A PCA (if you use all dimensions) preserves distances. Thus, distances based on the initial data and PCA scores using all dimensions should be identical. Note: if the PCA is based on a correlation matrix rather than a covariance matrix then you have to use standardized data to get equality. Mahalanobis distances are different as are Procrustes distances.
F. James Rohlf Distinguished Professor, Emeritus Depts: Anthropology and Ecology & Evolution Stony Brook University On 12/15/2020 9:47:38 AM, Bryan McLean <[email protected]> wrote: Dear morphometricians, I have a basic question that some quick literature searches havent answered yet, but which I believe will be answered quickly from the collective knowledge here. I wish to compare pairwise distances among specimens in PCA space derived from a) a suite of linear measurements and b) a 3D landmark-based approach. The goal is simply to ask whether one of the two approaches to describing shape provides "higher resolution" (i.e., more discriminating power). However, I dont think that raw (Euclidean or Mahalanobis) distances from the separate PCAs are comparable, since they explain different amounts of total variation. Is there a way to scale the among-specimen distances from each so they are comparable between the PCAs? OR - is there a totally different (eg non-PCA-based) way of approaching this simple question? Thanks in advance, Bryan -- You received this message because you are subscribed to the Google Groups "Morphmet" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected] [mailto:[email protected]]. To view this discussion on the web visit https://groups.google.com/d/msgid/morphmet2/CAFXGjdoCoKZOUZ-iFPRM4UuKxByzCt%2BKcksxs%2Bwew0tfHxK70g%40mail.gmail.com [https://groups.google.com/d/msgid/morphmet2/CAFXGjdoCoKZOUZ-iFPRM4UuKxByzCt%2BKcksxs%2Bwew0tfHxK70g%40mail.gmail.com?utm_medium=email&utm_source=footer]. -- You received this message because you are subscribed to the Google Groups "Morphmet" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/morphmet2/Mailbird-6abbbbf7-60c4-4c0f-a3eb-a49f1e20999e%40stonybrook.edu.
