# Hierarchical topological clustering

arXiv: https://arxiv.org/abs/2601.00892 · HTML: https://mlsanity.com/paper/2601.00892/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 41 references that are in the map.
- First posted on arXiv 31 Dec 2025.

## Builds on (most cited first, 4 of 4)

- [Geometry Helps to Compare Persistence Diagrams](https://mlsanity.com/paper/1606.03357/) (2016)
- [Towards a topological-geometrical theory of group equivariant non-expansive operators for data analysis and machine learning](https://mlsanity.com/paper/1812.11832/) (2018)
- [Fast Topological Clustering with Wasserstein Distance](https://mlsanity.com/paper/2112.00101/) (2021)
- [Multilevel Optimal Transport: a Fast Approximation of Wasserstein-1 distances](https://mlsanity.com/paper/1810.00118/) (2018)

## Abstract (arXiv)

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.