Weak hierarchies associated with similarity measures—An additive clustering technique

Bandelt H-J, Dress A (1989)
Bulletin of Mathematical Biology 51(1): 133-166.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Bandelt, Hans-Jürgen ; Dress, AndreasUniBi
Abstract / Bemerkung
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.
Erscheinungsjahr
1989
Zeitschriftentitel
Bulletin of Mathematical Biology
Band
51
Ausgabe
1
Seite(n)
133-166
ISSN
0092-8240
Page URI
https://pub.uni-bielefeld.de/record/1653355

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Bandelt H-J, Dress A. Weak hierarchies associated with similarity measures—An additive clustering technique. Bulletin of Mathematical Biology. 1989;51(1):133-166.
Bandelt, H. - J., & Dress, A. (1989). Weak hierarchies associated with similarity measures—An additive clustering technique. Bulletin of Mathematical Biology, 51(1), 133-166. https://doi.org/10.1007/BF02458841
Bandelt, H. - J., and Dress, A. (1989). Weak hierarchies associated with similarity measures—An additive clustering technique. Bulletin of Mathematical Biology 51, 133-166.
Bandelt, H.-J., & Dress, A., 1989. Weak hierarchies associated with similarity measures—An additive clustering technique. Bulletin of Mathematical Biology, 51(1), p 133-166.
H.-J. Bandelt and A. Dress, “Weak hierarchies associated with similarity measures—An additive clustering technique”, Bulletin of Mathematical Biology, vol. 51, 1989, pp. 133-166.
Bandelt, H.-J., Dress, A.: Weak hierarchies associated with similarity measures—An additive clustering technique. Bulletin of Mathematical Biology. 51, 133-166 (1989).
Bandelt, Hans-Jürgen, and Dress, Andreas. “Weak hierarchies associated with similarity measures—An additive clustering technique”. Bulletin of Mathematical Biology 51.1 (1989): 133-166.

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