geomstats swMATH ID: 24373 Software Authors: Nina Miolane, Johan Mathe, Claire Donnat, Mikael Jorda, Xavier Pennec Description: 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. Homepage: https://arxiv.org/abs/1805.08308 Source Code: https://github.com/geomstats/geomstats Dependencies: Python Keywords: Learning; arXiv_cs.LG; Mathematical Software; arXiv_cs.MS; Machine Learning; arXiv_stat.ML; Python; Riemannian Geometry Related Software: Pymanopt; Geoopt; McTorch; TensorFlow; PyGeometry; Python; GitHub; Julia; PyQuaternions; PyRiemann; pyquaternion; PyTorch; Theano; MVIRT; Manopt.jl; Manopt; ROPTLIB; Manifolds.jl; MNIST; StiefelLog Cited in: 9 Publications Standard Articles 1 Publication describing the Software Year geomstats: a Python Package for Riemannian Geometry in Machine Learning Nina Miolane, Johan Mathe, Claire Donnat, Mikael Jorda, Xavier Pennec 2018 all top 5 Cited by 34 Authors 4 Guigui, Nicolas 4 Pennec, Xavier 1 Absil, Pierre-Antoine 1 Arnaudon, Alexis 1 Brooks, Daniel R. 1 Cabanes, Yann 1 Chauchat, Paul 1 Donnat, Claire 1 Evangelista-Alvarado, Miguel Ángel 1 García-Portugués, Eduardo 1 Gerald, Thomas 1 Hajri, Hatem 1 Herzog, Roland 1 Heyder, Stefan 1 Holmes, Susan P. 1 Hou, Benjamin 1 Kainz, Bernhard 1 Koep, Niklas 1 Kühnel, Line 1 Le Brigant, Alice 1 Maignant, Elodie 1 Mathe, Johan 1 Miolane, Nina 1 Nguyen, Du Dinh 1 Peltre, Olivier 1 Pewsey, Arthur 1 Ruíz-Pantaleón, José Crispín 1 Shewmake, Christian 1 Sommer, Stefan 1 Steidl, Gabriele 1 Suárez-Serrato, Pablo 1 Thanwerdas, Yann 1 Trouvé, Alain 1 Zaatiti, Hadi all top 5 Cited in 6 Serials 1 Applied Mathematics and Computation 1 Journal of Optimization Theory and Applications 1 Test 1 Foundations of Computational Mathematics 1 Journal of Machine Learning Research (JMLR) 1 Oberwolfach Reports all top 5 Cited in 10 Fields 3 Differential geometry (53-XX) 3 Statistics (62-XX) 3 Numerical analysis (65-XX) 3 Computer science (68-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 General and overarching topics; collections (00-XX) 1 Algebraic geometry (14-XX) 1 Manifolds and cell complexes (57-XX) 1 Probability theory and stochastic processes (60-XX) 1 Operations research, mathematical programming (90-XX) Citations by Year