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) , Bernhard Kainz (6) , Claire Donnat (15) , Susan Holmes (1) , Xavier Pennec (2, 3)

1 Department of Statistics [Stanford]
2 UniCA - Université Côte d'Azur
3 EPIONE - E-Patient : Images, données & mOdèles pour la médeciNe numériquE
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 University
10 IRT SystemX
11 IMB - Institut de Mathématiques de Bordeaux
12 MLIA - Machine Learning and Information Access
13 CAOR - Centre de Robotique
14 WUSTL - Washington University in Saint Louis
15 Stanford University

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.

Domaines: Informatique [cs]; Géométrie différentielle [math.DG]

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, 2020, 21 (223), pp.1-9. ⟨hal-02536154v1⟩