Geomstats: a Python Package for Riemannian Geometry in Machine Learning

Nina Miolane, Johan Mathe, Claire Donnat, Mikael Jorda, Xavier Pennec

Abstract: We introduce geomstats, a Python package for Riemannian modelization and optimization over manifolds such as hyperspheres, hyperbolic spaces, SPD matrices or Lie groups of transformations. Our contribution is threefold. First, geomstats allows the flexible modeling of many a machine learning problem through an efficient and extensively unit-tested implementations of these manifolds, as well as the set of useful Riemannian metrics, exponential and logarithm maps that we provide. Moreover, the wide choice of loss functions and our implementation of the corresponding gradients allow fast and easy optimization over manifolds. Finally, geomstats is the only package to provide a unified framework for Riemannian geometry, as the operations implemented in geomstats are available with different computing backends (numpy,tensorflow and keras), as well as with a GPU-enabled mode–-thus considerably facilitating the application of Riemannian geometry in machine learning. In this paper, we present geomstats through a review of the utility and advantages of manifolds in machine learning, using the concrete examples that they span to show the efficiency and practicality of their implementation using our package

Keywords: Riemannian geometry, Python package, machine learning, deep learning

TL;DR: We introduce geomstats, an efficient Python package for Riemannian modelization and optimization over manifolds compatible with both numpy and tensorflow .

Code: [ geomstats/geomstats](https://github.com/geomstats/geomstats)

Community Implementations: [ 3 code implementations](https://www.catalyzex.com/paper/geomstats-a-python-package-for-riemannian/code)