Hi,
I would quibble with what you say below...the model is X=A*S where A
is the BOLD timecourse and S is the source image. A is the *mixing
matrix*...not the unmixing matrix. You actually can interpret the GIFT
timecourse (what todd sent) as BOLD activation or deactivation. The inverse
of A will not resemble BOLD activity.
VDC
> -----Original Message-----
> From: SPM (Statistical Parametric Mapping)
> [mailto:[log in to unmask]] On Behalf Of Joseph Dien
> Sent: Monday, November 26, 2007 3:24 PM
> To: [log in to unmask]
> Subject: Re: [SPM] independent component analysis of fMRI data
>
> 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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