Families of dendrograms

Details Families of dendrograms Families of dendrograms

2007-07-27

arxiv.org/abs/0707.4072v1

Statistics

Machine Learning

7 pages, 3 figures. To appear in: Proceedings of the 31st Annual Conference of the German Classification Society on Data Analy

Scientific paper

10.1007/978-3-540-78246-9_12

A conceptual framework for cluster analysis from the viewpoint of p-adic geometry is introduced by describing the space of all dendrograms for n datapoints and relating it to the moduli space of p-adic Riemannian spheres with punctures using a method recently applied by Murtagh (2004b). This method embeds a dendrogram as a subtree into the Bruhat-Tits tree associated to the p-adic numbers, and goes back to Cornelissen et al. (2001) in p-adic geometry. After explaining the definitions, the concept of classifiers is discussed in the context of moduli spaces, and upper bounds for the number of hidden vertices in dendrograms are given.

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