Abstract
The “raison d’être” of hierarchical clustering theory stems from one basic phenomenon: This is the notorious non-transitivity of similarity relations. In spite of the fact that very often two objects may be quite similar to a third without being that similar to each other, one still wants to classify objects according to their similarity. This should be achieved by grouping them into a hierarchy of non-overlapping clusters such that any two objects in one cluster appear to be more related to each other than they are to objects outside this cluster.
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References
Bandelt, H.-J., Dress, A. W. M.: Weak hierarchies associated with similarity measures — an additive clustering technique. Bull. Math. Bio1. 51, 133–166 (1989).
Dopazo, J., Sobrino, F., Palma, E. L., Domingo, E., Moya, A.: Gene encoding capsid protein VP1 of foot-and-mouth disease virus: A quasispecies model of molecular evolution. Proc. Natl. Acad. Sci. USA 85, 6811–6815 (1988).
Dress, A. W. M.: Trees, tight extensions of metric spaces, and the cohomological dimension of certain groups. Adv. in Math. 53, 321–402 (1984).
Dress, A. W. M.: On the computational complexity of composite systems. In: Fluctuations and Stochastic Phenomena. L. Garrido (ed.), Springer Lecture Notes in Physics 268, 377–388 (1986).
Eigen, M., Lindemann, B., Tietze, M., Winkler-Oswatitsch, R., Dress, A., v. Haeseler, A.: How old is the genetic code. Statistical geometry of tRNA provides an answer. to appear in Science.
Eigen, M., Winkler-Oswatitsch, R., Dress, A.: Statistical geometry in sequence space: A method of quantitative sequence analysis. Proc. Natl. Sci. USA 85, 5913–5917 (1988).
Eigen, M., Winkler-Oswatitsch, R.: Transfer-RNA: The early adaptor. Naturwissenschaften 68, 217–228 (1981).
Eigen, M., Winkler-Oswatitsch, R.: Transfer-RNA, an early gene? Naturwissenschaften 68, 282–292 (1981).
Fitch, W. M.: Towards defining the course of evolution: minimum change for a specific tree topology. Syst. Zool. 20, 406–416 (1971).
Felsenstein, J.: Statistical inference of phylogenies. J. R. Statist. Soc. A. 146, 246–272 (1983).
Fitch, W. M., Margoliash, E.: Construction of phylogenetic trees. Science 155, 279–284 (1967).
Ganter, B.: Composition and decomposition of data in formal concept analysis. In: Classification and Related Methods of Data Analysis. H. H. Bock (ed.). Elsevier Science Publisher, p. 561–566 (1988).
Ganter, B., Wille, R., Wolff, K. E. (eds.): Beiträge zur Begriffsanalyse, BI Wissenschaftsverlag, Mannheim, Wien, Zürich (1987).
Hartigan, E.: Minimum mutation fits to a given tree. Biometrics 29, 53–69 (1973).
Isbell, J. R.: Six theorems about metric spaces. Comment. Math. Heiv. 39 65–74 (1964–1965).
Mouden, C. W., Golden, S. S.: psbA genes indicate common ancestry of prochlorophytes and chloroplasts. Nature 337, 382–285 (1989).
Penny, D., Penny, P.: Search parallelism, comparisons and evalutation: Algorithms for evolutionary trees (this volume).
Sankoff, D., Cedergren, R. J.: Simultaneous comparison of three or more sequences related by a tree. In: Time warps, string edits, and macromolecules. D. Sankoff and J. B. Kruskal (eds.), Addison-Wesley, London, 253–263 (1983).
Sibley, C. G., Ahlquist, J. E.: Phylogeny and classification of New World Suboscine Passerine birds (Passeriformes: Oligomyodi: Tyrannides). American Ornithology Union Monograph 36, p. 396–426 (1985).
Seewaldt, E., Stackebrandt, E.: Partial sequences of 16S ribosomal RNA and the phylogeny of Prochloron. Nature 295, 618–620 (1982).
Steinhauer, D. A., Holland, J. J.: Rapid evolution of RNA viruses. Ann. Rev. Microbiol. 41, 409–433 (1987).
Turner, S., Burger-Wiersma, T., Giovannoni, S. J., Mur, L. R., Pace, N. R.: The relationship of a prochlorophyte Prochlorothrix hollandica to green chloroplasts. Nature 337, 380–382 (1989).
Wille, R.: Lattices in data analysis: How to draw them with a computer. In: J. Rival (ed.), Algorithms and Order, Dordrecht-Boston, Reidel, p. 33–58 (1989).
Winkler-Oswatitsch, R., Dress, A., Eigen, M.: Comparative sequence analysis. Chemica Scripta 26B, 59–66 (1986).
Wolters, J., Erdmann, V. A.: Cladistic analysis of 5SrRNA and 16SrRNA secondary and primary structure — the evolution of eukaryotes and their relation to archaebacteria. J. Mol. Evol. 24, 152–166 (1986).
Williams, P. L., Fitch, W. M.: Weighted parsimony: when not all changes have the same value. Submitted to Mol. Biol. and Evol. (1988).
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Dress, A.W.M., von Haeseler, A. (1990). Introduction. In: Dress, A., von Haeseler, A. (eds) Trees and Hierarchical Structures. Lecture Notes in Biomathematics, vol 84. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-10619-8_1
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DOI: https://doi.org/10.1007/978-3-662-10619-8_1
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