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arXiv · 0707.3536

Degenerating families of dendrograms

Patrick Erik Bradley
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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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Patrick Erik Bradley. 2007-07-24. Degenerating families of dendrograms. https://doi.org/10.1007/s00357-008-9009-5

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