Dear Narender,
> You wrote a while ago that Principle Coponents Analysis
> (PCA) could be used to characterise circuitry in which there was functional
> connectivity (FC), because areas that emerge in the resulting maximum
> intensity projections have correlated activity. As I understand it, FC is
> characterised by context-specific covariance in activity between brain
> areas, when covariance due purely to the presence of a context is accounted
> for. Surely PCA is inherantly incapable of characterising FC because it
> cannot distinguish between the different contexts in an experiment?
Functional connectivity is simply the observed covariance among
different brain systems. This covariance can have a number of
components (in the same way that variance is partitioned in statistical
models). If one component is 'context' then an eigenimage analysis
will only discount it if that component is removed from the data. For
example, in the first applications to PET data, the subject-effect was
removed prior to PCA. In this intance the subject-effect was treated
as an uninteresting context and was removed from the PCA. A more
interesting situation arises when the FC changes with context (c.f. a
condition x context interaction). In this case you may be interested
in these context-sensitive changes (if not then the interactions can be
removed from the data before PCA). Identifying modes that change with
context falls under the remit of nonlinear PCA and a treatment will be
found in the most recent edition of Human Brain Mapping (Special
edition).
With very best wishes - Karl
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