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Geomstats: A Python Package for Riemannian Geometry in Machine Learning

hal.structure.identifierDepartment of Statistics [Stanford]
dc.contributor.authorMIOLANE, Nina
hal.structure.identifierUniversité Côte d'Azur [UniCA]
hal.structure.identifierE-Patient : Images, données & mOdèles pour la médeciNe numériquE [EPIONE]
dc.contributor.authorGUIGUI, Nicolas
hal.structure.identifierStatistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne) [SAMM]
dc.contributor.authorLE BRIGANT, Alice
hal.structure.identifierFrog labs AI San Francisco
dc.contributor.authorMATHE, Johan
hal.structure.identifierImperial College London
dc.contributor.authorHOU, Benjamin
dc.contributor.authorTHANWERDAS, Yann
hal.structure.identifierTechnische Universität Ilmenau [TU ]
dc.contributor.authorHEYDER, Stefan
hal.structure.identifierInstitut de Mathématiques de Jussieu - Paris Rive Gauche [IMJ-PRG (UMR_7586)]
dc.contributor.authorPELTRE, Olivier
hal.structure.identifierRWTH Aachen University = Rheinisch-Westfälische Technische Hochschule Aachen [RWTH Aachen]
dc.contributor.authorKOEP, Niklas
hal.structure.identifierIRT SystemX
dc.contributor.authorZAATITI, Hadi
hal.structure.identifierIRT SystemX
dc.contributor.authorHAJRI, Hatem
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorCABANES, Yann
hal.structure.identifierMachine Learning and Information Access [MLIA]
dc.contributor.authorGERALD, Thomas
hal.structure.identifierCentre de Robotique [CAOR]
dc.contributor.authorCHAUCHAT, Paul
hal.structure.identifierWashington University in Saint Louis [WUSTL]
dc.contributor.authorSHEWMAKE, Christian
hal.structure.identifierChercheur indépendant
dc.contributor.authorBROOKS, Daniel
hal.structure.identifierImperial College London
dc.contributor.authorKAINZ, Bernhard
hal.structure.identifierStanford University
dc.contributor.authorDONNAT, Claire
hal.structure.identifierDepartment of Statistics [Stanford]
dc.contributor.authorHOLMES, Susan
hal.structure.identifierUniversité Côte d'Azur [UniCA]
hal.structure.identifierE-Patient : Images, données & mOdèles pour la médeciNe numériquE [EPIONE]
dc.contributor.authorPENNEC, Xavier
dc.date.accessioned2024-04-04T02:47:57Z
dc.date.available2024-04-04T02:47:57Z
dc.date.created2020-07
dc.date.issued2020-12-20
dc.identifier.issn1532-4435
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191694
dc.description.abstractEnWe 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.
dc.description.sponsorshipIdex UCA JEDI - ANR-15-IDEX-0001
dc.description.sponsorship3IA Côte d'Azur
dc.language.isoen
dc.publisherMicrotome Publishing
dc.rights.urihttp://creativecommons.org/licenses/by/
dc.subject.endifferential geometry
dc.subject.enRiemannian geometry
dc.subject.enstatistics
dc.subject.enmachine learning
dc.subject.enmanifold
dc.title.enGeomstats: A Python Package for Riemannian Geometry in Machine Learning
dc.typeArticle de revue
dc.subject.halInformatique [cs]
dc.subject.halMathématiques [math]/Géométrie différentielle [math.DG]
dc.description.sponsorshipEuropeG-Statistics - Foundations of Geometric Statistics and Their Application in the Life Sciences
bordeaux.journalJournal of Machine Learning Research
bordeaux.page1-9
bordeaux.volume21
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue223
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-02536154
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-02536154v1
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