Constructing Hierarchical Set Systems |
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| Authors: | Claudine Devauchelle Andreas W M Dress Alexander Grossmann Stefan Grünewald Alain Henaut |
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| Institution: | (1) Laboratoire Génome et Informatique, Tour Evry2, 523 Place des Terrasses, 91034 Evry Cedex, France;(2) Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22-26, 04103 Leipzig, Germany;(3) Linnaeus Centre for Bioinformatics, BMC, Box 598, SE 75124 Uppsala, Sweden |
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| Abstract: | In this note, it is shown that by applying ranking procedures to data that allow, for any three objects a1, a2, b in a collection X of objects of interest, to make consistent decisions about which of the two objects a1 or a2 is more similar to b, a family of cluster systems
 can be constructed that start with the associated Apresjan Hierarchy and keep growing until, for k = #X–1, the full set
 of all subsets of X is reached. Various ideas regarding canonical modifications of the similarity values so that these cluster systems contain as many clusters as possible for small values of k (and in particular for k := 0) and/or are rooted at a specific element in X, possible applications, e.g. concerning (i) the comparison of distinct dissimilarity data defined on the same set X or (ii) diversity optimization, and new tasks arising in ranking statistics are also discussed.Received November 15, 2003 |
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| Keywords: | 05C90 92B10 92D15 62G30 62-07 |
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