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
|
