Hi Ged,
Tensor ICA is a 3-way decomposition where the data is represented as
the (outer) product of a spatial map, a timecourse, and a subject (or
session, or both) vector.
Tensor-ICA is similar to normal first-level spatial-ICA in the sense
that the component separation is still being driven by forcing
statistical independence of the spatial components.
I think your question is slightly missing the point of normal ICA
anyway - normal ICA, just like PCA, does in effect look at both space
and time when doing the component "unmixing"; in the space that the
ICA unmixing is carried out, both spatial maps and timecourses are
all orthogonal to each other. The extra constraint in the case of ICA
is that it forces spatial maps to be not just orthogonal to each
other, but also statistically independent....
Hope this helps?
On 20 Feb 2007, at 13:44, Ged Ridgway wrote:
> Steve Smith wrote:
>> MELODIC is spatial ICA ("SICA") not temporal, because FMRI data
>> are not well-suited to TICA - primarily because you don't have
>> enough timepoints to generate an accurate temporal PDF.
>> I can't think of any reason why you would particularly want to run
>> temporal-ICA on FMRI data as opposed to spatial-ICA.
>
> Please forgive a question which is probably stupid in terms of both
> theory and motivation, but with Tensor ICA (the other TICA!)
> couldn't one look at both factors of space and time? Do you think
> this might have advantages/disadvantages?
>
> Thanks for your patience,
> Ged.
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Stephen M. Smith, Professor of Biomedical Engineering
Associate Director, Oxford University FMRIB Centre
FMRIB, JR Hospital, Headington, Oxford OX3 9DU, UK
+44 (0) 1865 222726 (fax 222717)
[log in to unmask] http://www.fmrib.ox.ac.uk/~steve
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