Hi Joe,
Yes, you are right we are discussing different things (sorry for the
confusion). Let me answer this message, then I would suggest you, I and
todd take it off the SPM list, since this discussion is not related to SPM
and I feel bad cluttering up everyone else's e-mails. ;-)
GIFT only does spatial ICA....and the terminology is as follows:
X = data matrix
A = mixing matrix (BOLD timecourse)
S = source image matrix
X ~= A*S;
GIFT forces the maximal value in S to be positive and if this requires a
sign change it is applied to A as well. But that's not really important
here. Since A*S approximates X, you can always tell the sign of the BOLD
changes by looking at a specific voxel in a given source image...if that
voxel is positive, then the BOLD signal change looks like the timecourse in
the A matrix...if the voxel is negative, then the BOLD signal change is
anti-correlated to the A matrix. In Todd's case it does look like a signal
decrease, however it's hard for me to tell since I don't know where the
spikes are, hence I suggested he apply his SPM design matrix to quantify
whether the A matrix is positively or negatively correlated to the spikes.
Hope this helps,
Vince
> -----Original Message-----
> From: Joseph Dien [mailto:[log in to unmask]]
> Sent: Tuesday, November 27, 2007 5:41 PM
> To: [log in to unmask]
> Cc: [log in to unmask]
> Subject: Re: [SPM] independent component analysis of fMRI data
>
> Vince,
> we're having some sort of miscommunication here. Anyway, sounds
> like we need to be defining the terms first. First of all, correct
> me if I am wrong, but I think your response only makes sense if the
> ICA was done as a temporal analysis, not a spatial analysis.
> Only in
> that case would the mixing matrix be the BOLD timecourse. Todd said
> originally that he was doing a spatial ICA. As I know you know,
> given your extensive expertise and publication record in ICA (so I'm
> just saying this for Todd's sake), that means that the voxels were
> the variables and the ICA activation is the time course. The
> weighting matrix would then represent the relationship of the voxels
> to each ICA component and would reflect a spatial map, not a BOLD
> time course.
>
> However, in Todd's response to me, he describes A as being ("the
> corresponding time course value") so perhaps that led you to
> think he
> was talking about a temporal ICA. I think we need a clarification
> from Todd on whether he did a spatial or temporal ICA. I think that
> is the source of the quibbles and that we are actually in agreement
> about things. I definitely acknowledge your mastery of ICA so I'm
> thinking that there is just miscommunication going on here.
>
> Also, we may be having some confusion about the terminology of the
> symbols. As you know, letters don't have inherent meanings in
> statistics and different authors use different naming conventions,
> which leads to much confusion. I was understanding Todd's
> statement as:
>
> X = the ICA activation matrix
> A = the unmixing matrix
> S = the original data matrix
>
> I see though that it is more common to define it as:
>
> S = the ICA activation matrix
> A = the mixing matrix
> X = the original data matrix
>
> in which case you definitely would not want to be looking at inv(A),
> I agree.
>
> My point, though, about interpreting the activation matrix is not
> affected by the terminology issue. A positive value on an ICA
> activation variable (for a spatial ICA) can correspond to either a
> BOLD activation or a BOLD deactivation depending on the particular
> voxel and that information must be obtained from an appropriate
> viewing of the weighting matrix information. It wasn't clear to me
> from Todd's posting whether he was taking that into account
> and so it
> could potentially be the solution to his puzzle.
>
> I should note that I know ICA but I am not familiar with the GIFT
> software so perhaps there is something about the GIFT output format
> that I am not aware of (that you could clarify as one of the authors
> of the GIFT software). If, for example, the software has a
> convention of always setting the spatial map so that the largest
> weights are positive, then this ambiguity would not be a problem as
> long as he was looking at the voxels that had the largest and hence
> positive weights (or as long as all his weights have the same
> sign).
> The figure he posted didn't have the numbers for the scale so I
> couldn't tell if that was the case for his analysis, hence my
> request
> for more information about his data.
>
> Cheers!
>
> Joe
>
>
>
>
> On Nov 26, 2007, at 4:31 PM, Vince Calhoun wrote:
>
> > 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
>
> --------------------------------------------------------------
> ----------
> --------
>
> 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
>
>
