I published a method, AHCS, based on that idea (generalized distances between groups as they are formed during the clustering process) a number of years ago. One has to be careful with it as it has some unexpected properties.
-------------------- F. James Rohlf, Distinguished Professor, Dept. Ecology & Evolution, Stony Brook University, Stony Brook, NY 11794-5345 Web: http://life.bio.sunysb.edu/ee/rohlf Morphometrics: http://life.bio.sunysb.edu/morph > -----Original Message----- > From: morphmet [mailto:[EMAIL PROTECTED] > Sent: Monday, May 02, 2005 9:51 AM > To: morphmet > Subject: Re: UPGMA in morphometrics > > > To use Mahalanobis distances for an agglomerative clustering > algorithm is a good thing. But this shouldn't be called > UPGMA, which measures the distance between two groups as the > average of all distances (however defined) between individual > members of the groups. The Mahalanobis distance is not taken > between individual members, but between the groups as wholes. > > As far as I understand. > > > Oyvind Hammer > Geological Museum > University of Oslo > > > On Sun, 1 May 2005, morphmet wrote: > > > > > Hi all, > > > > in literature, several people have been using Procrustes > distances as > > the data for a cluster-analysis, more specifically UPGMA. > When doing > > so, the Procrustes distances between the consensus > configurations of > > each OTU are used to calculate a tree based on shape similarities > > between the consensusses. However, when using Procrustes distances, > > one is ignoring possible differences in the amount of within-group > > variation (or is assuming it is the same for all the > OTU's), not? The > > Procrustes distance between the means of three groups can be the > > identical, but because of overlapping variations within two > of them, > > the shape distance will in many cases be much lower. > > > > So my question is, whether it is not wiser to use the Squared > > Mahalanobis distances of a canonical variate analysis > (based on weight > > matrix), as a measure of shape distance between group means for a > > UPGMA, as this does take into account the amount of within-group > > variation (and as I understood even standardises it). Does > this make > > sense or is there some mathematical-statistical pitfall behind it? > > > > cheers > > > > Dominique Adriaens > > > > > > > > > > > > Prof. Dr. Dominique Adriaens > > > > Ghent University > > > > Evolutionary Morphology of Vertebrates & Zoology Museum > > > > K.L. Ledeganckstraat 35, B-9000 Gent > > > > BELGIUM > > > > tel: +32 9 264.52.19, fax: +32 9 264.53.44 > > > > E-mail: [EMAIL PROTECTED] > > > > URL: http://www.fun-morph.ugent.be/ > > > > http://www.zoologymuseum.ugent.be/ > > > > > > > > > > > > -- > > Replies will be sent to the list. > > For more information visit http://www.morphometrics.org > > > > > -- > Replies will be sent to the list. > For more information visit http://www.morphometrics.org > -- Replies will be sent to the list. For more information visit http://www.morphometrics.org
