[Eeglablist] ICs with identical topographies

[Arnaud Delorme]

Regarding this issue. Below is some feedback from Jason Palmer our local ICA math expert:
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These components [Maximilien's components available here]
are most likely slightly different. The thing to plot would
be the difference (after reversing the polarity/sign of one of the
components) of the map and activations. The difference should not be exactly
zero.

ICA can produce these "dependent subspaces" even if the data is really full
rank. These components will have mutual information with each other, but
should have close to 0 MI with other components.

I'm currently editing the wiki to add info about MI and dependent subspaces.
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Also, the time courses might be slightly time delayed, resulting in
instantaneous independence. A movie of the backprojected sum of the maps
might indicate a dynamic "wiggle" in the map (potential distribution), which
would result from the dynamic (non-static spatial potential distribution)
nature of the generating source.
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Theoretically there should be no benefit from doing a second ICA after backprojecting, beyond doing ICA for more iterations … though in the runica case, this could be significant given that it essentially stops after a certain time, regardless of convergence. ICA is supposed to first determine the rank of the data, PCA out extraneous dimensions, then run ICA on the full rank pca data.
 
However as we were discussing previously, rank determination isn’t foolproof, so you can end up running ICA on data with a few very small dimensions, which after sphering become essentially numerical noise subspaces. Any associated component maps should be flat. So ICA might use the “extra” dimensions to better separate out a signal (subspace) that was not separated out from the rest as well with a single component. This might reduce the overall cost function (approximately the total MI) more than adding random garbage maps to account for the numerical noise subspace  (which is likely Gaussian).
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So Amica might actually produce a numerical noise subspace since it really tries do fit the density and minimize MI, which from my analysis should require independent subspaces—I believe the analysis still holds for Gaussian subspaces.
 
Runica might be more prone to produce identical maps in the non-full rank case because it uses fixed density approximations which may be better fit (lower cost) with duplicate maps and possibly slightly time shifted activations, etc., than with the actual subspace basis, which would have Gaussian sources, not sub- or super-Gaussian.

Jason Palmer

On Aug 22, 2011, at 11:27 AM, Tarik S Bel-Bahar wrote:

> It does not seem there has been enough systematic work examining how estimates of brain dynamics might be distorted by removal of ICs, and the subsequent reconstruction of the eeg data. The assumption, of course, if you stay with IC space, that ignoring artifactual ICs should actually add to the validity of cognitive components.
> 
> There are several papers comparing cleaning methods, including one from the faster or adjust groups. the work in this area seems scattered and unintegrated. The field awaits a proper comparision of cleaning toolboxes, as well as the wide variety of in-house cleaning codes.
> 
> On Aug 22, 2011 10:58 AM, "Baris Demiral" <demiral.007 at googlemail.com> wrote:
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