[The "Dennis' posting" referred to below was a private message from me
acting as moderator and requesting clarification on the computation of
dimensionality for the tangent projection. -the Moderator (dslice, d is
for Dennis)]
Following on from Dennis' posting the reduced number of variables
submitted to PCA arises because of the tangent projection, not because
of the dimensionality issue after GPA.
The tangent projection is described in equation (4.35) in the Dryden and
Mardia Staistical Shape Analysis book, page 77. Note the dimensions of
the pole (gamma, preshape)on bottom of page 76,(k-1)m. The result is a
set of (k-1)m variables for each specimen which are submitted to PCA.
The maths is pretty heavy (ie I certainly don't understand it) but in
essence it's because the tangent projection uses the preshapes.
Back to the practicalities - In answer to Oliver's question, it would
not make much sense to interpet the loadings of these variables on PCs
one by one.
One could interpret the loadings of GPA registered coordinates (ie
omitting the tangent projection - fine when variations are small) but I
prefer to interpret shape variations using transformation grids because
the deformations of these are not dependent on registration.
Paul O'Higgins
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