Metadata-Version: 1.1
Name: POT
Version: 0.3.1
Summary: Python Optimal Transport Library
Home-page: https://github.com/rflamary/POT
Author: Remi Flamary, Nicolas Courty
Author-email: remi.flamary@gmail.com, ncourty@gmail.com
License: MIT
Download-URL: https://github.com/rflamary/POT/archive/0.3.1.tar.gz
Description: # POT: Python Optimal Transport
        
        [![PyPI version](https://badge.fury.io/py/POT.svg)](https://badge.fury.io/py/POT)
        [![Build Status](https://travis-ci.org/rflamary/POT.svg?branch=master)](https://travis-ci.org/rflamary/POT)
        [![Documentation Status](https://readthedocs.org/projects/pot/badge/?version=latest)](http://pot.readthedocs.io/en/latest/?badge=latest)
        
        
        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:
        ```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
        
        ### Short examples
        
        * Import the toolbox
        ```python
        import ot
        ```
        * Compute Wasserstein distances
        ```python
        # a,b are 1D histograms (sum to 1 and positive)
        # M is the ground cost matrix
        Wd=ot.emd2(a,b,M) # exact linear program
        Wd_reg=ot.sinkhorn2(a,b,M,reg) # entropic regularized OT
        # if b is a matrix compute all distances to a and return a vector
        ```
        * Compute OT matrix
        ```python
        # a,b are 1D histograms (sum to 1 and positive)
        # M is the ground cost matrix
        T=ot.emd(a,b,M) # exact linear program
        T_reg=ot.sinkhorn(a,b,M,reg) # entropic regularized OT
        ```
        * Compute Wasserstein barycenter
        ```python
        # A is a n*d matrix containing d  1D histograms
        # M is the ground cost matrix
        ba=ot.barycenter(A,M,reg) # reg is regularization parameter
        ```
        
        
        
        
        ### Examples and Notebooks
        
        The examples folder contain several examples and use case for the library. The full documentation is available on [Readthedocs](http://pot.readthedocs.io/).
        
        
        Here is a list of the Python notebooks available [here](https://github.com/rflamary/POT/blob/master/notebooks/) if you want a quick look:
        
        * [1D optimal transport](https://github.com/rflamary/POT/blob/master/notebooks/Demo_1D_OT.ipynb)
        * [OT Ground Loss](https://github.com/rflamary/POT/blob/master/notebooks/Demo_Ground_Loss.ipynb)
        * [Multiple EMD computation](https://github.com/rflamary/POT/blob/master/notebooks/Demo_Compute_EMD.ipynb)
        * [2D optimal transport on empirical distributions](https://github.com/rflamary/POT/blob/master/notebooks/Demo_2D_OT_samples.ipynb)
        * [1D Wasserstein barycenter](https://github.com/rflamary/POT/blob/master/notebooks/Demo_1D_barycenter.ipynb)
        * [OT with user provided regularization](https://github.com/rflamary/POT/blob/master/notebooks/Demo_Optim_OTreg.ipynb)
        * [Domain adaptation with optimal transport](https://github.com/rflamary/POT/blob/master/notebooks/Demo_2D_OT_DomainAdaptation.ipynb)
        * [Color transfer in images](https://github.com/rflamary/POT/blob/master/notebooks/Demo_Image_ColorAdaptation.ipynb)
        * [OT mapping estimation for domain adaptation](https://github.com/rflamary/POT/blob/master/notebooks/Demo_2D_OTmapping_DomainAdaptation.ipynb)
        * [OT mapping estimation for color transfer in images](https://github.com/rflamary/POT/blob/master/notebooks/Demo_Image_ColorAdaptation_mapping.ipynb)
        * [Wasserstein Discriminant Analysis](https://github.com/rflamary/POT/blob/master/notebooks/Demo_Wasserstein_Discriminant_Analysis.ipynb)
        
        You can also see the notebooks with [Jupyter nbviewer](https://nbviewer.jupyter.org/github/rflamary/POT/tree/master/notebooks/).
        
        ## Acknowledgements
        
        The contributors to this library are:
        
        * [Rémi Flamary](http://remi.flamary.com/)
        * [Nicolas Courty](http://people.irisa.fr/Nicolas.Courty/)
        * [Laetitia Chapel](http://people.irisa.fr/Laetitia.Chapel/)
        * [Michael Perrot](http://perso.univ-st-etienne.fr/pem82055/) (Mapping estimation)
        * [Léo Gautheron](https://github.com/aje) (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](http://gpeyre.github.io/) (Wasserstein Barycenters in Matlab)
        * [Nicolas Bonneel](http://liris.cnrs.fr/~nbonneel/) ( C++ code for EMD)
        * [Antoine Rolet](https://arolet.github.io/) ( Mex file for EMD )
        * [Marco Cuturi](http://marcocuturi.net/) (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](https://people.csail.mit.edu/sparis/publi/2011/sigasia/Bonneel_11_Displacement_Interpolation.pdf). In ACM Transactions on Graphics (TOG) (Vol. 30, No. 6, p. 158). ACM.
        
        [2] Cuturi, M. (2013). [Sinkhorn distances: Lightspeed computation of optimal transport](https://arxiv.org/pdf/1306.0895.pdf). 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](https://arxiv.org/pdf/1412.5154.pdf). 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](https://hal.archives-ouvertes.fr/hal-01377236/document), 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](https://arxiv.org/pdf/1507.00504.pdf), 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](https://arxiv.org/pdf/1307.5551.pdf). 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](https://arxiv.org/pdf/1510.06567.pdf). arXiv preprint arXiv:1510.06567.
        
        [8] M. Perrot, N. Courty, R. Flamary, A. Habrard, [Mapping estimation for discrete optimal transport](http://remi.flamary.com/biblio/perrot2016mapping.pdf), Neural Information Processing Systems (NIPS), 2016.
        
        [9] Schmitzer, B. (2016). [Stabilized Sparse Scaling Algorithms for Entropy Regularized Transport Problems](https://arxiv.org/pdf/1610.06519.pdf). arXiv preprint arXiv:1610.06519.
        
        [10] Chizat, L., Peyré, G., Schmitzer, B., & Vialard, F. X. (2016). [Scaling algorithms for unbalanced transport problems](https://arxiv.org/pdf/1607.05816.pdf). arXiv preprint arXiv:1607.05816.
        
        [11] Flamary, R., Cuturi, M., Courty, N., & Rakotomamonjy, A. (2016). [Wasserstein Discriminant Analysis](https://arxiv.org/pdf/1608.08063.pdf). arXiv preprint arXiv:1608.08063.
        
Platform: linux
Platform: macosx
Platform: windows
Classifier: Development Status :: 4 - Beta
Classifier: Intended Audience :: Developers
Classifier: Environment :: Console
Classifier: Operating System :: OS Independent
Classifier: Operating System :: MacOS
Classifier: Operating System :: POSIX
Classifier: Programming Language :: Python
Classifier: Topic :: Utilities
Requires: numpy
Requires: scipy
Requires: cython
Requires: matplotlib
