[Eeglablist] why ICA is reference-free?
japalmer29 at gmail.com
Thu Mar 20 20:17:30 PDT 2014
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
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)
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.
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?
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.
Iman M.Rezazadeh, Ph.D
Semel Intitute, UCLA , Los Angeles
& Center for Mind and Brain, UC DAVIS, Davis
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