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

TL;DR

AuToMATo is an out-of-the-box, persistence-based clustering algorithm that combines topological data analysis with bootstrapping, outperforming many existing methods without requiring parameter tuning.

Contribution

It introduces AuToMATo, a new clustering method that leverages persistent homology and bootstrapping, providing default parameters for robust, parameter-free clustering.

Findings

AuToMATo performs favorably against state-of-the-art algorithms.

It often outperforms well-tuned alternative algorithms.

The implementation is available in Python and integrates with scikit-learn.

Abstract

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.