Hi Jane,

Yes, that is perfectly correct. You are changing a bit the meaning of "n" in your notation, some times referring to the n-th source voxel (in R_n), and other times referring to the n-th subject (in r_n(x,y)). So just for clarity and changing a bit the notation: the R_x matrix has size [#-of-voxels by #-of-subjects], and the element (y,n) of this matrix R_x(y,n) will contain the functional correlation between the x-th voxel (the source) and the y-th voxel (the target) for the n-th subject (i.e. r_n(x,y)).

After that, fc-MVPA will compute the SVD of the matrix R_x (for each source voxel x) and keep the right singular vectors, which can be effectively computed as the eigenvectors of the much smaller R_x' * R_x matrix (a [#-of-subjects by #-of-subjects] matrix).

And regarding your specific questions, the total set of voxels included as x and y in your matrices is determined in CONN by the analysis mask (defined in the Setup.Options tab). The voxels included in y can also be further limited by the ICA-mask (for masked-ICA analyses only; this is defined in CONN in the first-level analysis tab by clicking on "masked-ICA" checkbox and selecting there your ICA-mask). To be  precise, x ranges over all voxels specified in your general analysis mask, and y ranges over all voxels specified in the conjunction of your general analysis mask and your specific ICA-mask (if applicable). The index x controls at which voxels CONN will compute fc-MVPA components, and the index y controls which portion of the correlation matrix (between a given voxel and the rest of the brain) will be used in the dimensionality reduction step.

Hope this heps

Alfonso

Originally posted by JANE OCONNOR:

Hi CONN team,

I have created a mock up of the single subject matrix (screenshot attached) as I understand it would be set up for dimensionality reduction. Is there a way in CONN to determine how many total voxel were used, or the dimensionality of the individual correlation matrix?

My figure and explanation is based on how I understood Nieto-Castanon, A. (2022). Brain-wide connectome inferences using functional connectivity MultiVariate Pattern Analyses (fc-MVPA).  

Does the correlation matrix I created for the source voxel make sense and do you detect any obvious errors? for context I have n=35. 

For each voxel ( ) a Pearson correlation,  is calculated for that voxel ( ) and every other voxel’s ( ) BOLD time series.

Where  represents the matrix for n source voxel and     represents the Pearson correlation coefficient of the time series (BOLD) between voxel ( ) and voxel ( ).