readme

1 files changed, 121 insertions, 121 deletions

diff --git a/README.md b/README.md
index c96731c..8bd833c 100644
--- a/README.md
+++ b/README.md
@@ -1,58 +1,60 @@
 # POT: Python Optimal Transport
 
-[![PyPI version](https://badge.fury.io/py/POT.svg)](https://badge.fury.io/py/POT)
-[![Anaconda Cloud](https://anaconda.org/conda-forge/pot/badges/version.svg)](https://anaconda.org/conda-forge/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)
-[![Downloads](https://pepy.tech/badge/pot)](https://pepy.tech/project/pot)
-[![Anaconda downloads](https://anaconda.org/conda-forge/pot/badges/downloads.svg)](https://anaconda.org/conda-forge/pot)
-[![License](https://anaconda.org/conda-forge/pot/badges/license.svg)](https://github.com/rflamary/POT/blob/master/LICENSE)
-
+import ot
+[![PyPI version](https: // badge.fury.io / py / POT.svg)](https: // badge.fury.io / py / POT)
+[![Anaconda Cloud](https: // anaconda.org / conda - forge / pot / badges / version.svg)](https: // anaconda.org / conda - forge / 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)
+[![Downloads](https: // pepy.tech / badge / pot)](https: // pepy.tech / project / pot)
+[![Anaconda downloads](https: // anaconda.org / conda - forge / pot / badges / downloads.svg)](https: // anaconda.org / conda - forge / pot)
+[![License](https: // anaconda.org / conda - forge / pot / badges / license.svg)](https: // github.com / rflamary / POT / blob / master / LICENSE)
 
 
 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 Network Flow solver for the linear program/ Earth Movers Distance [1].
-* Entropic regularization OT solver with Sinkhorn Knopp Algorithm [2], stabilized version [9][10] and greedy Sinkhorn [22] with optional GPU implementation (requires cupy).
-* Sinkhorn divergence [23] and entropic regularization OT  from empirical data.
-* Smooth optimal transport solvers (dual and semi-dual) for KL and squared L2 regularizations [17].
-* Non regularized Wasserstein barycenters [16] with LP solver (only small scale).
-* Bregman projections for Wasserstein barycenter [3], convolutional barycenter [21] and unmixing [4].
-* Optimal transport for domain adaptation with group lasso regularization [5]
-* Conditional gradient [6] and Generalized conditional gradient for regularized OT [7].
-* Linear OT [14] and Joint OT matrix and mapping estimation [8].
-* Wasserstein Discriminant Analysis [11] (requires autograd + pymanopt).
-* Gromov-Wasserstein distances and barycenters ([13] and regularized [12])
-* Stochastic Optimization for Large-scale Optimal Transport (semi-dual problem [18] and dual problem [19])
-* Non regularized free support Wasserstein barycenters [20].
-* Unbalanced OT with KL relaxation distance and barycenter [10, 25].
-* Screening Sinkhorn Algorithm for OT [26].
-* JCPOT algorithm for multi-source domain adaptation with target shift [27].
-
-Some demonstrations (both in Python and Jupyter Notebook format) are available in the examples folder.
+* OT Network Flow solver for the linear program / Earth Movers Distance[1].
+* Entropic regularization OT solver with Sinkhorn Knopp Algorithm[2], stabilized version[9][10] and greedy Sinkhorn[22] with optional GPU implementation(requires cupy).
+* Sinkhorn divergence[23] and entropic regularization OT from empirical data.
+* Smooth optimal transport solvers(dual and semi - dual) for KL and squared L2 regularizations[17].
+* Non regularized Wasserstein barycenters[16] with LP solver(only small scale).
+* Bregman projections for Wasserstein barycenter[3], convolutional barycenter[21] and unmixing[4].
+* Optimal transport for domain adaptation with group lasso regularization[5]
+* Conditional gradient[6] and Generalized conditional gradient for regularized OT[7].
+* Linear OT[14] and Joint OT matrix and mapping estimation[8].
+* Wasserstein Discriminant Analysis[11](requires autograd + pymanopt).
+* Gromov - Wasserstein distances and barycenters([13] and regularized[12])
+* Stochastic Optimization for Large - scale Optimal Transport(semi - dual problem[18] and dual problem[19])
+* Non regularized free support Wasserstein barycenters[20].
+* Unbalanced OT with KL relaxation distance and barycenter[10, 25].
+* Screening Sinkhorn Algorithm for OT[26].
+* JCPOT algorithm for multi - source domain adaptation with target shift[27].
+
+Some demonstrations(both in Python and Jupyter Notebook format) are available in the examples folder.
 
 #### Using and citing the toolbox
 
 If you use this toolbox in your research and find it useful, please cite POT using the following bibtex reference:
 ```
+
+
 @misc{flamary2017pot,
-title={POT Python Optimal Transport library},
-author={Flamary, R{'e}mi and Courty, Nicolas},
-url={https://github.com/rflamary/POT},
-year={2017}
-}
+      title = {POT Python Optimal Transport library},
+      author = {Flamary, R{'e}mi and Courty, Nicolas},
+      url = {https: // github.com / rflamary / POT},
+      year = {2017}
+      }
 ```
 
 ## Installation
 
-The library has been tested on Linux, MacOSX and Windows. It requires a C++ compiler for building/installing the EMD solver and relies on the following Python modules:
+The library has been tested on Linux, MacOSX and Windows. It requires a C + + compiler for building / installing the EMD solver and relies on the following Python modules:
 
-- Numpy (>=1.11)
-- Scipy (>=1.0)
-- Cython (>=0.23)
-- Matplotlib (>=1.5)
+- Numpy ( >= 1.11)
+- Scipy ( >= 1.0)
+- Cython ( >= 0.23)
+- Matplotlib ( >= 1.5)
 
 #### Pip installation
 
@@ -68,35 +70,33 @@ pip install POT
 ```
 or get the very latest version by downloading it and then running:
 ```
-python setup.py install --user # for user install (no root)
+python setup.py install - -user  # for user install (no root)
 ```
 
 
-
 #### Anaconda installation with conda-forge
 
-If you use the Anaconda python distribution, POT is available in [conda-forge](https://conda-forge.org). To install it and the required dependencies:
+If you use the Anaconda python distribution, POT is available in [conda - forge](https: // conda - forge.org). To install it and the required dependencies:
 ```
-conda install -c conda-forge pot
+conda install - c conda - forge pot
 ```
 
 #### Post installation check
 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
+Some sub - modules require additional dependences which are discussed below
 
-* **ot.dr** (Wasserstein dimensionality reduction) depends on autograd and pymanopt that can be installed with:
+* **ot.dr ** (Wasserstein dimensionality reduction) depends on autograd and pymanopt that can be installed with:
 ```
 pip install pymanopt autograd
 ```
-* **ot.gpu** (GPU accelerated OT) depends on cupy that have to be installed following instructions on [this page](https://docs-cupy.chainer.org/en/stable/install.html).
+* **ot.gpu ** (GPU accelerated OT) depends on cupy that have to be installed following instructions on[this page](https: // docs - cupy.chainer.org / en / stable / install.html).
 
 
 obviously you need CUDA installed and a compatible GPU.
@@ -107,156 +107,156 @@ obviously you need CUDA installed and a compatible GPU.
 
 * 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
+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
+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
+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/).
+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:
+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/plot_OT_1D.ipynb)
-* [OT Ground Loss](https://github.com/rflamary/POT/blob/master/notebooks/plot_OT_L1_vs_L2.ipynb)
-* [Multiple EMD computation](https://github.com/rflamary/POT/blob/master/notebooks/plot_compute_emd.ipynb)
-* [2D optimal transport on empirical distributions](https://github.com/rflamary/POT/blob/master/notebooks/plot_OT_2D_samples.ipynb)
-* [1D Wasserstein barycenter](https://github.com/rflamary/POT/blob/master/notebooks/plot_barycenter_1D.ipynb)
-* [OT with user provided regularization](https://github.com/rflamary/POT/blob/master/notebooks/plot_optim_OTreg.ipynb)
-* [Domain adaptation with optimal transport](https://github.com/rflamary/POT/blob/master/notebooks/plot_otda_d2.ipynb)
-* [Color transfer in images](https://github.com/rflamary/POT/blob/master/notebooks/plot_otda_color_images.ipynb)
-* [OT mapping estimation for domain adaptation](https://github.com/rflamary/POT/blob/master/notebooks/plot_otda_mapping.ipynb)
-* [OT mapping estimation for color transfer in images](https://github.com/rflamary/POT/blob/master/notebooks/plot_otda_mapping_colors_images.ipynb)
-* [Wasserstein Discriminant Analysis](https://github.com/rflamary/POT/blob/master/notebooks/plot_WDA.ipynb)
-* [Gromov Wasserstein](https://github.com/rflamary/POT/blob/master/notebooks/plot_gromov.ipynb)
-* [Gromov Wasserstein Barycenter](https://github.com/rflamary/POT/blob/master/notebooks/plot_gromov_barycenter.ipynb)
-* [Fused Gromov Wasserstein](https://github.com/rflamary/POT/blob/master/notebooks/plot_fgw.ipynb)
-* [Fused Gromov Wasserstein Barycenter](https://github.com/rflamary/POT/blob/master/notebooks/plot_barycenter_fgw.ipynb)
+* [1D optimal transport](https: // github.com / rflamary / POT / blob / master / notebooks / plot_OT_1D.ipynb)
+* [OT Ground Loss](https: // github.com / rflamary / POT / blob / master / notebooks / plot_OT_L1_vs_L2.ipynb)
+* [Multiple EMD computation](https: // github.com / rflamary / POT / blob / master / notebooks / plot_compute_emd.ipynb)
+* [2D optimal transport on empirical distributions](https: // github.com / rflamary / POT / blob / master / notebooks / plot_OT_2D_samples.ipynb)
+* [1D Wasserstein barycenter](https: // github.com / rflamary / POT / blob / master / notebooks / plot_barycenter_1D.ipynb)
+* [OT with user provided regularization](https: // github.com / rflamary / POT / blob / master / notebooks / plot_optim_OTreg.ipynb)
+* [Domain adaptation with optimal transport](https: // github.com / rflamary / POT / blob / master / notebooks / plot_otda_d2.ipynb)
+* [Color transfer in images](https: // github.com / rflamary / POT / blob / master / notebooks / plot_otda_color_images.ipynb)
+* [OT mapping estimation for domain adaptation](https: // github.com / rflamary / POT / blob / master / notebooks / plot_otda_mapping.ipynb)
+* [OT mapping estimation for color transfer in images](https: // github.com / rflamary / POT / blob / master / notebooks / plot_otda_mapping_colors_images.ipynb)
+* [Wasserstein Discriminant Analysis](https: // github.com / rflamary / POT / blob / master / notebooks / plot_WDA.ipynb)
+* [Gromov Wasserstein](https: // github.com / rflamary / POT / blob / master / notebooks / plot_gromov.ipynb)
+* [Gromov Wasserstein Barycenter](https: // github.com / rflamary / POT / blob / master / notebooks / plot_gromov_barycenter.ipynb)
+* [Fused Gromov Wasserstein](https: // github.com / rflamary / POT / blob / master / notebooks / plot_fgw.ipynb)
+* [Fused Gromov Wasserstein Barycenter](https: // github.com / rflamary / POT / blob / master / notebooks / plot_barycenter_fgw.ipynb)
 
 
-You can also see the notebooks with [Jupyter nbviewer](https://nbviewer.jupyter.org/github/rflamary/POT/tree/master/notebooks/).
+You can also see the notebooks with [Jupyter nbviewer](https: // nbviewer.jupyter.org / github / rflamary / POT / tree / master / notebooks / ).
 
 ## Acknowledgements
 
 This toolbox has been created and is maintained by
 
-* [Rémi Flamary](http://remi.flamary.com/)
-* [Nicolas Courty](http://people.irisa.fr/Nicolas.Courty/)
+* [Rémi Flamary](http: // remi.flamary.com / )
+* [Nicolas Courty](http: // people.irisa.fr / Nicolas.Courty / )
 
-The contributors to this library are 
+The contributors to this library are
 
-* [Alexandre Gramfort](http://alexandre.gramfort.net/)
-* [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)
-* [Nathalie Gayraud](https://www.linkedin.com/in/nathalie-t-h-gayraud/?ppe=1)
-* [Stanislas Chambon](https://slasnista.github.io/)
-* [Antoine Rolet](https://arolet.github.io/)
-* Erwan Vautier (Gromov-Wasserstein)
-* [Kilian Fatras](https://kilianfatras.github.io/)
-* [Alain Rakotomamonjy](https://sites.google.com/site/alainrakotomamonjy/home)
-* [Vayer Titouan](https://tvayer.github.io/)
-* [Hicham Janati](https://hichamjanati.github.io/) (Unbalanced OT)
-* [Romain Tavenard](https://rtavenar.github.io/) (1d Wasserstein)
-* [Mokhtar Z. Alaya](http://mzalaya.github.io/) (Screenkhorn)
+* [Alexandre Gramfort](http: // alexandre.gramfort.net / )
+* [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)
+* [Nathalie Gayraud](https: // www.linkedin.com / in / nathalie - t - h - gayraud /?ppe=1)
+* [Stanislas Chambon](https: // slasnista.github.io / )
+* [Antoine Rolet](https: // arolet.github.io / )
+* Erwan Vautier(Gromov - Wasserstein)
+* [Kilian Fatras](https: // kilianfatras.github.io / )
+* [Alain Rakotomamonjy](https: // sites.google.com / site / alainrakotomamonjy / home)
+* [Vayer Titouan](https: // tvayer.github.io / )
+* [Hicham Janati](https: // hichamjanati.github.io / ) (Unbalanced OT)
+* [Romain Tavenard](https: // rtavenar.github.io / ) (1d Wasserstein)
+* [Mokhtar Z. Alaya](http: // mzalaya.github.io / ) (Screenkhorn)
 
-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):
+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)
-* [Marco Cuturi](http://marcocuturi.net/) (Sinkhorn Knopp in Matlab/Cuda)
+* [Gabriel Peyré](http: // gpeyre.github.io / ) (Wasserstein Barycenters in Matlab)
+* [Nicolas Bonneel](http: // liris.cnrs.fr / ~nbonneel /) (C++ code for EMD)
+* [Marco Cuturi](http: // marcocuturi.net / ) (Sinkhorn Knopp in Matlab/Cuda)
 
 
 ## Contributions and code of conduct
 
-Every contribution is welcome and should respect the [contribution guidelines](CONTRIBUTING.md). Each member of the project is expected to follow the [code of conduct](CODE_OF_CONDUCT.md).
+Every contribution is welcome and should respect the[contribution guidelines](CONTRIBUTING.md). Each member of the project is expected to follow the[code of conduct](CODE_OF_CONDUCT.md).
 
 ## Support
 
 You can ask questions and join the development discussion:
 
-* On the [POT Slack channel](https://pot-toolbox.slack.com)
-* On the POT [mailing list](https://mail.python.org/mm3/mailman3/lists/pot.python.org/)
+* On the[POT Slack channel](https: // pot - toolbox.slack.com)
+* On the POT [mailing list](https: // mail.python.org / mm3 / mailman3 / lists / pot.python.org / )
 
 
-You can also post bug reports and feature requests in Github issues. Make sure to read our [guidelines](CONTRIBUTING.md) first.
+You can also post bug reports and feature requests in Github issues. Make sure to read our[guidelines](CONTRIBUTING.md) first.
 
 ## 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.
+[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).
+[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.
+[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.
+[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
+[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.
+[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.
+[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 (2016), [Mapping estimation for discrete optimal transport](http://remi.flamary.com/biblio/perrot2016mapping.pdf), Neural Information Processing Systems (NIPS).
+[8] M. Perrot, N. Courty, R. Flamary, A. Habrard(2016), [Mapping estimation for discrete optimal transport](http: // remi.flamary.com / biblio / perrot2016mapping.pdf), Neural Information Processing Systems(NIPS).
 
-[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.
+[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.
+[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.
+[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.
 
-[12] Gabriel Peyré, Marco Cuturi, and Justin Solomon (2016), [Gromov-Wasserstein averaging of kernel and distance matrices](http://proceedings.mlr.press/v48/peyre16.html)  International Conference on Machine Learning (ICML).
+[12] Gabriel Peyré, Marco Cuturi, and Justin Solomon(2016), [Gromov - Wasserstein averaging of kernel and distance matrices](http: // proceedings.mlr.press / v48 / peyre16.html)  International Conference on Machine Learning(ICML).
 
-[13] Mémoli, Facundo (2011). [Gromov–Wasserstein distances and the metric approach to object matching](https://media.adelaide.edu.au/acvt/Publications/2011/2011-Gromov%E2%80%93Wasserstein%20Distances%20and%20the%20Metric%20Approach%20to%20Object%20Matching.pdf). Foundations of computational mathematics 11.4 : 417-487.
+[13] Mémoli, Facundo(2011). [Gromov–Wasserstein distances and the metric approach to object matching](https: // media.adelaide.edu.au / acvt / Publications / 2011 / 2011 - Gromov % E2 % 80 % 93Wasserstein % 20Distances % 20and % 20the % 20Metric % 20Approach % 20to % 20Object % 20Matching.pdf). Foundations of computational mathematics 11.4: 417 - 487.
 
-[14] Knott, M. and Smith, C. S. (1984).[On the optimal mapping of distributions](https://link.springer.com/article/10.1007/BF00934745), Journal of Optimization Theory and Applications Vol 43.
+[14] Knott, M. and Smith, C. S. (1984).[On the optimal mapping of distributions](https: // link.springer.com / article / 10.1007 / BF00934745), Journal of Optimization Theory and Applications Vol 43.
 
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