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Journal Articles Journal of Machine Learning Research Year : 2020

Geomstats: A Python Package for Riemannian Geometry in Machine Learning

Nina Miolane
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  • PersonId : 1086601
Benjamin Hou
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  • PersonId : 1086602
Yann Thanwerdas
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Stefan Heyder
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Hadi Zaatiti
Hatem Hajri
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Yann Cabanes
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Thomas Gerald
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Paul Chauchat
Christian Shewmake
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Daniel Brooks
Bernhard Kainz
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Claire Donnat
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Susan Holmes
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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
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Dates and versions

hal-02536154 , version 1 (08-04-2020)
hal-02536154 , version 2 (21-12-2020)




  • HAL Id : hal-02536154 , version 2


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-02536154v2⟩
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