Eigenanalysis analysis and metric multidimensional scaling on hierarchical structures

Abstract

The known hierarchical clustering scheme is equivalent to the concept of ul- trametric distance. AII distance can be represented in a spatial model using multidimensional scaling. We relate both clases of representations of proxim- ity data in an algebraic way, obtaining Borne results and relations on clusters and the eigenvalues of the inner product matrix for an ultrametric distance. Principal coordinate analysis on an ultrametric distance gives two classes of independent coordinates, describing compact clusters and representing objects inside every cluster.