[FieldTrip] MVAR analysis on rank deficient EEG data (due to removal of ICA components)

[Vink-5, J.J.]

Dear fieldtrip community,

I'm currently working with 60 channel sensor space EEG data, which has been preprocessed using ICA, resulting in a rank deficient dataset. However, when I'm trying to evaluate the rank of my data using Matlab's rank function, it tells me that the data is full rank, which is somewhat confusing.

The data clearly is not full rank, because when I want to perform an MVAR analysis it either tells me the data is singular or not positive definite. I read up a lot on rank deficiency and how this is introduced through ICA. My current understanding is that the reconstruction of the full 60 channel EEG data after removal of ICA components reduces the rank due to linear dependencies between the original channels and the reconstruction of the data without the removed ICA components. Consequently, people have suggested to remove channels in order to restore data rank. However, how do I know which channels contain these linear dependencies? Simply removing channels does not resolve this issue.

Performing PCA prior to MVAR analysis could potentially resolve this. Does anybody know whether you can reconstruct sensor space directed connectivity from a PCA-based MVAR model?

Best,

Jord

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