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

Marius Huber, Sara Kalisnik Hintz, Patrick Schnider

Keywords: clustering, persistent homology, topological data analysis, tda, mapper algorithm

TL;DR: We present an out-of-the-box clustering algorithm based on persistent homology that uses a bootstrap procedure to automate a threshold selection in an existing clustering algorithm.

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.

Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

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Submission Number: 10024