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

[Matti Stenroos]

Dear Jord,

Indeed, if you drop components (= time-series & topography) away using 
ICA, the rank of your data will go down. Matlab rank routine is, 
however, not very good tool for assessing rank --- for example, even 
mixing double and single precision floating point numbers in your 
decomposition process may yield "full numerical rank", even though the 
real rank is lower.

In my opinion, the easiest way to assess the rank is to use svd: just 
take a measurement (or noise) covariance matrix C, do s = svd(C), and 
plot s or log10(s). You should see a clear drop in the svd spectrum at 
the point, when the "true rank" is reached. Then you can project the 
rest out, and after that, also the rank function should show correct rank.

Cheers,
  Matti


On 2018-08-10 11:14, Vink-5, J.J. wrote:
> 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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> https://doi.org/10.1371/journal.pcbi.1002202
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