[Eeglablist] Appropriate procedure for statistically testing ICA component strengths?

[logant at email.arizona.edu]

Hi everyone. I have a question regarding an appropriate procedure for
statistically testing ICA component strengths.

Consider a visual stimulation EEG experiment with two different
conditions, and
ICA decomposition of the EEG data produces similar components for each
condition.  By similar I mean similar scalp topographies and time courses,
verified by correlating the component maps and/or back projections or by using
some form of cluster analysis.  From this, one then assumes that these
components are the same distribution of cortical sources that are activated in
each condition of the experiment.  Next, suppose then that one wanted to test
to see if the ?strength? of a common component differs between the two
conditions.  What is the best way to do this?

A straightforward approach would be to do tests on the component back
projections (i.e. the outer product of the component activation matrix
with the
component map matrix), as these preserve scaling and polarity information, and
are in the original physical dimensions of the EEG, e.g. microvolts.  However
this inevitably leads to the problem of testing the response over a
multiplicity of electrodes, and this would have to be dealt with via
bootstrapping and/or permutation testing with some sort of correction for
multiple comparisons across electrodes.

Another way to do this comparison would be to test the component activations
themselves, either at a peak in activity or on a time point by time point
basis.  One difficulty with this is that scaling information is spread between
the component activations and the component maps, as the ICA algorithm
normalizes neither.  However this might be circumvented by normalizing the
component maps (they are just vectors after all) and then multiplying the
activation time courses by the respective normalization constant. That is, for
the activation timecourse of the ith component, Ai(t) (a row vector), and the
corresponding component map, Mi (a column vector), first normalize Mi

Mi =>  Mi? = M/|M|,

where the " ' " symbol merely denotes a transformed variable, NOT a matrix or
vector transposition (as it denotes in some programming languages such as
Matlab).

Then for that component, the back projection could be written,

Ai(t) x Mi  =  Ai(t) x |Mi|*Mi' = Ai(t)? x Mi'

=> Ai(t)' = |Mi|*Ai(t)   since |Mi| is a scalar.

Ai(t)? is now in units of microvolts, and preserves ?global? scaling
information, although the ?local? scale at a given electrode site would
still be determined by the component back projection (A? x M?) at the site.
Computing A(t)? for the two conditions of the experiment, could one then apply
a statistical test? The advantage of this procedure is that there is no
need to
concern oneself with tests across multiple electrode sites (as is the case
using the back projection method), as only one time series is used to
summarize
how the strength of a given component unfolds over time.

Does anyone on this listserve have any idea about the validity of such an
approach?


Regards,

Logan Trujillo

Department of Psychology
University of Arizona
Tucson, Arizona, USA