Geomstats: A Python Package for Riemannian Geometry in Machine Learning
| العنوان: | Geomstats: A Python Package for Riemannian Geometry in Machine Learning |
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| المؤلفون: | Nina Miolane, Nicolas Guigui, Alice Le Brigant, Johan Mathe, Benjamin Hou, Yann Thanwerdas, Stefan Heyder, Olivier Peltre, Niklas Koep, Hadi Zaatiti, Hatem Hajri, Yann Cabanes, Thomas Gerald, Paul Chauchat, Christian Shewmake, Daniel Brooks, Bernhard Kainz, Claire Donnat, Susan Holmes, Xavier Pennec |
| المساهمون: | Department of Statistics [Stanford], Stanford University, Université Côte d'Azur (UCA), E-Patient : Images, données & mOdèles pour la médeciNe numériquE (EPIONE), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne) (SAMM), Université Paris 1 Panthéon-Sorbonne (UP1), Frog labs AI San Francisco, Imperial College London, Technische Universität Ilmenau (TU ), Institut de Mathématiques de Jussieu - Paris Rive Gauche (IMJ-PRG (UMR_7586)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Rheinisch-Westfälische Technische Hochschule Aachen (RWTH), IRT SystemX (IRT SystemX), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Machine Learning and Information Access (MLIA), LIP6, Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Centre de Robotique (CAOR), MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Washington University in Saint Louis (WUSTL), Chercheur indépendant, ERC G-Statistics No 786854, ANR UCAJEDI No ANR-15-IDEX-01, 3IA Côte d'Azur ANR-19-P3IA-0002, Inria@SiliconValley, GeomStats, G-Statistics, ANR-15-IDEX-0001,UCA JEDI,Idex UCA JEDI(2015), ANR-19-P3IA-0002,3IA@cote d'azur,3IA Côte d'Azur(2019), European Project: 786854,H2020 Pilier ERC,ERC AdG(2018), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Rheinisch-Westfälische Technische Hochschule Aachen University (RWTH), IRT SystemX, Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Mines Paris - PSL (École nationale supérieure des mines de Paris), Asclepios, Project-Team, Idex UCA JEDI - - UCA JEDI2015 - ANR-15-IDEX-0001 - IDEX - VALID, 3IA Côte d'Azur - - 3IA@cote d'azur2019 - ANR-19-P3IA-0002 - P3IA - VALID, G-Statistics - Foundations of Geometric Statistics and Their Application in the Life Sciences - ERC AdG - - H2020 Pilier ERC2018-09-01 - 2023-08-31 - 786854 - VALID |
| المصدر: | HAL Journal of Machine Learning Research Journal of Machine Learning Research, Microtome Publishing, 2020, 21 (223), pp.1-9 Journal of Machine Learning Research, 2020, 21 (223), pp.1-9 |
| بيانات النشر: | Microtome Publishing, 2020. |
| سنة النشر: | 2020 |
| مصطلحات موضوعية: | Technology, Science & Technology, manifold, [INFO] Computer Science [cs], Computer Science, Artificial Intelligence, 17 Psychology and Cognitive Sciences, Automation & Control Systems, machine learning, statistics, [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG], Computer Science, MANIFOLDS, Artificial Intelligence & Image Processing, [INFO]Computer Science [cs], 08 Information and Computing Sciences, differential geometry, Riemannian geometry, [MATH.MATH-DG] Mathematics [math]/Differential Geometry [math.DG] |
| الوصف: | International audience; 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. |
| وصف الملف: | application/pdf |
| اللغة: | English |
| تدمد: | 1532-4435 1533-7928 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::8cb7f51a3a95696af7654c621e432e3e http://hdl.handle.net/20.500.12278/113146 |
| حقوق: | OPEN |
| رقم الأكسشن: | edsair.dedup.wf.001..8cb7f51a3a95696af7654c621e432e3e |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 15324435 15337928 |
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