Dear FSL users, dear dr. Beckmann,
Thank you for the reply to my previous question about the Z-transformation.
I was wondering what the data matrix X actually looks like since first PCA is applied in order to reduce dimensionality. The original fMRI data is a TxN matrix with T the timepoints and N the voxels. In the matrix after PCA, X looks like PCxN right? Every row now represents one of the principal components?
In PCA analysis, the data is projected onto the principal component vectors. Isn't this a bit of a contradictionary effect compared to ICA? What I mean is that in PCA you first want to project the original data into the space of eigenvectors (linear mixing?) and than you want to disentangle the mixing with ICA?
Furthermore I understand that it holds that independent components are uncorrelated (not vice versa). I don't quite get why the ICA works on data after PCA. Can someone comment on this?
So, the number of independent components was determined from PCA. When I apply ICA, I often find multiple components representing the same brain network (based on visual classification with resting state atlasses available on the internet). Does this sound familiar to you? How can you explain this? It looks like the number of component determined from PCA is not always optimal?
Thank you!
Debby
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