Degenerating Families of Dendrograms

2007/07/24 by Patrick Erik Bradley · 3 citations
Computer Science · Mathematics · #Machine Learning in Healthcare #Topological and Geometric Data Analysis #advanced mathematical theories #stat.ML

paper · pdf · doi:10.1007/s00357-008-9009-5

published as J. Classif. 25, 27-42 (2008) · 13 pages, 8 figures

arxiv created 2007/07/24 · openalex publication_date 2008/06/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

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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