geomstats: a Python Package for Riemannian Geometry in Machine Learning. We introduce geomstats, a python package that performs computations on manifolds such as hyperspheres, hyperbolic spaces, spaces of symmetric positive definite matrices and Lie groups of transformations. We provide efficient and extensively unit-tested implementations of these manifolds, together with useful Riemannian metrics and associated Exponential and Logarithm maps. The corresponding geodesic distances provide a range of intuitive choices of Machine Learning loss functions. We also give the corresponding Riemannian gradients. The operations implemented in geomstats are available with different computing backends such as numpy, tensorflow and keras. We have enabled GPU implementation and integrated geomstats manifold computations into keras deep learning framework. This paper also presents a review of manifolds in machine learning and an overview of the geomstats package with examples demonstrating its use for efficient and user-friendly Riemannian geometry.

References in zbMATH (referenced in 11 articles , 1 standard article )

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  1. Guigui, Nicolas; Pennec, Xavier: Numerical accuracy of ladder schemes for parallel transport on manifolds (2022)
  2. Nguyen, Du: Closed-form geodesics and optimization for Riemannian logarithms of Stiefel and flag manifolds (2022)
  3. Evangelista-Alvarado, Miguel; Ruíz-Pantaleón, José Crispín; Suárez-Serrato, Pablo: Examples of symbolic and numerical computation in Poisson geometry (2021)
  4. Guigui, Nicolas; Maignant, Elodie; Trouvé, Alain; Pennec, Xavier: Parallel transport on Kendall shape spaces (2021)
  5. Guigui, Nicolas; Pennec, Xavier: A reduced parallel transport equation on Lie groups with a left-invariant metric (2021)
  6. Pewsey, Arthur; García-Portugués, Eduardo: Recent advances in directional statistics (2021)
  7. Seth D. Axen, Mateusz Baran, Ronny Bergmann, Krzysztof Rzecki: Manifolds.jl: An Extensible Julia Framework for Data Analysis on Manifolds (2021) arXiv
  8. Absil, Pierre-Antoine (ed.); Herzog, Roland (ed.); Steidl, Gabriele (ed.): Mini-workshop: Computational optimization on manifolds. Abstracts from the mini-workshop held November 15--21, 2020 (online meeting) (2020)
  9. Miolane, Nina; Guigui, Nicolas; Le Brigant, Alice; Mathe, Johan; Hou, Benjamin; Thanwerdas, Yann; Heyder, Stefan; Peltre, Olivier; Koep, Niklas; Zaatiti, Hadi; Hajri, Hatem; Cabanes, Yann; Gerald, Thomas; Chauchat, Paul; Shewmake, Christian; Brooks, Daniel; Kainz, Bernhard; Donnat, Claire; Holmes, Susan; Pennec, Xavier: Geomstats: a Python package for Riemannian geometry in machine learning (2020)
  10. Kühnel, Line; Sommer, Stefan; Arnaudon, Alexis: Differential geometry and stochastic dynamics with deep learning numerics (2019)
  11. Nina Miolane, Johan Mathe, Claire Donnat, Mikael Jorda, Xavier Pennec: geomstats: a Python Package for Riemannian Geometry in Machine Learning (2018) arXiv