Degenerating families of dendrograms

Details Degenerating families of dendrograms Degenerating families of dendrograms

2007-07-24

arxiv.org/abs/0707.3536v1

J. Classif. 25, 27-42 (2008)

Statistics

Machine Learning

13 pages, 8 figures

Scientific paper

10.1007/s00357-008-9009-5

Dendrograms used in data analysis are ultrametric spaces, hence objects of nonarchimedean geometry. It is known that there exist $p$-adic representation of dendrograms. Completed by a point at infinity, they can be viewed as subtrees of the Bruhat-Tits tree associated to the $p$-adic projective line. The implications are that certain moduli spaces known in algebraic geometry are $p$-adic parameter spaces of (families of) dendrograms, and stochastic classification can also be handled within this framework. At the end, we calculate the topology of the hidden part of a dendrogram.

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