On the Local Ultrametricity of Finite Metric Data

TL;DR

This paper introduces new local ultrametricity measures for finite metric data, leveraging p-adic Mumford curves and Radon measures, with experimental validation on the iris dataset.

Contribution

It proposes a novel approach to measure local ultrametricity using p-adic geometry and applies it to real data, expanding the tools for analyzing metric datasets.

Findings

New ultrametricity measures based on p-adic Mumford curves

Experimental validation on iris dataset

Potential for improved data analysis techniques

Abstract

New local ultrametricity measures for finite metric data are proposed through the viewpoint that their Vietoris-Rips corners are samples from p-adic Mumford curves endowed with a Radon measure coming from a regular differential 1-form. This is experimentally applied to the iris dataset.