Hi Ged,
yep, that's right. The melodic output (melodic_IC) are re-scaled Z-
stats maps based on the residual noise (see figure 4 in the technical
report) - not the vanilla ICA maps. Also, the temporal mean - removed
before the estimation - get's re-introduced. Overall, this is just a
global (per map) shift and re-scale and has no influence on the
thresholding probabilities. However, it means that spatial have
individual std deviations =/= 1 and mean =/= 0. Also, the Z-stats re-
scale means that co-variances are non zero. If you run melodic with
the --Oall option then it will also output melodic_oIC, a version of
the maps which are not re-scaled to become Z-scores. These are
therefore orthogonal (though still have the temporal mean re-
introduced, i.e. have non-unit std deviation and non-zero mean).
Hope this helps
cheers
Christian
On 6 Mar 2007, at 19:01, Ged Ridgway wrote:
> 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.
--
Christian F. Beckmann
Oxford University Centre for Functional
Magnetic Resonance Imaging of the Brain,
John Radcliffe Hospital, Headington, Oxford OX3 9DU, UK
Email: [log in to unmask] - http://www.fmrib.ox.ac.uk/~beckmann/
Phone: +44(0)1865 222551 Fax: +44(0)1865 222717
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