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Journal Articles Journal of Machine Learning Research Year : 2020

Geomstats: A Python Package for Riemannian Geometry in Machine Learning

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Nina Miolane
  • Function : Author
  • PersonId : 1086601
Benjamin Hou
  • Function : Author
  • PersonId : 1086602
Yann Thanwerdas
  • Function : Author
  • PersonId : 1048229
Stefan Heyder
  • Function : Author
  • PersonId : 1086603
Hadi Zaatiti
Hatem Hajri
  • Function : Author
  • PersonId : 1086606
Yann Cabanes
  • Function : Author
  • PersonId : 1073446
Thomas Gerald
  • Function : Author
  • PersonId : 1086607
Paul Chauchat
Christian Shewmake
  • Function : Author
  • PersonId : 1086609
Daniel Brooks
Bernhard Kainz
  • Function : Author
  • PersonId : 1086610
Claire Donnat
  • Function : Author
  • PersonId : 1086608
Susan Holmes
  • Function : Author
  • PersonId : 943876

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 http://geomstats.ai.
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Dates and versions

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

Licence

Attribution - CC BY 4.0

Identifiers

  • HAL Id : hal-02536154 , version 2

Cite

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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