Families of dendrograms

TL;DR

This paper introduces a novel geometric framework for understanding dendrograms in cluster analysis using p-adic geometry, relating dendrogram spaces to moduli spaces of p-adic spheres, and discusses classifiers and bounds within this context.

Contribution

It presents a new conceptual framework connecting dendrograms to p-adic geometry and moduli spaces, offering insights into their structure and classification.

Findings

Embedded dendrograms into Bruhat-Tits trees.

Established bounds for hidden vertices in dendrograms.

Related dendrogram spaces to moduli spaces of p-adic spheres.

Abstract

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.