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Journal of Classification

, Volume 25, Issue 1, pp 27–42 | Cite as

Degenerating Families of Dendrograms

  • Patrick Erik Bradley
Article

Abstract

Dendrograms used in data analysis are ultrametric spaces, hence objects of nonarchimedean geometry. It is known that there exist p-adic representations 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 in fact p-adic parameter spaces 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.

Keywords

Dendrograms p-adic numbers Bruhat-Tits tree Moduli spaces 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Institut für Industrielle Bauproduktion, Fakultät für ArchitekturUniversität KarlsruheKarlsruheGermany

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