Geomstats: A Python Package for Riemannian Geometry in Machine Learning
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 \url{geomstats.ai}.
Authors 18
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Affiliation as printed
Department of Statistics [Stanford] (Stanford University, School of Humanities and Sciences, Stanford, CA 94305-4065 - United States)
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Affiliation as printed
SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne) (UR4543 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne) Centre Pierre Mendès France 90 Rue de Tolbiac - 75634 Paris Cedex 13 - France)
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Affiliation as printed
Frog labs AI San Francisco (San Francisco, CA 94103, États-Unis - United States)
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Affiliation as printed
Imperial College London (South Kensington Campus, London SW7 2AZ - United Kingdom)
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Technische Universität Ilmenau
Affiliation as printed
TU - Technische Universität Ilmenau (Ilmenau Ehrenbergstr. 29 98693 Ilmenau - Germany)
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Institut de Mathématiques de Jussieu-Paris Rive Gauche · Sorbonne Université · Université Paris Diderot
Affiliation as printed
IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche (Sorbonne Université - IMJ - Case 247 - 4 place Jussieu 75252 Paris cedex 05 / Université Paris Diderot - Bât. Sophie Germain, case 7012 - France)
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Niklas Koep Aachen
Affiliation as printed
RWTH - Rheinisch-Westfälische Technische Hochschule Aachen University (RWTH Aachen Templergraben 55 52062 Aachen (Hausanschrift) 52056 Aachen (Postanschrift) - Germany)
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Institut de Recherche Technologique SystemX
Affiliation as printed
IRT SystemX (Institut de recherche technologique SystemX - 8 Avenue de la Vauve, 91120 Palaiseau - France)
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Institut de Recherche Technologique SystemX
Affiliation as printed
IRT SystemX (Institut de recherche technologique SystemX - 8 Avenue de la Vauve, 91120 Palaiseau - France)
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Institut de Mathématiques de Bordeaux
Affiliation as printed
IMB - Institut de Mathématiques de Bordeaux (351 cours de la Libération 33405 TALENCE CEDEX - France)
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Affiliation as printed
MLIA - Machine Learning and Information Access (France)
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Affiliation as printed
CAOR - Centre de Robotique (60, boulevard Saint-Michel 75272 Paris cedex 06 - France)
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Washington University in St. Louis
Affiliation as printed
WUSTL - Washington University in Saint Louis (1 Brookings Dr, St. Louis, MO 63130 - United States)
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Affiliation as printed
Chercheur indépendant (France)
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Affiliation as printed
Imperial College London (South Kensington Campus, London SW7 2AZ - United Kingdom)
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Affiliation as printed
Stanford University (450 Serra Mall, Stanford, CA 94305-2004 - United States)
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Affiliation as printed
Department of Statistics [Stanford] (Stanford University, School of Humanities and Sciences, Stanford, CA 94305-4065 - United States)
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