Unfortunately, we cannot uncheck the registration part.
And about another issue:
What I said is, although sets "A" and "B" are different, set "B" is just set "A" after pre-processing and registration. So there should be no difference between them in view of number of components since the dimensionality estimation is done after "pre-processing and registration steps".
I try to show my thoughts in following way, therefore you can correct me if I am wrong:
First situation:
Set A ->(Pre_Stats and Registration) -> Set B -> dimensionality estimation. and ICA analysis
Second situation:
Set B -> dimensionality estimation and ICA analysis.
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