[Eeglablist] why ICA is reference-free?
Jason Palmer
japalmer29 at gmail.com
Mon Mar 24 00:39:31 PDT 2014
Hi Iman,
When you do re-referencing, you impose a condition on the estimated map
vectors. E.g. average reference enforces the sum over the channels of the
map potential to equal zero (that the map be orthogonal to e, the vector of
all 1's). Average mastoid reference will guarantee that the average of the
mastoid channels in all the learned maps will be zero. Basically you make
all the learned maps orthogonal to a certain direction, and you lose a
degree of freedom, or a dimension in the rank of the data.
If the head had perfect sensor coverage over the head "sphere", and there
was limited shunting of electric field due to bone and tissue, then a source
inside the head would be expected to sum to zero by charge conservation-any
instantaneous increase in charge in one area must be accompanied by decrease
in the charge in another area.
However, e.g. in the case of a radial source on the cortical surface, the
negative field detected by electrodes on the side of the head/neck opposite
the radial source may not have sufficient coverage or may be shunted to the
extent that the source should appears to have a net positive charge, with
weaker negative field detected relative to positive field. So the "actual"
net charge may be non-zero.
Average reference though enforces zero net charge, and thus will in effect
add a negative constant to each channel, decreasing the positivity,
increasing the negativity, resulting in a radial dipolar source that appear
to be deeper in the head than it actually is.
In dipole fitting, a number of factors are taken into consideration,
including residual variance of a dipolar model, and physiological
plausibility given say a known MRI. I would suggest that dipole fitting of a
learned ICA map be carried out by optimizing the fit and plausibility of the
source over both (1) dipole location/orientation, and (2) unknown constant
channel offset, particularly for radial sources.
I believe that radial sources are often localized to deeper than MRI
cortical surface, which is consistent with this idea. However, given the
imprecision in tissue conductance values (see Akalin-Acar and Makeig 2013),
and the general controversy over the nature of EEG sources themselves (are
they confined to cortical patches, or do they represent a larger scale
charge redistribution involving sub-cortical and cortical regions?), it is
difficult to be certain of anything.
The main point about ICA being reference-free is that it however you
reference the data, it won't limit the ability of ICA to find the source.
You are just imposing the reference condition on the estimated map and
losing a degree of freedom (location along a single dimension). If you
presume that radial sources are confined to cortical patches, then the depth
ambiguity can be resolved using prior MRI information.
Note: this should not be taken as an official position of any organizations
or communities, just my own comments argued such as they are.
Best,
Jason
From: Iman M.Rezazadeh [mailto:irezazadeh at ucdavis.edu]
Sent: Friday, March 21, 2014 12:24 AM
To: japalmer at ucsd.edu; 'EEGLAB List'
Subject: RE: [Eeglablist] why ICA is reference-free?
Thanks a lot Jason!
It was really informative. Could you please elaborate this "So when you do
dipole localization with a given map, there is really an arbitrary additive
constant, but presumably only one value of this constant will be consistent
with a physiological source."?
Best
Iman
-------------------------------------------------------------
Iman M.Rezazadeh, Ph.D
Research Associate II
Semel Intitute, UCLA , Los Angeles
& Center for Mind and Brain, UC DAVIS, Davis
From: Jason Palmer [mailto:japalmer29 at gmail.com]
Sent: Thursday, March 20, 2014 8:18 PM
To: 'Iman M.Rezazadeh'; 'EEGLAB List'
Subject: RE: [Eeglablist] why ICA is reference-free?
Hi Iman,
The reference used in average referencing, or single channel or avg
fiducials reference, is a linear function of the data. So e.g. in avg
reference,
r(t) = e^T * x(t) / n
where e is a vector of all ones, e = [1 1 1 . ]^T, and ^T means transpose,
and n is number of channels.
Re-referencing the data is equivalent to doing:
y(t) = x(t) - e*e^T*x(t) / n
= (I - e*e^T/n) * x(t)
Where I is the identity matrix, which shows that the re-referenced data is
just a matrix times the original data, and has rank reduced by 1. Similarly
for avgs of subsets of channels, which use I - e*g^T with a general vector
g, instead of I - e*e^T.
So we can look at the new data as generated by,
y(t) = M' * s(t)
where,
M' = (I - e*g^T)*M
= M - e*(g^T*M)
This new mixing matrix is just the original matrix with a single constant
potential subtracted from each mixing map (generally different number for
each map, but same number for each channel of a map).
So what the reference does is essentially add a constant to each channel.
Average reference will tend to produce maps such that the sum over the
channels of the potential of each map is zero, consistent with charge
conservation and dipolarity.
So when you do dipole localization with a given map, there is really an
arbitrary additive constant, but presumably only one value of this constant
will be consistent with a physiological source.
Hope that is helpful.
Best,
Jason
From: eeglablist-bounces at sccn.ucsd.edu
[mailto:eeglablist-bounces at sccn.ucsd.edu] On Behalf Of Iman M.Rezazadeh
Sent: Monday, March 17, 2014 4:31 PM
To: 'EEGLAB List'
Subject: [Eeglablist] why ICA is reference-free?
Hi,
Could you please elaborate why ICA is reference-free? In other words, does
different kinds of referencing methods (avg-ref or .) effect on ICA maps and
source series ?
Suppose: x(t) is the signal then we have s(t)=M(^-1). x(t) ;where s(t) is
source signals and M is the mixing matrix.
Now how come for y=x(t)-r(t) - where r(t) is another reference- result
same/different maps and source series would be obtained and how could
someone get the same dipole locations with different re-referencing methods?
It would be great if someone gives in depth methodological and mathematical
explanations rather than just qualitative explanations.
Best
Iman
-------------------------------------------------------------
Iman M.Rezazadeh, Ph.D
Research Fellow
Semel Intitute, UCLA , Los Angeles
& Center for Mind and Brain, UC DAVIS, Davis
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