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First a little bit of background.

I'm interested in exploring the performance of Independent Component Analysis (ICA) in the context of disentangling intracranial EEG signals. These signals are measures of voltage along time at different points in space. If we understand intracranial EEG as a mixture of different signals generated by different neural elements, say, different neuronal populations, ¿would be possible to recover these components (representing different neuronal elements) from the mixture using ICA? At the core of this idea is the assumption that components are statistically independents, maybe pretty unrealistic since a natural consequence of neuronal connectivity is the correlated neuronal activity.

So, my question is. I have some benchmark signals that have been generated in a realistic computational model of the cerebral cortex microcircuit. Each signal is a temporal series representing the activity of a neuronal population. Before mixing the signals and apply ICA, I would like test about the independence assumption. Then, I'm looking for methods (and software) to test the independence between these signals: measures of mutual information, linear and non-linear correlations, whatever (I suppose). Any way to support or reject the assumption of independence.

I'm sorry for the lack of mathematical formality, and maybe accuracy, in the question. I'm not an expert. Feel free to correct me if I've made an error above. Thank you in advance!

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    $\begingroup$ To my understanding, there is no requirement of independence per se in the incoming signals themselves (otherwise what would be the point of the ICA?). Its the results that are independent. What is important for the ICA is that the data are "full rank". That is, none of the input signals can be completely defined by some combination of the other signals. For example if the average reference was also an input signal. Note that the AR would not have to correlate particular well with any other channel. Matlab has the function "rank" for this. Which EEGLAB uses to check prior to ICA. $\endgroup$ – Mensen Jan 4 '19 at 14:33
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Partially answered in comments:

To my understanding, there is no requirement of independence per se in the incoming signals themselves (otherwise what would be the point of the ICA?). Its the results that are independent. What is important for the ICA is that the data are "full rank". That is, none of the input signals can be completely defined by some combination of the other signals. For example if the average reference was also an input signal. Note that the AR would not have to correlate particular well with any other channel. Matlab has the function "rank" for this. Which EEGLAB uses to check prior to ICA.

– Mensen

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