Geomstats: A Python Package for Riemannian Geometry in Machine Learning

• URL: http://arxiv.org/abs/2004.04667v1
• Date: Tue, 7 Apr 2020 20:41:50 GMT
• Title: Geomstats: A Python Package for Riemannian Geometry in Machine Learning
• Authors: Nina Miolane, Alice Le Brigant, Johan Mathe, Benjamin Hou, Nicolas Guigui, Yann Thanwerdas, Stefan Heyder, Olivier Peltre, Niklas Koep, Hadi Zaatiti, Hatem Hajri, Yann Cabanes, Thomas Gerald, Paul Chauchat, Christian Shewmake, Bernhard Kainz, Claire Donnat, Susan Holmes, Xavier Pennec
• Abstract summary: We introduce Geomstats, an open-source Python toolbox for computations and statistics on nonlinear equations. We provide object-oriented and extensively unit-tested implementations. We show that Geomstats provides reliable building blocks to foster research in differential geometry and statistics. The source code is freely available under the MIT license at urlgeomstats.ai.
• Score: 5.449970675406181
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 \url{geomstats.ai}.

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