[Eeglablist] ICA suggests weirdly low rank

[Makoto Miyakoshi]

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

On Wed, Jun 12, 2024 at 11:01 AM Евгений Машеров via eeglablist <
eeglablist at sccn.ucsd.edu> wrote:

>
> Average referenced channels are linearly dependent. Sum of channels equal
> to 0.  Matrix of values has incomplete rank n-1.
> Except this mathematically cause, may be physical causes - contact between
> electrodes or electrolyte bridges/
>
> Eugen Masherov, Burdenko NSI
>
>
> > Dear list members,
> >
> > I am experiencing some issues running pop_runica, namely that it
> > produces weirdly *low* rank.
> >
> > I have a 27-channel infant dataset recorded with a single channel
> > reference (Fz), for which I perform the following steps before running
> > ICA: filter, remove bad channels, interpolate, re-reference to average
> > reference and adding Fz back to the data, epochize (this does not reduce
> > the amount of data by much, just truncates the continuous data), reject
> > only extremely large artifacts.
> >
> > I understand from previous discussions as well as the papers on this
> > issue that my data becomes rank deficient by n if I interpolate n
> > channels. (Is rank reduced further by -1 due to average re-ferencing
> > even if the original reference is added back to the data?) When I run
> > pop_runica on a 27 channel data set in which channels have been
> > interpolated, however, eeglab returns a substantially lower rank, e.g.
> > 22 when two channels have been interpolated (which should be 25; or 24
> > if average referencing reduces futher).
> >
> > From what I have read in the mailing list, most people experience the
> > opposite, i.e. rank() failing to identify rank deficiency, but I haven't
> > found anything on weirdly low rank. Does anyone have an idea what may be
> > causing this?
> >
> > Also, I am unsure whether I should "force" it to compute 25 ICs using
> > the gui or the 'pca' option, could this be detremental to ICA results?
> >
> > I would appreciate any ideas on this, also let me know if I failed to
> > include any details on the data.
> >
> > Thank you & best,
> >
> > Ivonne
> >
> > --
> >
> > *Dr. rer. nat. Ivonne Weyers (she/her)*
> > Psycholinguistics Group
> > Institute of Linguistics
> > University of Vienna
> > Sensengasse 3A, Room 06.12
> > 1090 Wien
> >
> > ivonne.weyers at univie.ac.at
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