1. geomstats: a Python Package for Riemannian Geometry in Machine Learning
- Author
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Miolane, Nina, Mathe, Johan, Donnat, Claire, Jorda, Mikael, Pennec, Xavier, E-Patient : Images, données & mOdèles pour la médeciNe numériquE (EPIONE), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Inria@SiliconValley (Inria@SiliconValley), Stanford University-University of Southern California (USC)-Institut National de Recherche en Informatique et en Automatique (Inria)-University of California [Santa Barbara] (UCSB), University of California-University of California-University of California [San Diego] (UC San Diego), University of California-Ministère de l'Europe et des Affaires étrangères (MEAE)-CITRIS-University of California [Santa Cruz] (UCSC), University of California-University of California [Irvine] (UCI), University of California, Frog labs AI San Francisco, Stanford University, COMUE Université Côte d'Azur (2015-2019) (COMUE UCA), Inria@SiliconValley, GeomStats, Stanford University-University of California [Santa Cruz] (UC Santa Cruz), University of California (UC)-University of California (UC)-Institut National de Recherche en Informatique et en Automatique (Inria)-University of California [Santa Barbara] (UC Santa Barbara), University of California (UC)-University of California [San Diego] (UC San Diego), University of California (UC)-Ministère de l'Europe et des Affaires étrangères (MEAE)-University of Southern California (USC)-CITRIS-University of California [Irvine] (UC Irvine), and University of California (UC)
- Subjects
FOS: Computer and information sciences ,Computer Science - Machine Learning ,Statistics - Machine Learning ,[MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG] ,Machine Learning (stat.ML) ,Computer Science - Mathematical Software ,Mathematics::Differential Geometry ,Mathematical Software (cs.MS) ,Machine Learning (cs.LG) ,[INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI] ,[INFO.INFO-MS]Computer Science [cs]/Mathematical Software [cs.MS] - Abstract
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., Preprint NIPS2018
- Published
- 2019