A note on extensions of approximate ultrametrics

TL;DR

This paper discusses methods for extending ultrametrics from a subset of a metric space to the entire space while approximately maintaining original distances.

Contribution

It introduces new techniques for extending ultrametrics with minimal distortion, enhancing their applicability in metric space analysis.

Findings

Extended ultrametrics preserve distances within a bounded approximation.

Proposed methods improve upon existing ultrametric extension techniques.

Applications include hierarchical clustering and data analysis.

Abstract

An ultrametric defined on a subset S of a metric space X can be extended to X while roughly preserving distances between pairs in S x X.