# AuToMATo: An Out-Of-The-Box Persistence-Based Clustering Algorithm

arXiv: https://arxiv.org/abs/2408.06958 · HTML: https://mlsanity.com/paper/2408.06958/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 38 references that are in the map.
- First posted on arXiv 13 Aug 2024.

## Builds on (most cited first, 9 of 9)

- [Efficient Parameter-free Clustering Using First Neighbor Relations](https://mlsanity.com/paper/1902.11266/) (2019)
- [giotto-tda: A Topological Data Analysis Toolkit for Machine Learning and Data Exploration](https://mlsanity.com/paper/2004.02551/) (2020)
- [Geometry Helps to Compare Persistence Diagrams](https://mlsanity.com/paper/1606.03357/) (2016)
- [The Topology ToolKit](https://mlsanity.com/paper/1805.09110/) (2018)
- [Adjusting for Chance Clustering Comparison Measures](https://mlsanity.com/paper/1512.01286/) (2015)
- [Robust Topological Inference: Distance To a Measure and Kernel Distance](https://mlsanity.com/paper/1412.7197/) (2014)
- [Statistical Analysis and Parameter Selection for Mapper](https://mlsanity.com/paper/1706.00204/) (2017)
- [A framework for benchmarking clustering algorithms](https://mlsanity.com/paper/2209.09493/) (2022)
- [Homology-Preserving Multi-Scale Graph Skeletonization Using Mapper on Graphs](https://mlsanity.com/paper/1804.11242/) (2018)

## Built on by (most cited first, 3 of 3)

- [Topological Data Analysis for Unsupervised Anomaly Detection and Customer Segmentation on Banking Data](https://mlsanity.com/paper/2508.14136/) (2025)
- [PHIDA: Persistence-Guided Node-to-Cluster Mapping for Online Clustering](https://mlsanity.com/paper/2605.08673/) (2026)
- [ToMAToMP: Robust and Multi-Parameter Topological Clustering](https://mlsanity.com/paper/2605.14824/) (2026)

## Abstract (arXiv)

We present AuToMATo, a novel clustering algorithm based on persistent homology. While AuToMATo is not parameter-free per se, we provide default choices for its parameters that make it into an out-of-the-box clustering algorithm that performs well across the board. AuToMATo combines the existing ToMATo clustering algorithm with a bootstrapping procedure in order to separate significant peaks of an estimated density function from non-significant ones. We perform a thorough comparison of AuToMATo (with its parameters fixed to their defaults) against many other state-of-the-art clustering algorithms. We find not only that AuToMATo compares favorably against parameter-free clustering algorithms, but in many instances also significantly outperforms even the best selection of parameters for other algorithms. AuToMATo is motivated by applications in topological data analysis, in particular the Mapper algorithm, where it is desirable to work with a clustering algorithm that does not need tuning of its parameters. Indeed, we provide evidence that AuToMATo performs well when used with Mapper. Finally, we provide an open-source implementation of AuToMATo in Python that is fully compatible with the standard scikit-learn architecture.