Characterizing Properties for Q-Clustering

TL;DR

This paper provides an axiomatic characterization of two Q-Clustering algorithms, Max-Sum and Single-Linkage, using tree-based properties, and explores their interactions to refine clustering taxonomy.

Contribution

It introduces a novel axiomatic framework for characterizing key Q-Clustering algorithms with tree constructions, clarifying their properties and interactions.

Findings

Characterization of Max-Sum using Gomory-Hu trees

Characterization of Single-Linkage using Maximum Spanning Tree

Insights into how properties interact and refine clustering taxonomy

Abstract

We uniquely characterize two members of the Q-Clustering family in an axiomatic framework. We introduce properties that use known tree constructions for the purpose of characterization. To characterize the Max-Sum clustering algorithm, we use the Gomory-Hu construction, and to characterize Single-Linkage, we use the Maximum Spanning Tree. Although at first glance it seems these properties are `obviously' all that are necessary to characterize Max-Sum and Single-Linkage, we show that this is not the case, by investigating how subsets of properties interact. We conclude by proposing additions to the taxonomy of clustering paradigms currently in use.