[Eeglablist] Re-referencing/rank/ICA

[Makoto Miyakoshi]

Dear Ivonne,

> With regard to re-referencing: if I recorded the data with an online
average reference and then re-reference to averaged mastoids offline, I
don't really understand why I woud need to add an additional channel in
this case? Actually, re-referencing should not affect rank at all in
this case or should it?

You have online average reference data? That's rare, it is my first-time
encounter.

Imagine you have only Fz and Cz.
In the following, Fz, Cz refers to potentials at Fz and Cz to infinity,
respectively.
Average reference recording will give you

Fz_data = Fz - (Fz+Cz)/2 = Fz/2 - Cz/2.
Cz_data = Cz- (Fz+Cz)/2 = -Fz/2 + Cz/2
                                        = - (Fz_data)

So your Fz_data and Cz_data are basically the same thing with opposite
polarity.
This represents rank deficiency by one.
As long as you start with this data, you should not included the
zero-filled (initial reference) channel. This zero-filled channel is, so to
say, to cause rank deficiency (since ANY monopolar EEG recording is a
difference potential from the ref electrode, the number of independent data
must be nbchan-1 including the ref channel.)
Only when you start with 'full ranked data' that is ONLY possible when not
including the initial reference channel (zero-filled), do you need to add
such zero-filled channel (this is equivalent to add +1 to the denominator
i.e.EEG.nbchan+1)

> Actually, re-referencing should not affect rank at all in this case or
should it?

You are right, it does not affect data rank.

Makoto



On Thu, Jul 9, 2020 at 10:23 AM Ivonne Weyers <
ivonne.weyers at uni-osnabrueck.de> wrote:

> Dear Makoto,
>
> thanks for the quick reply, I really appreciate it! I was able to fix
> the problem by adjusting the eigenvalue cutoff in the pop_runica()
> function (l.531), the original cutoff was 10^-7. I might specify rank
> via the pca option regardless, however, just to be safe (and since I am
> merely using ICA to reject eye-movement artifacts).
>
> With regard to re-referencing: if I recorded the data with an online
> average reference and then re-reference to averaged mastoids offline, I
> don't really understand why I woud need to add an additional channel in
> this case? Actually, re-referencing should not affect rank at all in
> this case or should it?
>
> Thanks again and best,
>
> Ivonne
>
> Am 02/07/2020 um 22:20 schrieb Makoto Miyakoshi:
> > Dear Ivonne,
> >
> > The smallest eigenvalue of 10^-20 is still regarded as 'independent' in
> > terms of rank() but for practical application of ICA the algorithm may
> > behave as if rank-deficiency is present. I believe I discussed this issue
> > with Jason Palmer last time. Isn't the current 'heuristic' minimum
> > eigenvalue cutoff something like 10^-8? You should be able to find it in
> > runica() function, if I remember correctly.
> >
> > If you can specify data rank by using the pca option, that would be the
> > best to avoid this kind of problems.
> >
> > So what you described seems correct, except
> >
> >>   (deficient by 1 due to re-referencing)
> > A proper re-referencing should not reduce rank. See below.
> >
> https://sccn.ucsd.edu/wiki/Makoto's_preprocessing_pipeline#Why_should_we_add_zero-filled_channel_before_average_referencing.3F_.2803.2F04.2F2020_Updated.29
> >
> >
> > Makoto
> >
> > On Tue, Jun 30, 2020 at 3:14 AM Ivonne Weyers <
> > ivonne.weyers at uni-osnabrueck.de> wrote:
> >
> >> Dear all,
> >>
> >> I have a question regarding rank computation before ICA. So far, I have
> >> been using the built in MATLAB function rank(), but it has now returned
> >> weird results (as has been talked about here
> >> <https://sccn.ucsd.edu/pipermail/eeglablist/2012/004670.html>), which
> is
> >> why I would simply like to specify rank individually for each data set
> >> in the pca option. I would greatly appreciate it if someone could
> >> confirm my following reasoning for the rank adjustment.
> >>
> >> My data have been recorded from 28 channels with average reference, 27
> >> of which will enter the ICA (the monopolar EOG channel is excluded- yes,
> >> I could also include it). The 27 channels have been re-ferenced to
> >> average mastoids (TP9, TP10- is it correct to include these in the ICA
> >> at all?). For some subjects, a maximum of two channels have been
> >> interpolated.
> >>
> >> So my question is: if 27 channels enter the ICA, rank would be 26 for
> >> datasets without any interpolated channels (deficient by 1 due to
> >> re-referencing) and 26 - (number of interpolated channels) for those
> >> with interpolations?
> >>
> >> Thank you & best,
> >>
> >> Ivonne
> >>
> >> --
> >> Ivonne Weyers, M.A.
> >> Research Group Psycho- and Neurolinguistics
> >> Institute of Cognitive Science
> >> University of Osnabrück
> >> Room 50/104
> >> Wachsbleiche 27
> >> 49090 Osnabrück
> >> Germany
> >>
> >> Phone: +49 (0) 541-969-2247
> >> e-mail: ivonne.weyers at uni-osnabrueck.de
> >> _______________________________________________
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> --
> Ivonne Weyers, M.A.
> Research Group Psycho- and Neurolinguistics
> Institute of Cognitive Science
> University of Osnabrück
> Room 50/104
> Wachsbleiche 27
> 49090 Osnabrück
> Germany
>
> Phone: +49 (0) 541-969-2247
> e-mail: ivonne.weyers at uni-osnabrueck.de
> _______________________________________________
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