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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