Hierarchical topological clustering

TL;DR

This paper introduces a hierarchical topological clustering algorithm that identifies meaningful clusters and outliers in complex datasets without assuming specific data structures, demonstrating its effectiveness on diverse real-world data.

Contribution

The paper presents a novel hierarchical topological clustering method applicable with any distance metric, capable of detecting outliers and arbitrary-shaped clusters.

Findings

Successfully identified meaningful clusters in image, medical, and economic datasets.

Effectively detected outliers and clusters of arbitrary shape.

Outperforms traditional clustering methods in complex data scenarios.

Abstract

Topological methods have the potential of exploring data clouds without making assumptions on their the structure. Here we propose a hierarchical topological clustering algorithm that can be implemented with any distance choice. The persistence of outliers and clusters of arbitrary shape is inferred from the resulting hierarchy. We demonstrate the potential of the algorithm on selected datasets in which outliers play relevant roles, consisting of images, medical and economic data. These methods can provide meaningful clusters in situations in which other techniques fail to do so.