Thank you! On Wednesday, November 1, 2017 at 6:18:41 AM UTC+3, f.james.rohlf wrote: > > Note that the distinction between full and partial Procrustes is not very > important if shape variation is in fact very small. > > > > In a partial Procrustes superimposition there is an additional step that > projects the aligned specimens onto the tangent space. Without that step > the shapes are still in the curved space of GPA aligned shapes. As a > result, there will be one less eigenvalue than expected that is “exactly” > equal to zero (i.e., around 10^-16). Its size depends on the amount of > curvature of the space around the GPA consensus shape and that depends on > the amount of shape variation in the sample and thus is data dependent. > > > > However, it seems reasonable to me to apply this extra step if one is > going to use multivariate methods that assume that one has a linear space. > This was discussed in Rohlf, F. J. 1999. Shape statistics: Procrustes > superimpositions and tangent spaces. Journal of Classification, 16:197-223. > Slice 2001. Syst. Biol. 50:141–149 is also relevant. > > > > _ _ _ _ _ _ _ _ _ > > F. James Rohlf, Distinguished Prof. Emeritus > > [image: univautosig] > > Depts. of Anthropology and of Ecology & Evolution > > >
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