Weak hierarchies associated with similarity measures—An additive clustering technique |
| |
Authors: | H -J Bandelt A W M Dress |
| |
Institution: | 1. Fakult?t für Mathematik, Universit?t Bielefeld, Postfach 8640, D-4800, Bielefeld 1, F.R.G.
|
| |
Abstract: | A new and apparently rather useful and natural concept in cluster analysis is studied: given a similarity measure on a set
of objects, a sub-set is regarded as a cluster if any two objectsa, b inside this sub-set have greater similarity than any third object outside has to at least one ofa, b. These clusters then form a closure system which can be described as a hypergraph without triangles. Conversely, given such
a system, one may attach some weight to each cluster and then compose a similarity measure additively, by letting the similarity
of a pair be the sum of weights of the clusters containing that particular pair. The original clusters can be reconstructed
from the obtained similarity measure. This clustering model is thus located between the general additive clustering model
of Shepard and Arabie (1979) and the standard hierarchical model. Potential applications include fitting dendrograms with
few additional nonnested clusters and simultaneous representation of some families of multiple dendrograms (in particular,
two-dendrogram solutions), as well as assisting the search for phylogenetic relationships by proposing a somewhat larger system
of possibly relevant “family groups”, from which an appropriate choice (based on additional insight or individual preferences)
remains to be made. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|