Geomstats is a Python package for computations, statistics, machine learning and deep learning on manifolds.

The package is organized into two main modules: geometry and learning. The module geometry implements differential geometry: manifolds, Lie groups, fiber bundles, shape spaces, information manifolds, Riemannian metrics, and more. The module learning implements statistics and learning algorithms for data on manifolds. Users can choose between backends: NumPy, Autograd or PyTorch.

Code
Continuous Integration
Code coverage (np, autograd, torch)
Documentation
Community

Keep in touch with the community by joining us on our slack workspace!

NEWS:

• 2023: Discover our information_geometry module , and its paper Parametric information geometry with the package Geomstats by Alice Le Brigant, Jules Deschamps, Antoine Collas, and Nina Miolane, published in the ACM Transactions of Mathematical Software.
• 2023: Discover our foundational paper Introduction to Riemannian Geometry and Geometric Statistics: From Basic Theory to Implementation with Geomstats by Nicolas Guigui, Nina Miolane and Xavier Pennec, published in Foundations and Trends in Machine Learning.
• 2021-2022: The white papers summarizing the findings from our ICLR 2021 and 2022 challenges of computational differential geometry and topology are available here (2021) and here (2022).
• To get an overview of geomstats, see our introductory video.
• To understand how geomstats is built, check out these slides.
• To get started with geomstats, see the examples and notebooks directories.
• The documentation of geomstats can be found on the documentation website.
• Interested in information geometry? Go to our information_geometry module.
• To follow the scientific literature on geometric statistics, follow our twitter-bot @geomstats!

If you find geomstats useful, please kindly cite:

• our research paper :

@article{JMLR:v21:19-027,
  author  = {Nina Miolane and Nicolas Guigui and Alice Le Brigant and Johan Mathe and Benjamin Hou and Yann Thanwerdas and Stefan Heyder and Olivier Peltre and Niklas Koep and Hadi Zaatiti and Hatem Hajri and Yann Cabanes and Thomas Gerald and Paul Chauchat and Christian Shewmake and Daniel Brooks and Bernhard Kainz and Claire Donnat and Susan Holmes and Xavier Pennec},
  title   = {Geomstats:  A Python Package for Riemannian Geometry in Machine Learning},
  journal = {Journal of Machine Learning Research},
  year    = {2020},
  volume  = {21},
  number  = {223},
  pages   = {1-9},
  url     = {http://jmlr.org/papers/v21/19-027.html}
}

• and Geomstats software version (citation automatically generated by Zenodo at the bottom right of this link).

We would sincerely appreciate citations to both the original research paper and the software version, to acknowledge authors who started the codebase and made the library possible, together with the crucial work of all contributors who are continuously implementing pivotal new geometries and important learning algorithms, as well as refactoring, testing and documenting the code to democratize geometric statistics and (deep) learning and foster reproducible research in this field.

From a terminal (OS X & Linux), you can install geomstats and its requirements with pip3 as follows:

pip3 install geomstats

This method installs the latest version of geomstats that is uploaded on PyPi. Note that geomstats is only available with Python3.

From a terminal (OS X & Linux) or an Anaconda prompt (Windows), you can install geomstats and its requirements with conda as follows:

conda install -c conda-forge geomstats

This method installs the latest version of geomstats that is uploaded on conda-forge. Note that geomstats is only available with Python3.

From a terminal (OS X & Linux), you can install geomstats and its requirements via git as follows:

git clone https://github.com/geomstats/geomstats.git
cd geomstats
pip3 install .

This method installs the latest GitHub version of geomstats.

Note that this only installs the minimum requirements. To add the optional, development, continuous integration and documentation requirements, refer to the file pyproject.toml.

Developers should git clone the main branch of this repository, together with the development requirements and the optional requirements to enable autograd and pytorch backends:

pip3 install geomstats[dev,opt]

Additionally, we recommend installing our pre-commit hook, to ensure that your code follows our Python style guidelines:

pre-commit install

Geomstats can run seamlessly with numpy, autograd or pytorch. Note that autograd and pytorch and requirements are optional, as geomstats can be used with numpy only. By default, the numpy backend is used. The visualizations are only available with this backend.

To get the autograd and pytorch versions compatible with geomstats, install the optional requirements:

pip3 install geomstats[opt]

To install only the requirements for a given backend do:

pip3 install geomstats[<backend_name>]

You can choose your backend by setting the environment variable GEOMSTATS_BACKEND to numpy, autograd or pytorch, and importing the backend module. From the command line:

export GEOMSTATS_BACKEND=<backend_name>

and in the Python3 code:

import geomstats.backend as gs

To use geomstats for learning algorithms on Riemannian manifolds, you need to follow three steps:

• instantiate the manifold of interest,
• instantiate the learning algorithm of interest,
• run the algorithm.

The data should be represented by a gs.array. This structure represents numpy arrays, autograd or pytorch tensors, depending on the choice of backend.

The following code snippet shows the use of tangent Principal Component Analysis on simulated data on the space of 3D rotations.

from geomstats.geometry.special_orthogonal import SpecialOrthogonal
from geomstats.learning.pca import TangentPCA

so3 = SpecialOrthogonal(n=3, point_type="vector")

data = so3.random_uniform(n_samples=10)

tpca = TangentPCA(space=so3, n_components=2)
tpca = tpca.fit(data)
tangent_projected_data = tpca.transform(data)

All geometric computations are performed behind the scenes. The user only needs a high-level understanding of Riemannian geometry. Each algorithm can be used with any of the manifolds and metric implemented in the package.

To see additional examples, go to the examples or notebooks directories.

See our contributing guidelines!

Interested? Contact us and join the next hackathons. Previous Geomstats events include:

• January 2020: hackathon at Inria Sophia-Antipolis, Nice, France
• April 2020: remote online hackathon
• March - April 2021: hackathon, hybrid at Inria Sophia-Antipolis / remotely with contributors from around the world
• July 2021: hackathon at the Geometric Science of Information (GSI) conference, Paris, France
• August 2021: international Coding Challenge at the International Conference on Learning Representations (ICLR), remotely
• December 2021: fixit hackathon at the Sorbonne Center for Artificial Intelligence, Paris, France.
• February 2022: hackathon, hybrid at Inria Sophia-Antipolis / remotely with contributors from around the world
• April 2022: in-person hackathon at the Villa Cynthia, Saint Raphael, France.
• April 2022: international Coding Challenge at the International Conference on Learning Representations (ICLR), remotely.
• June 2022: hackathon at the University of Washington (UW).
• October 17-21, 2022: hackathon during the trimester Geometry and Statistics in Data Sciences, in Paris.

This work is supported by:

• the National Science Foundation (grant 2313150).
• the National Science Foundation (NSF CAREER award, grant 2240158).
• the Inria-Stanford associated team GeomStats,
• the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreement G-Statistics No. 786854),
• the French society for applied and industrial mathematics (SMAI),
• the National Science Foundation (grant NSF DMS RTG 1501767).