POT: Python Optimal Transport
=============================
|PyPI version| |Build Status| |Documentation Status|
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 [1].
- Entropic regularization OT solver with Sinkhorn Knopp Algorithm [2]
and stabilized version [9][10] with optional GPU implementation
(required cudamat).
- Bregman projections for Wasserstein barycenter [3] and unmixing [4].
- Optimal transport for domain adaptation with group lasso
regularization [5]
- Conditional gradient [6] and Generalized conditional gradient for
regularized OT [7].
- Joint OT matrix and mapping estimation [8].
- Wasserstein Discriminant Analysis [11] (requires autograd +
pymanopt).
Some demonstrations (both in Python and Jupyter Notebook format) are
available in the examples folder.
Installation
------------
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 # for user install (no root)
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:
.. code:: python
import ot
Note that for easier access the module is name ot instead of pot.
Dependencies
~~~~~~~~~~~~
Some sub-modules require additional dependences which are discussed
below
- **ot.dr** (Wasserstein dimensionality rediuction) depends on autograd
and pymanopt that can be installed with:
::
pip install pymanopt autograd
- **ot.gpu** (GPU accelerated OT) depends on cudamat that have to be
installed with:
::
git clone https://github.com/cudamat/cudamat.git
cd cudamat
python setup.py install --user # for user install (no root)
obviously you need CUDA installed and a compatible GPU.
Examples
--------
The examples folder contain several examples and use case for the
library. The full documentation is available on
`Readthedocs `__
Here is a list of the Python notebooks if you want a quick look:
- `1D optimal
transport `__
- `2D optimal transport on empirical
distributions `__
- `1D Wasserstein
barycenter `__
- `OT with user provided
regularization `__
- `Domain adaptation with optimal
transport `__
- `Color transfer in
images `__
- `OT mapping estimation for domain
adaptation `__
- `OT mapping estimation for color transfer in
images `__
You can also see the notebooks with `Jupyter
nbviewer `__.
Acknowledgements
----------------
The contributors to this library are:
- `Rémi Flamary `__
- `Nicolas Courty `__
- `Laetitia Chapel `__
- `Michael Perrot `__
(Mapping estimation)
- `Léo Gautheron `__ (GPU implementation)
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):
- `Gabriel Peyré `__ (Wasserstein Barycenters
in Matlab)
- `Nicolas Bonneel `__ ( C++ code for
EMD)
- `Antoine Rolet `__ ( Mex file for EMD )
- `Marco Cuturi `__ (Sinkhorn Knopp in
Matlab/Cuda)
References
----------
[1] 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.
[2] Cuturi, M. (2013). `Sinkhorn distances: Lightspeed computation of
optimal transport `__. In Advances
in Neural Information Processing Systems (pp. 2292-2300).
[3] 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.
[4] 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.
[5] 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
[6] Ferradans, S., Papadakis, N., Peyré, G., & Aujol, J. F. (2014).
`Regularized discrete optimal
transport `__. SIAM Journal on
Imaging Sciences, 7(3), 1853-1882.
[7] Rakotomamonjy, A., Flamary, R., & Courty, N. (2015). `Generalized
conditional gradient: analysis of convergence and
applications `__. arXiv preprint
arXiv:1510.06567.
[8] M. Perrot, N. Courty, R. Flamary, A. Habrard, `Mapping estimation
for discrete optimal
transport `__,
Neural Information Processing Systems (NIPS), 2016.
[9] Schmitzer, B. (2016). `Stabilized Sparse Scaling Algorithms for
Entropy Regularized Transport
Problems `__. arXiv preprint
arXiv:1610.06519.
[10] Chizat, L., Peyré, G., Schmitzer, B., & Vialard, F. X. (2016).
`Scaling algorithms for unbalanced transport
problems `__. arXiv preprint
arXiv:1607.05816.
[11] Flamary, R., Cuturi, M., Courty, N., & Rakotomamonjy, A. (2016).
`Wasserstein Discriminant
Analysis `__. arXiv preprint
arXiv:1608.08063.
.. |PyPI version| image:: https://badge.fury.io/py/POT.svg
:target: https://badge.fury.io/py/POT
.. |Build Status| image:: https://travis-ci.org/rflamary/POT.svg?branch=master
:target: https://travis-ci.org/rflamary/POT
.. |Documentation Status| image:: https://readthedocs.org/projects/pot/badge/?version=latest
:target: http://pot.readthedocs.io/en/latest/?badge=latest