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Article Dans Une Revue Proceedings of Machine Learning Research Année : 2022

RipsNet: a general architecture for fast and robust estimation of the persistent homology of point clouds

Résumé

The use of topological descriptors in modern machine learning applications, such as persistence diagrams (PDs) arising from Topological Data Analysis (TDA), has shown great potential in various domains. However, their practical use in applications is often hindered by two major limitations: the computational complexity required to compute such descriptors exactly, and their sensitivity to even low-level proportions of outliers. In this work, we propose to bypass these two burdens in a data-driven setting by entrusting the estimation of (vectorization of) PDs built on top of point clouds to a neural network architecture that we call RipsNet. Once trained on a given data set, RipsNet can estimate topological descriptors on test data very efficiently with generalization capacity. Furthermore, we prove that RipsNet is robust to input perturbations in terms of the 1-Wasserstein distance, a major improvement over the standard computation of PDs that only enjoys Hausdorff stability, yielding RipsNet to substantially outperform exactly-computed PDs in noisy settings. We showcase the use of RipsNet on both synthetic and real-world data. Our implementation will be made freely and publicly available as part of the open-source library Gudhi.
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hal-03867083 , version 1 (24-11-2022)

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  • HAL Id : hal-03867083 , version 1

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Felix Hensel, Marc Glisse, Frédéric Chazal, Thibault de Surrel, Mathieu Carriere, et al.. RipsNet: a general architecture for fast and robust estimation of the persistent homology of point clouds. Proceedings of Machine Learning Research, 2022, Proceedings of Topological, Algebraic, and Geometric Learning Workshops 2022, 196, pp.96-106. ⟨hal-03867083⟩
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