----- Forwarded message from Vaibhav Patel
<vaibhav.np2...@gmail.com> -----
Date: Thu, 29 Aug 2013
20:51:45 -0400
From: Vaibhav Patel <vaibhav.np2...@gmail.com>
Reply-To: Vaibhav Patel <vaibhav.np2...@gmail.com>
Subject:
Statistical Reconstruction using PLS
To:
morphmet@morphometrics.org
Dear morphmetors,
I am attempting a cranial reconstruction following the Statistical Reconstruction method described in Gunz et al. "Principles for the virtual reconstruction of hominin crania."Journal of Human Evolution 57.1 (2009): 48-62. Namely, I use the following protocol:
1. Partition the GPA aligned landmarks of each sample skull into
two blocks: X corresponding to the observable landmarks on the damaged specimen,
and Y corresponding to the missing landmarks. (DO NOT re-perform GPA on the
separate X and Y blocks, to retain relative positions)
2. Convert the GPA aligned landmarks X and Y to procrustes residuals X0 and Y0
by subtracting off the corresponding subsets in the consensus landmark set.
3. Submit the X0 and Y0 blocks to SIMPLS (employed in Matlab's plsregress), and
obtain the PLS regression coefficients beta.
4. Ordinary-Procrustes-align the damaged specimen's observable landmarks to the
X-part of the consensus, then subtract off the X-part to obtain procrustes
residuals.
5. Multiply the procrustes residuals of the preceding step with beta to predict
the residuals of the missing landmarks.
6. Add these predicted residuals to the Y-part of the consensus to get the
coordinates of the missing landmarks in shape space.
7. Back out of shape space by using the reverse transformation of step 4 and
obtain the "real space" estimates for the missing landmarks.
Would this be one valid interpretation/implementation of the statistical technique described in Gunz et al (2009)? Specifically in step 4, I fear that using OPA to align the observable landmarks to the X-part of the consensus results in "too close" a fit.
Any advice would be tremendously useful. Thanks,
Vai
----- End forwarded message
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