Yeah, that's right! Although I work with ICA (and just published a
comprehensive comparison with PCA in Human Brain Mapping), I started
with PCA so I think about it from that perspective. Come to think of
it though, the unmixing matrix (A) in ICA corresponds to the factor
scoring matrix in PCA. It's the mixing matrix that corresponds to PCA
factor loadings (the ICA terminology is rather clearer I think). So
what I mean is, does the mixing matrix times the activation score
result in a positive or a negative spike at the voxels of interest?
You get the mixing matrix by taking the inverse of A. In plain
English, for your analysis, an ICA component will represent voxels
that go in opposite directions, so your positive time course in
matrix X (the "activation matrix") will represent an activation at
some voxels and a deactivation at other voxels. The ICA terminology
is a little confusing when applied to fMRI data since "activation" is
being used in two different ways here. You can't interpret the ICA
activation matrix X directly as being either a BOLD activation or a
deactivation. You need to figure out what it means for the
particular voxel you are interested in. The clearest way to do this
is to compute X*inv(A)=S which will regenerate the portion of the
BOLD signal that is being accounted for by this component alone and
then see if it is being modeled as an activation or a deactivation in
the voxels that you are interested in. So the question is whether
this is what you have already done. If not, then this is my
recommendation to you.
Cheers!
Joe
On Nov 26, 2007, at 3:23 PM, [log in to unmask] wrote:
>
>
> Hi Joe,
>
> I think I know what you mean, but let me respond here just so
> we're clear. I may be using terminology that is different than
> yours to describe the same thing. I'm not quite sure what you mean
> by 'the loading' but, given the context of the message, I think you
> mean the value in the A matrix (the corresponding time course
> value, i.e. x = As, the ICA model) that corresponds with that
> particular voxel's spatial weight (the activation as you say)? I
> just never call it the loading, that is why I am asking.
>
> Thx
>
> Todd
>
> Quoting Joseph Dien <[log in to unmask]>:
>
>> Hi,
>> that's what I mean. At least when I look at it, there are no
>> values attached to the color scale (as in the attached figure). So
>> anyway, the question is, have you verified that the product of the
>> loading and the activation is indeed negative? If the product is
>> positive, then the mystery is solved.
>
>
------------------------------------------------------------------------
--------
Joseph Dien
Assistant Professor of Psychology
Department of Psychology
419 Fraser Hall (by the coke machine)
1415 Jayhawk Blvd
University of Kansas
Lawrence, KS 66045-7556
E-mail: [log in to unmask]
Office: 785-864-9822 (note: no voicemail)
Fax: 785-864-5696
http://people.ku.edu/~jdien/Dien.html
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