[Eeglablist] Is average reference not recommended on 10-20 system?

[Scott Makeig]

Kyle and all -

If your concern with re-referencing is mixing of  (e.g. nearby) CHANNEL
signals,
I suggest you re-orient your thinking to removing the mixing of
SOURCE signals in the collected data in the form you study it.

What SOURCE signals do I mean here?   For one, discrete *non-brain* sources
whose potentials are mixed into scalp EEG signals - eye movements,
individual scalp muscle activities, etc.  For another, dominant *brain*
(cortical) sources of scalp EEG.  What are these? They must reflect
coherent activity across cortical territory, as incoherent activity (with
random phase differences over time) within cortical micro-domains (think
columns, minicolumns, or the like) will be eliminated from the summed scalp
signals by phase cancellation (+ and - potentials projected to the scalp
electrodes summing to ~0).

The (by far) most efficient way to remove mixing of SOURCE signals from
scalp data is decomposition of the data by Independent Component Analysis
(ICA). ICA decomposition finds spatial filters (or, if you like,
'superchannels') in the data that express single SOURCE signals and
eliminate (or highly minimize) contamination from other SOURCE signals.
ICA decomposition is 'reference-free' in the sense that any re-referencing
of the data does not affect the independent component (IC) signals. Note:
all re-referencing amounts to linear spatial filtering, multiplying the
data by a (channels-in, channels-out) matrix. Each EEG channel is ALSO a
spatial filter being (most typically) the DIFFERENCE between summed
projected SOURCE signal values at (at least) TWO electrodes...

Surprisingly (or not), high-density scalp EEG can *largely* be confined in
a low-dimensional box (to see this, apply PCA and check the eigenvalue
spectrum - how many large dimension values does it contain?). ICA
decomposition can efficiently separate out the local *brain* (cortical)
effective source signals (and their projection pattern to the scalp,
thereby revealing their brain locations), allowing their individual (or
comparative) study with much higher resolution / SNR than is expressed in
the raw scalp recording channels - while at the same time eliminating (or
highly minimizing) linfluences of *non-brain* ('artifact') sources in their
computed activities.

Notes:

1. The above is true (and the ICA decomposition results most useful) in
favorable cases - e.g., using enough data, etc.
2. The *appearance* of the Independent Component (IC) scalp maps does
depend on the referencing of the decomposed data. For example, using a Cz
electrode reference will make all IC (and EEG) scalps maps have 0 value at
Cz (of course).  Re-referencing the data to some other reference (say A2,
linked earlobes, etc.) will change the 'look' of the IC maps (as well as
each raw data map), but will NOT change their implied source location IN
the head (as estimated by standard algorithms).

SO - Unless your true interest is in the effect of the scalp  on EEG
signals (dandruff?), the true nature of the data is as a sum of
volume-conducted potentials time series from SOURCES (brain + non-brain).
Most people work with EEG to observe/understand more about what the
activities of the BRAIN SOURCES of the EEG can tell about brain
functioning. For this, the best approach is to study not the recorded
channel data, but its derived (max. independent) SOURCE signals.

p.s. The situation with fMRI data is parallel - in fMRI the recorded sensor
channels are radio-frequency 'wiggles,' but no neuroimaging researcher
looks at these.at all. Instead s/he studies the transform of their data by
an algorithm that separates their highly mixed signals into (BOLD) activity
within the native brain space.

Scott Makeig

On Wed, Jul 26, 2023 at 10:49 AM Kyle Lepage via eeglablist <
eeglablist at sccn.ucsd.edu> wrote:

> Thank you for the video.  In the video, rCAR is not compared to the other
> references.  In the provided link it is.
> rCAR has the advantage over CAR that a spatially localized event will not
> introduce a small, negatively correlated signal on all of the
> other channels in the CAR adjusted data.  This effect becomes smaller with
> larger numbers of electrodes, until the spatially local signal begins to
> affect more than one electrode with the increasing electrode density.  At
> that point, increasing electrode density will not further reduce the
> negative correlation.
>
> All the best,
>   Kyle
>
> On Tue, Jul 25, 2023 at 10:02 PM Arnaud Delorme <adelorme at ucsd.edu> wrote:
>
> > Dear Kyle,
> >
> > This is a video that compares the different references.
> >
> >
> https://urldefense.com/v3/__https://www.youtube.com/watch?v=ioIETUX4G4k__;!!Mih3wA!ATAO9wJVcnvwyp1FqsiCTGBOkY2WWngk1bFGpbMRlI7Rk7oOYclWBR1240RzgrRZbvJnbLFIjTZ9KVrQcOjmuMI3fg$
> >
> > Arno
> >
> > > On Jul 24, 2023, at 4:10 AM, Kyle Lepage via eeglablist <
> > eeglablist at sccn.ucsd.edu> wrote:
> > >
> > > Hi, you might try:
> > >
> > > @article{lepage2014statistically,
> > >  title={A statistically robust EEG re-referencing procedure to
> > > mitigate reference effect},
> > >  author={Lepage, Kyle Q and Kramer, Mark A and Chu, Catherine J},
> > >  journal={Journal of neuroscience methods},
> > >  volume={235},
> > >  pages={101--116},
> > >  year={2014},
> > >  publisher={Elsevier}
> > > }
> > >
> > >
> >
> https://urldefense.com/v3/__https://www.mathworks.com/matlabcentral/fileexchange/64643-apply-rcar/?s_tid=LandingPageTabfx__;!!Mih3wA!DnegK98ehdTXFqLwanApFI6uX5CRADC5cc0HYGAMKvej1yK8Dq8xPj0PAXwHyWmXP_RdnbAgdJjXQmHz3Yx67WF9Pw$
> > >
> > > Best,
> > >
> > >  Kyle
> > >
> > >
> > > On Fri, Jun 16, 2023 at 12:09 PM Cedric Cannard via eeglablist <
> > > eeglablist at sccn.ucsd.edu> wrote:
> > >
> > >> Hi Makoto,
> > >>
> > >> This is basically what I was referring to yes. Doesn't this paragraph
> > you
> > >> sent support this recommendation?
> > >>
> > >> "As the number of electrodes increases the error in the approximation
> is
> > >> expected to decrease. [...] with large numbers of electrodes (say
> > >> 128 or more), we have found that the average reference often performs
> > >> reasonably well as an estimate of reference-independent potentials in
> > >> simulation studies (Srinivasan et al. 1998)."
> > >>
> > >> However, I should have provided a more nuanced response. Both average
> > and
> > >> REST/ininfity references are both considered superior to all other
> known
> > >> references, especially with 64+ channels. However, I now tend to
> > recommend
> > >> and use REST because, while it faces the same limitations caused by
> low
> > >> electrode coverage and density (i.e., spherical harmonics degree < 7
> > with
> > >> less than 128 channels; Srinivasan et al. 1998), the error can be
> > reduced
> > >> as the head model improves. See here for great discussion on this:
> > >>
> >
> https://urldefense.com/v3/__https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2967671/__;!!Mih3wA!GHxYARW27MxFaJ2eDEyohyAmJb8T3foIM3Ee70lzdOc35_OV2YZVDGWwy4ZnfyPRe7E06ijETkbzKxADMMhzKOjCew$
> > >>
> > >> "idealized simulations (Marzetti et al, 2007; Qin et al, 2010) where
> the
> > >> head model used to estimate G is very similar to model used to
> estimate
> > >> errors, REST outperforms AVE. From this argument we see that the
> choice
> > >> between AVE and REST largely boils down to questions of genuine head
> > model
> > >> accuracy [...]. The most popular head model consists of 3 or 4
> > concentric
> > >> spherical shells representing, brain, CSF, skull, and scalp tissue
> (Rush
> > >> and Driscoll, 1969; Nunez, 1981; Nunez and Srinivasan, 2006). The
> > spherical
> > >> symmetry allows for relatively simple analytic solutions to the
> forward
> > >> problem. On the other hand [...], despite these limitations, simple
> head
> > >> models can be extremely useful, typically by proving that many EEG
> > analysis
> > >> methods proposed over the past 50 years or so will NOT work. For
> > example,
> > >> the so-called quiet reference myth is easily discredited with simple
> > models
> > >> (Rush and Driscoll, 1969; Nunez, 1981; Nunez and Westdorp, 1994; Nunez
> > and
> > >> Srinivasan, 2006). Or, distortion by reference and volume conduction
> is
> > >> shown to produce very large errors in scalp coherence estimates (Nunez
> > et
> > >> al, 1997, 1999; Srinivasan et al, 1996, 1998; Marzetti et al, 2007).
> > >> Moderate head model inaccuracy does not change the central conclusions
> > of
> > >> these studies. Simulations using simple head models then provide a
> > critical
> > >> “filter” through which mathematical methods must first pass to be
> > >> considered further by serious scientists. We must be continually
> > reminded
> > >> that fancy mathematics can never trump physical principles. The Qin et
> > al
> > >> (2010) study has passed this important first test by showing that REST
> > >> works with simple head models and certain assumed source
> distributions,
> > but
> > >> its accuracy with read heads and other source distributions is
> unknown.
> > For
> > >> this reason, I suggest that REST and AVE be adopted as reference
> > partners,
> > >> at least until better information becomes available."
> > >>
> > >> In conclusion, they are similar, but REST seems to be the most
> promising
> > >> in the long term (along with Surface Laplacian methods), as the head
> > models
> > >> improve. It already performs slightly better than AVE (e.g.,
> > >>
> >
> https://urldefense.com/v3/__https://www.sciencedirect.com/science/article/abs/pii/S1388245710004153__;!!Mih3wA!GHxYARW27MxFaJ2eDEyohyAmJb8T3foIM3Ee70lzdOc35_OV2YZVDGWwy4ZnfyPRe7E06ijETkbzKxADMMhgoEdbtw$
> > >> and
> > >>
> >
> https://urldefense.com/v3/__https://www.frontiersin.org/articles/10.3389/fnins.2017.00205/full?ref=https:**Agithubhelp.com__;Ly8!!Mih3wA!GHxYARW27MxFaJ2eDEyohyAmJb8T3foIM3Ee70lzdOc35_OV2YZVDGWwy4ZnfyPRe7E06ijETkbzKxADMMg1UjXsBA$
> > >> ), and will keep improving over the years. That's why I tend to use it
> > and
> > >> recommend it now.
> > >>
> > >> Additionally, REST (and especially the new regularized REST) may
> present
> > >> new advantages (e.g., the effective rank deficiency issue although
> this
> > is
> > >> pretty much solved now with the recent solution, data recorded with
> > >> monopolar reference, etc.). See:
> > >>
> > >>
> >
> https://urldefense.com/v3/__https://link.springer.com/article/10.1007/s10548-019-00706-y__;!!Mih3wA!GHxYARW27MxFaJ2eDEyohyAmJb8T3foIM3Ee70lzdOc35_OV2YZVDGWwy4ZnfyPRe7E06ijETkbzKxADMMjinh8EZg$
> > >>
> > >>
> >
> https://urldefense.com/v3/__https://iopscience.iop.org/article/10.1088/1741-2552/aaa13f__;!!Mih3wA!GHxYARW27MxFaJ2eDEyohyAmJb8T3foIM3Ee70lzdOc35_OV2YZVDGWwy4ZnfyPRe7E06ijETkbzKxADMMhHPAIx-Q$
> > >>
> > >>
> >
> https://urldefense.com/v3/__https://www.sciencedirect.com/science/article/pii/S1388245723005941__;!!Mih3wA!GHxYARW27MxFaJ2eDEyohyAmJb8T3foIM3Ee70lzdOc35_OV2YZVDGWwy4ZnfyPRe7E06ijETkbzKxADMMiRFwJb5w$
> > >>
> > >> Note that the EEG reference conversation will go to infinity ;)
> > >>
> > >> Cedric
> > >>
> > >>
> > >> Sent with Proton Mail secure email.
> > >>
> > >> ------- Original Message -------
> > >> On Thursday, June 15th, 2023 at 2:25 PM, Makoto Miyakoshi via
> > eeglablist <
> > >> eeglablist at sccn.ucsd.edu> wrote:
> > >>
> > >>
> > >>> Dear Jinwon and Cedric,
> > >>>
> > >>> Let's confirm the problem first. 'Electric Fields of the Brain' by
> > Nunez
> > >>> and Srinivasan (2006) (hereafter EFB) p.295 says:
> > >>>
> > >>> ...The surface integral of the potential over a volume conductor
> > >> containing
> > >>> dipole sources must be zero as a consequence of current conservation
> > >>> (Bertrand et al. 1985). In this case, the surface integral can be
> > >> estimated
> > >>> by the second term on the right-hand side of (7.10); that is, by
> > >> averaging
> > >>> the measured potentials and changing the sign of this average. (...)
> > >> Since
> > >>> we cannot measure the potentials on a closed surface surrounding the
> > >> brain,
> > >>> the first term on the right-hand side of (7.10) will not generally
> > >> vanish.
> > >>> The distribution of potential on the underside of the head (within
> the
> > >> neck
> > >>> region) cannot be measured. Furthermore, the average potential for
> any
> > >>> group of electrode positions, given by the second term on the
> > right-hand
> > >>> side of (7.10), can only approximate the surface integral over the
> > volume
> > >>> conductor. For example, this is expected to be a very poor
> > approximation
> > >> if
> > >>> applied with the standard 10/20 electrode system. As the number of
> > >>> electrodes increases the error in the approximation is expected to
> > >>> decrease. Thus, like any other choice of reference, the average
> > reference
> > >>> provides biased estimates of reference-independent potentials.
> > >>> Nevertheless, when used in studies with large numbers of electrodes
> > (say
> > >>> 128 or more), we have found that the average reference often performs
> > >>> reasonably well as an estimate of reference-independent potentials in
> > >>> simulation studies (Srinivasan et al. 1998).
> > >>>
> > >>> So the problem is that the difference between the real average and
> > >>> electrode-sampled average becomes worse, and it is actually very bad
> > when
> > >>> you are using 20 channels supported by 10-20 systems.
> > >>>
> > >>> Cedric, I do not see they are against using average reference when <
> > 128
> > >>> ch. Did you find that description elsewhere from the book?
> > >>>
> > >>> Jinwon, that said, from the linear algebraic point of view, it makes
> no
> > >>> sense to say one choice of reference electrode, including average of
> > >>> arbitrary combinations of electrodes, is 'worse' than another.When
> you
> > >> use
> > >>> average reference with low number of electrodes (say 20 or 30), you
> may
> > >> be
> > >>> criticized that your electrode average is severely deviated from the
> > true
> > >>> surface average. But using average reference does not mean you are
> > >> making a
> > >>> claim that your electrode average at a given frame be zero. Compared
> > with
> > >>> using Fz, Cz, Pz, or (digitally linked) mastoid/earlobe (physically
> > liked
> > >>> mastoid/earlobe is out of question) as a reference electrode, your
> > >> average
> > >>> potential may be still useful for certain purposes. Clarifying the
> > merit
> > >> of
> > >>> using average reference in your case over other choices of reference
> > >>> requires elaborated simulations which may not be easy or even
> > realistic.
> > >>> But my point is that blindly following the rule 'average reference
> > >> applied
> > >>> to less than 64 ch == bad' is ridiculous. For example, depending on
> > your
> > >>> targeted EEG phenomenon, if it has a dominant low spatial frequency,
> > >>> relatively low spatial sampling by a relatively low number of
> > electrodes
> > >>> (which is hopefully uniformly distributed) could be more tolerable.
> > >>>
> > >>> If your reviewer does not write much comment on your experimental
> > design
> > >> or
> > >>> result interpretation but just writes this kind of general and
> trivial
> > >>> technical things about EEG, that is not a good reviewer. Send me the
> > >>> reviewer's comment in a separate email and I can assess it further
> for
> > >> you.
> > >>>
> > >>> Makoto
> > >>>
> > >>>
> > >>>
> > >>>
> > >>> On Thu, Jun 15, 2023 at 1:35 PM 장진원 via eeglablist
> > >> eeglablist at sccn.ucsd.edu
> > >>>
> > >>> wrote:
> > >>>
> > >>>> Dear all,
> > >>>>
> > >>>> One of my reviewers has suggested that because average reference
> > >> relies on
> > >>>> the assumption that the electrode coverage represents a sphere, it
> is
> > >> not
> > >>>> good to average-reference with electrodes less than 64. I have used
> > the
> > >>>> average-referencing as recommended on
> > >>>>
> > >>>>
> > >>
> >
> https://urldefense.com/v3/__https://eeglab.org/tutorials/05_Preprocess/rereferencing.html__;!!Mih3wA!D_yQ2dwBfLAhlMiue98MMVMBa2NNnbOxZRm_SDLtYScegpGg5wR7Ly9SmCRGov3uc7pP5TS6NKxNf9Zs2cdtn560dQ$
> > >>>> , so I wonder
> > >>>> what could be the alternative.
> > >>>>
> > >>>> Best Regards,
> > >>>> Jinwon Chang
> > >>>> _______________________________________________
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-- 
Scott Makeig, Research Scientist and Director, Swartz Center for
Computational Neuroscience, Institute for Neural Computation, University of
California San Diego, La Jolla CA 92093-0559, http://sccn.ucsd.edu/~scott