I took a bit of time to think about the interesting discussion on
semilandmarks, "homology function" and isotropy (and a bit longer for
the message to be sent for problems with email filters).
We all agree that semilandmarks can be useful. We may disagree on: when
they're needed (I don't think that "cool pictures" is a good reason);
whether they have cons and not only pros; and on what sliding does.
Benedikt has rightly pointed out that the issue of homology is a complex
one. In this respect, I would not call minBEN (or minPRD) sliding
"homology functions". It's clever maths and does exactly what Jim said
in his message. However, I don't think we can generalize on what the
best choice is (including not adding semilandmarks, non-sliding -as
mentioned by others- or sliding with one or the other method).
Gunz et al., that is cited to justify why minBEN is best, use a specific
definition of homology, i.e. geometric homology: is there a
GENERALIZABLE demonstration (not just few examples, theoretical and ad
hoc or real ones) that 'biological homology' (which may be defined using
different criteria) is the same as geometric homology in all or at least
most cases (organisms, structures etc.)?
If there isn't, one should be open to all options.
On the issues with highly multivariate Procrustes variables, it is true
that real data have their own (true) covariance plus the covariance
added by the superimposition (plus that of sliding, if this is done).
With true covariance some issues will be probably less serious. This is
also said multiple times in my recent paper on false positives in many
tests of modularity/integration.
However, the covariance introduced by the superimposition will be always
there and whether it is negligible will (I guess) be totally dependent
on the structure and the set of points used to measure it. One might
simulate some scenarios but again generalizability can't be based on few
examples. That the superimposition introduces covariance that is not
originally there is, in contrast, always the case, as recognized since
the early days of GMM.
Last point, and here we get into the difficult maths I can't understand
(with apologies for my dumbness): I am not convinced that the isotropic
model is uninformative.
If data, that originally have only random noise (circular variation as
in random digitizing error), produce a pattern that is not circular in
an analysis, that's for me an alarm bell. Indeed, if I got it right (not
sure ... with more apologies), the isotropic model has been extensively
used in the past and among other things is, if I am correct, behind
Mitteroecker et al. (Journal of Human Evolution 46 (2004) 679–698) form
" The reader is encouraged to simulate isotropic
variations around a general mean form in two or
three dimensions, compute Centroid Size and
Procrustes shape coordinates, then produce the
principal component structure of the size–shape
spaces following this instruction. The resulting
distributions should be spherical, without any
pattern information" (p. 695).
Thanks again for comments and clarifications. Please, if someone does
not feel like sending them to the list, feel free to reply to me
personally: I won't share answers sent directly to me without asking.
Dr. Andrea Cardini
Researcher, Dipartimento di Scienze Chimiche e Geologiche, Università di
Modena e Reggio Emilia, Via Campi, 103 - 41125 Modena - Italy
tel. 0039 059 2058472
Adjunct Associate Professor, School of Anatomy, Physiology and Human
Biology, The University of Western Australia, 35 Stirling Highway,
Crawley WA 6009, Australia
E-mail address: alcard...@gmail.com, andrea.card...@unimore.it
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