Christian Beckmann wrote:
> nope, when using spatial ICA (as implemented in melodic) the time
> courses are not restricted to be orthogonal. The spatial maps, however,
> are not only orthogonal but are being optimised to be as statistically
> independent as possible.
Hi Christian,
I expect I am being stupid, but when I try to check that the spatial
maps are orthogonal, they don't appear to be...
My understanding of the tech report and melodic output is that the 4D
melodic_IC contains 3D volumes corresponding to the rows of S, and
that these components should be independent (and hence also orthogonal
as vectors, right?) and also that they are assumed to have unit
variance (with the time-courses in the A matrix taking up the
non-unity variance) according to the tech rep.
But looking at the FEEDS data in MATLAB, I get unexpected results:
>> cd ~/Common/src/fsl-3.3/feeds-3.3.9/results/fmri.ica/
>> IC = read_avw_img('melodic_IC');
>> i1 = IC(:,:,:,1);
>> i2 = IC(:,:,:,2);
>> mean(i1(:))
ans =
0.0060
>> mean(i2(:))
ans =
0.0172
>> var(i1(:))
ans =
0.2584
>> var(i2(:))
ans =
0.4065
>> norm(i1(:))
ans =
149.1037
>> norm(i2(:))
ans =
187.0637
>> i1(:)'*i2(:)
ans =
2.2768e+03
>> cov(i1(:), i2(:))
ans =
0.2584 0.0264
0.0264 0.4065
Apologies if I am being idiotic, and thanks in advance for your time,
Ged.
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