, which is an invalid way
> to
> > re-reference the data.
> >
> > If you are curious, here is the recent paper discussing this issue. Note
> > that this paper was motivated by discussions on this mailing list.
> >
> https://urldefense.com/v3/__https://www.frontiersin.org/articles/10.3389/frsip.2023.1064138/full__;!!Mih3wA!BGpWl3IPPtL4Xe_3seDjV0fOrNUPhiSC3N4CIZuiSdVRExXxhamOn45qE5-PrqEIbhCMu_W_1An0ORQE7IKL8gFB7og$
> >
> > Makoto
> >
>