Python Optimal Transport Library
This open source Python library provide several solvers for optimization problems related to Optimal Transport for signal, image processing and machine learning.
It provides the following solvers:
- OT solver for the linear program/ Earth Movers Distance .
- Entropic regularization OT solver with Sinkhorn Knopp Algorithm .
- Bregman projections for Wasserstein barycenter  and unmixing .
- Optimal transport for domain adaptation with group lasso regularization 
- Conditional gradient  and Generalized conditional gradient for regularized OT .
We are also currently working on the following features:
- [ ] Image color adaptation demo
- [ ] Scikit-learn inspired classes for domain adaptation
- [ ] Mapping estimation as proposed in 
Some demonstrations (both in Python and Jupyter Notebook format) are available in the examples folder.
The Library has been tested on Linux and MacOSX. It requires a C++ compiler for using the EMD solver and rely on the following Python modules:
- Numpy (>=1.11)
- Scipy (>=0.17)
- Cython (>=0.23)
- Matplotlib (>=1.5)
Under debian based linux the dependencies can be installed with
sudo apt-get install python-numpy python-scipy python-matplotlib cython
To install the library, you can install it locally (after downloading it) on you machine using
python setup.py install --user
The toolbox is also available on PyPI with a possibly slightly older version. You can install it with:
pip install POT
After a correct installation, you should be able to import the module without errors:
Note that for easier access the module is name ot instead of pot.
The examples folder contain several examples and use case for the library. The full documentation is available on Readthedoc
Here is a list of the Python notebook if you want a quick look:
The contributors to this library are:
This toolbox benefit a lot from open source research and we would like to thank the following persons for providing some code (in various languages):
 Bonneel, N., Van De Panne, M., Paris, S., & Heidrich, W. (2011, December). Displacement interpolation using Lagrangian mass transport. In ACM Transactions on Graphics (TOG) (Vol. 30, No. 6, p. 158). ACM.
 Cuturi, M. (2013). Sinkhorn distances: Lightspeed computation of optimal transport. In Advances in Neural Information Processing Systems (pp. 2292-2300).
 Benamou, J. D., Carlier, G., Cuturi, M., Nenna, L., & Peyré, G. (2015). Iterative Bregman projections for regularized transportation problems. SIAM Journal on Scientific Computing, 37(2), A1111-A1138.
 S. Nakhostin, N. Courty, R. Flamary, D. Tuia, T. Corpetti, Supervised planetary unmixing with optimal transport, Whorkshop on Hyperspectral Image and Signal Processing : Evolution in Remote Sensing (WHISPERS), 2016.
 N. Courty; R. Flamary; D. Tuia; A. Rakotomamonjy, “Optimal Transport for Domain Adaptation,” in IEEE Transactions on Pattern Analysis and Machine Intelligence , vol.PP, no.99, pp.1-1
 Ferradans, S., Papadakis, N., Peyré, G., & Aujol, J. F. (2014). Regularized discrete optimal transport. SIAM Journal on Imaging Sciences, 7(3), 1853-1882.
 Rakotomamonjy, A., Flamary, R., & Courty, N. (2015). Generalized conditional gradient: analysis of convergence and applications. arXiv preprint arXiv:1510.06567.
 M. Perrot, N. Courty, R. Flamary, A. Habrard, “Mapping estimation for discrete optimal transport”, Neural Information Processing Systems (NIPS), 2016.