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Geomstats: A Python Package for Riemannian Geometry in Machine Learning

Nina Miolane 1 Nicolas Guigui 2, 3 Alice Le Brigant 4 Johan Mathe 5 Benjamin Hou 6 Yann Thanwerdas 2, 3 Stefan Heyder 7 Olivier Peltre 8 Niklas Koep 9 Hadi Zaatiti 10 Hatem Hajri 10 Yann Cabanes 11 Thomas Gerald 12 Paul Chauchat 13 Christian Shewmake 14 Daniel Brooks 15 Bernhard Kainz 6 Claire Donnat 16 Susan Holmes 1 Xavier Pennec 2, 3
1 Department of Statistics [Stanford]
2 UCA - Université Côte d'Azur
3 EPIONE - E-Patient : Images, données & mOdèles pour la médeciNe numériquE
CRISAM - Inria Sophia Antipolis - Méditerranée
4 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)
5 Frog labs AI San Francisco
6 Imperial College London
7 TU - Technische Universität Ilmenau
8 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
9 RWTH - Rheinisch-Westfälische Technische Hochschule Aachen
10 IRT SystemX - IRT SystemX
11 IMB - Institut de Mathématiques de Bordeaux
12 MLIA - Machine Learning and Information Access
LIP6
13 CAOR - Centre de Robotique
14 Washington University in St Louis
15 Chercheur indépendant
16 Stanford University
Abstract : We introduce Geomstats, an open-source Python toolbox for computations and statistics on nonlinear manifolds, such as hyperbolic spaces, spaces of symmetric positive definite matrices, Lie groups of transformations, and many more. We provide object-oriented and extensively unit-tested implementations. Among others, manifolds come equipped with families of Riemannian metrics, with associated exponential and logarithmic maps, geodesics and parallel transport. Statistics and learning algorithms provide methods for estimation, clustering and dimension reduction on manifolds. All associated operations are vectorized for batch computation and provide support for different execution backends, namely NumPy, PyTorch and TensorFlow, enabling GPU acceleration. This paper presents the package, compares it with related libraries and provides relevant code examples. We show that Geomstats provides reliable building blocks to foster research in differential geometry and statistics, and to democratize the use of Riemannian geometry in machine learning applications. The source code is freely available under the MIT license at http://geomstats.ai.
Keywords : differential geometry Riemannian geometry statistics machine learning manifold
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Journal articles
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https://hal.inria.fr/hal-02536154
Contributor : Project-Team Asclepios <>
Submitted on : Monday, December 21, 2020 - 12:27:36 PM
Last modification on : Thursday, February 25, 2021 - 11:28:02 AM

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Distributed under a Creative Commons Attribution 4.0 International License

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  • HAL Id : hal-02536154, version 2

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IRT-SYSTEMX | INRIA-SILICONVALLEY | INSMI | PSL | UNIV-PARIS1 | ENSMP_CAOR | ENSMP | IMJ | SAMM | SAMOS | UNIV-COTEDAZUR | IDEX-UNIV-COTEDAZUR | SORBONNE-UNIVERSITE | LIP6 | CNRS | IMB | UP-SCIENCES | SU-SCIENCES | UNIV-PARIS | 3IA-COTEDAZUR | INRIA | SU-TI | INSTITUT-TELECOM | PARISTECH | PRAIRIE-IA

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Nina Miolane, Nicolas Guigui, Alice Le Brigant, Johan Mathe, Benjamin Hou, et al.. Geomstats: A Python Package for Riemannian Geometry in Machine Learning. Journal of Machine Learning Research, Microtome Publishing, 2020, 21 (223), pp.1-9. ⟨hal-02536154v2⟩

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