HI Christian and Appu:

On Fri, 20 Dec 2002, Christian Beckmann wrote:

> Hi Appu,
>
> Appu Mohanty wrote:
> > I came accross two ways of doing ICA with fMRI data. In one method, ICA is
> > performed directly on the fMRI time series data resulting in components.
> > The ICA derived components are then correlated with the design matrix to
> > identify the task-related components. In the other method the fMRI times
> > series data is cross correlated with the design matrix and the ICA is
> > performed on the result of the cross correlation to yield eigenimages. I
> > think both methods could be implemented in FEAT.  Are there any suggestions
> > about which might be a better method? Is there any other method that is
> > commonly used?
> >
>
> ICA on fmri data is normally either done in the temporal or the spatial
> domain, the later being what is more common and what is offered with
> melodic. Calculating correlation scores first and performing ICA on the
> output strikes me as not very sensible: when you correlate against a
> pre-defined time-course I'd expect you to have an associated 'meaning'
> for each regressor. Those regressor time-courses jointly form a basis
> set that encodes your believe in the temporal characteristics of signal
> in the data and it is not at all obvious why if you're willing to
> strictly constrain your signal representation in the first place (by
> pre-specification of regressors) and then mess everything up again by
> looking for a different basis representation that now asks for spatial
> independence. It seems you loose exactly what can make ICA a powerful
> technique (the exploratory waythat a basis representation is generated)
> by forcing the result to be within the span of your original regressors.

If I understand correctly what Appu is proposing it is a Partial Least Squares
with PCA replaced by ICA. This makes some sense to me, to the extent that
independent is different from/better than uncorrelated. You are asking for the
structure of the common subspace between the design and data matrices. Why not
use ICA to look at it, assuming it wil produce different results from PCA?

> > My other question is about how to do an ICA on a group of subjects.
> > The following is a well established (though not very common) procedure
> > in the event-related brain potential literature. Has a similar procedure
> > been used in the fMRI literature? Is it (or: how much of it is) implemented
> > in FSL? If this procedure is not used then what is usually recommended for
> > doing ICA on a group of subjects?
> >
> >       Assume that the data set for the entire experiment consists of
> > multiple subjects, multiple conditions per subject, multiple electrodes,
> > and multiple time-point observations for each electrode. (The electrode
> > can be seen as corresponding to MR voxels, and the time points to the MR
> > time series across TRs.)
> >       Put all of the data into a single matrix, with columns = time
> > points and rows = everything else, not distinguishing subjects,
> > conditions, or electrodes. Conduct a PCA or ICA, producing factors and
> > factor loadings as a function of time.
> >       For the time-point vector in each subject x condition x electrode
> > cell, apply the factor loading to the vector, producing a factor
> > score. The factor scores are suitable dependent variables in an ANOVA
> > (or whatever). The ANOVA could have condition and electrode as factors,
> > with subjects as the within-cell replications to estimate
> > error. Rejecting the null hypothesis means that the factor scores vary
> > systematically as a function of conditions and/or electrodes.
> >
> > All of the above can also be done by exchanging electrodes and time
> > points, so that with columns = electrodes and rows = everything
> > else. The result is that the factor loadings are a function of electrode
> > location rather than time.

> Group analysis is a difficult thing; yes, you can always concatenate in
> space or time or whatever to form a new single data set - you still need
> to think hard about what domain you then enforce independence and if
> that really makes sense. If you concatenate subjects/runs in time you'll
> end up with an analysis that asks for a single spatial map but will
> allow for different temporal characteristics for each subject/run and
> vice versa if you concatenate in space. You can do both using avwmerge
> on the data but either way there are many problems with these
> approaches: If you concatenate in space you'll enforce a single
> time-course that is the same for each subject. Even in the case of very
> simple experiments the temporal characteristics of the hdrf can vary
> between subjects though. Conversely, when you concatenate in time you'll
> enforce a spatial maps for any one of the subjects. This can potentially
> be very restrictive wrt processes that do occur in some of the subjects
> but not others. An alternative has been suggested in
>
> Calhoun V, Adali T, Pearlson G, Pekar J. A Method for Making Group
> Inferences from Functional MRI Data Using Independent Component
> Analysis. Hum Brain Map 2001; 14: 140-151.
>
> This, however, has the added complication of generating an analysis
> where at the first PCA stage you allow for a completely different
> separation into what will be the noise and what will be the signal+
> noise space retained for further analysis.
>
> With melodic 2 I'd personally do the following
> - run each subject/ run separately
> - find the relevant spatial maps (if there's more than one you're in
> trouble, a problem which is hidden using any of the approaches above at
> different expenses)
> - coregister all low-res brains to the same reference image and apply
> the transformation to each of the relevant probability map (these are
> saved using the --Ostats option at the command line or the 'Output full
> stats folder' using the GUI)
> - at this point you have a set of probability maps of that you can
> average and overlay ontop of the reference image

How about Didier's version of multiway analysis, Principal Tensor Analysis
(PTAk: http://www.fmrib.ox.ac.uk/~didier/work/tensor.html) as a way of dealing
with this problem of finding the common subspace across subjects plus each
subjects unique subspace? There are also some ICA approaches to this problem
(e.g., http://www.ipl.iit.edu/IPL-Conferance_papers/2002_ICIP_ICA.PDF) Any plans
to include something like this in FSL?

> hope this all makes sense
> happy christmas everyone
> Christian
>
>
> --
>   Christian F. Beckmann
>   Address: 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 222782 Fax: +44(0)1865 222717 Mob: +44(0)7811 189123
>

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