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* OT Network Flow solver for the linear program/ Earth Movers Distance [1].
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* Entropic regularization OT solver with Sinkhorn Knopp Algorithm [2], stabilized version [9][10] and greedy Sinkhorn [22] with optional GPU implementation (requires cupy).
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POT provides the following generic OT solvers (links to examples):
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*[OT Network Simplex solver](https://pythonot.github.io/auto_examples/plot_OT_1D.html) for the linear program/ Earth Movers Distance [1] .
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*[Conditional gradient](https://pythonot.github.io/auto_examples/plot_optim_OTreg.html)[6] and [Generalized conditional gradient](https://pythonot.github.io/auto_examples/plot_optim_OTreg.html) for regularized OT [7].
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* Entropic regularization OT solver with [Sinkhorn Knopp Algorithm](https://pythonot.github.io/auto_examples/plot_OT_1D.html)[2] , stabilized version [9][10], greedy Sinkhorn [22] and [Screening Sinkhorn [26]](https://pythonot.github.io/auto_examples/plot_screenkhorn_1D.html) with optional GPU implementation (requires cupy).
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* Bregman projections for [Wasserstein barycenter](https://pythonot.github.io/auto_examples/plot_barycenter_lp_vs_entropic.html)[3], [convolutional barycenter](https://pythonot.github.io/auto_examples/plot_convolutional_barycenter.html)[21] and unmixing [4].
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* Sinkhorn divergence [23] and entropic regularization OT from empirical data.
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* Smooth optimal transport solvers (dual and semi-dual) for KL and squared L2 regularizations [17].
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* Non regularized Wasserstein barycenters [16] with LP solver (only small scale).
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* Bregman projections for Wasserstein barycenter [3], convolutional barycenter [21] and unmixing [4].
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* Optimal transport for domain adaptation with group lasso regularization and Laplacian regularization [5][30]
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* Conditional gradient [6] and Generalized conditional gradient for regularized OT [7].
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* Linear OT [14] and Joint OT matrix and mapping estimation [8].
* Gromov-Wasserstein distances and barycenters ([13] and regularized [12])
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* Stochastic Optimization for Large-scale Optimal Transport (semi-dual problem [18] and dual problem [19])
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* Non regularized free support Wasserstein barycenters [20].
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* Unbalanced OT with KL relaxation distance and barycenter [10, 25].
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* Screening Sinkhorn Algorithm for OT [26].
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* JCPOT algorithm for multi-source domain adaptation with target shift [27].
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* Partial Wasserstein and Gromov-Wasserstein (exact [29] and entropic [3] formulations).
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Some demonstrations (both in Python and Jupyter Notebook format) are available in the examples folder.
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*[Smooth optimal transport solvers](https://pythonot.github.io/auto_examples/plot_OT_1D_smooth.html) (dual and semi-dual) for KL and squared L2 regularizations [17].
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* Non regularized [Wasserstein barycenters [16]](https://pythonot.github.io/auto_examples/plot_barycenter_lp_vs_entropic.html)) with LP solver (only small scale).
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*[Gromov-Wasserstein distances](https://pythonot.github.io/auto_examples/plot_gromov.html) and [GW barycenters](https://pythonot.github.io/auto_examples/plot_gromov_barycenter.html) (exact [13] and regularized [12])
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*[Fused-Gromov-Wasserstein distances solver](https://pythonot.github.io/auto_examples/plot_fgw.html#sphx-glr-auto-examples-plot-fgw-py) and [FGW barycenters](https://pythonot.github.io/auto_examples/plot_barycenter_fgw.html)[24]
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*[Stochastic solver](https://pythonot.github.io/auto_examples/plot_stochastic.html) for Large-scale Optimal Transport (semi-dual problem [18] and dual problem [19])
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* Non regularized [free support Wasserstein barycenters](https://pythonot.github.io/auto_examples/plot_free_support_barycenter.html)[20].
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*[Unbalanced OT](https://pythonot.github.io/auto_examples/plot_UOT_1D.html) with KL relaxation and [barycenter](https://pythonot.github.io/auto_examples/plot_UOT_barycenter_1D.html)[10, 25].
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*[Partial Wasserstein and Gromov-Wasserstein](https://pythonot.github.io/auto_examples/plot_partial_wass_and_gromov.html) (exact [29] and entropic [3]
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formulations).
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POT provides the following Machine Learning related solvers:
with [group lasso regularization](https://pythonot.github.io/auto_examples/plot_otda_classes.html), [Laplacian regularization](https://pythonot.github.io/auto_examples/plot_otda_laplacian.html)[5][30] and [semi
*[Linear OT mapping](https://pythonot.github.io/auto_examples/plot_otda_linear_mapping.html)[14] and [Joint OT mapping estimation](https://pythonot.github.io/auto_examples/plot_otda_mapping.html)[8].
*[JCPOT algorithm for multi-source domain adaptation with target shift](https://pythonot.github.io/auto_examples/plot_otda_jcpot.html)[27].
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Some demonstrations are available in the [documentation](https://pythonot.github.io/auto_examples/index.html).
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#### Using and citing the toolbox
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If you use this toolbox in your research and find it useful, please cite POT using the following bibtex reference:
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If you use this toolbox in your research and find it useful, please cite POT
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using the following bibtex reference:
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```
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Rémi Flamary and Nicolas Courty, POT Python Optimal Transport library, Website: https://pythonot.github.io/, 2017
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```
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In Bibtex format:
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```
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@misc{flamary2017pot,
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title={POT Python Optimal Transport library},
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author={Flamary, R{'e}mi and Courty, Nicolas},
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url={https://github.com/rflamary/POT},
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url={https://pythonot.github.io/},
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year={2017}
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}
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```
@@ -136,35 +151,11 @@ T_reg=ot.sinkhorn(a,b,M,reg) # entropic regularized OT
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ba=ot.barycenter(A,M,reg) # reg is regularization parameter
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```
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### Examples and Notebooks
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The examples folder contain several examples and use case for the library. The full documentation is available on [https://PythonOT.github.io/](https://PythonOT.github.io/).
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Here is a list of the Python notebooks available [here](https://github.com/PythonOT/POT/blob/master/notebooks/) if you want a quick look:
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