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Some statistical properties and comparisons of these new multiway methods are still needed to
complete our first ideas. The application on a verbal study with 12 subjects gave some insights
on their different interests.
It seems rather obvious that when looking for activation with a regular paradigm one certainly
expects the variance criterion to give good results especially if the subject dispersion (between
groups and /or within groups) is expected to be relatively Gaussian in the direction of interest.
In that purpose Single-ICA achieve similar results as in using PTA3. This is because of the first
step of reducing the dimensionality (using variance criterion) in te ICA algorithm. Without this
first step too many time-courses have to be fit. Probably with a drastic dimension reduction using
a variance criterion, the real interest of ICA is less evident and certainly the rank-one approach
is an other way of reducing the dimensionality enforcing initial Gaussianity by forcing
independence of *time and subject* in the unmixing component. .
Finding complicated group structures and/or expecting non regular paradigm would be better
achieved with Negentropy approach, but the Multiple-ICA approach has too many degrees of freedom
for that purpose. In reducing the degree of freedom on the independent Components the rank-one
Multiple-ICA should give better results than the Multiple-ICA. Nonetheless using special
metrics[9,4] with PTAk may provide interesting alternatives and may be a rank-one Single-ICA using
these special metrics on the time-subject unmixing would allow to find these
Another 3-way ICA methods can be thought fixing the independence criterion on two dimensions
(*space* and *time*). This is the other rank-one ICA approach *i.e.* like a
Multiple-ICA but looking for a rank-one independent components.

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Didier Leibovici
2001-09-06