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Merge pull request #140 from ievred/laplace_da
[MRG] Laplace regularized OTDA
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‎README.md

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[![PyPI version](https://badge.fury.io/py/POT.svg)](https://badge.fury.io/py/POT)
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[![Anaconda Cloud](https://anaconda.org/conda-forge/pot/badges/version.svg)](https://anaconda.org/conda-forge/pot)
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[![Build Status](https://travis-ci.org/rflamary/POT.svg?branch=master)](https://travis-ci.org/rflamary/POT)
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[![Build Status](https://travis-ci.org/rflamary/POT.svg?branch=master)](https://travis-ci.org/PythonOT/POT)
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[![Documentation Status](https://readthedocs.org/projects/pot/badge/?version=latest)](http://pot.readthedocs.io/en/latest/?badge=latest)
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[![Downloads](https://pepy.tech/badge/pot)](https://pepy.tech/project/pot)
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[![Anaconda downloads](https://anaconda.org/conda-forge/pot/badges/downloads.svg)](https://anaconda.org/conda-forge/pot)
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[![License](https://anaconda.org/conda-forge/pot/badges/license.svg)](https://github.com/rflamary/POT/blob/master/LICENSE)
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[![License](https://anaconda.org/conda-forge/pot/badges/license.svg)](https://github.com/PythonOT/POT/blob/master/LICENSE)
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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 [5]
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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].
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* Wasserstein Discriminant Analysis [11] (requires autograd + pymanopt).
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The examples folder contain several examples and use case for the library. The full documentation is available on [Readthedocs](http://pot.readthedocs.io/).
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Here is a list of the Python notebooks available [here](https://github.com/rflamary/POT/blob/master/notebooks/) if you want a quick look:
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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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* [1D optimal transport](https://github.com/rflamary/POT/blob/master/notebooks/plot_OT_1D.ipynb)
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* [OT Ground Loss](https://github.com/rflamary/POT/blob/master/notebooks/plot_OT_L1_vs_L2.ipynb)
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* [Multiple EMD computation](https://github.com/rflamary/POT/blob/master/notebooks/plot_compute_emd.ipynb)
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* [2D optimal transport on empirical distributions](https://github.com/rflamary/POT/blob/master/notebooks/plot_OT_2D_samples.ipynb)
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* [1D Wasserstein barycenter](https://github.com/rflamary/POT/blob/master/notebooks/plot_barycenter_1D.ipynb)
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* [OT with user provided regularization](https://github.com/rflamary/POT/blob/master/notebooks/plot_optim_OTreg.ipynb)
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* [Domain adaptation with optimal transport](https://github.com/rflamary/POT/blob/master/notebooks/plot_otda_d2.ipynb)
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* [Color transfer in images](https://github.com/rflamary/POT/blob/master/notebooks/plot_otda_color_images.ipynb)
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* [OT mapping estimation for domain adaptation](https://github.com/rflamary/POT/blob/master/notebooks/plot_otda_mapping.ipynb)
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* [OT mapping estimation for color transfer in images](https://github.com/rflamary/POT/blob/master/notebooks/plot_otda_mapping_colors_images.ipynb)
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* [Wasserstein Discriminant Analysis](https://github.com/rflamary/POT/blob/master/notebooks/plot_WDA.ipynb)
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* [Gromov Wasserstein](https://github.com/rflamary/POT/blob/master/notebooks/plot_gromov.ipynb)
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* [Gromov Wasserstein Barycenter](https://github.com/rflamary/POT/blob/master/notebooks/plot_gromov_barycenter.ipynb)
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* [Fused Gromov Wasserstein](https://github.com/rflamary/POT/blob/master/notebooks/plot_fgw.ipynb)
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* [Fused Gromov Wasserstein Barycenter](https://github.com/rflamary/POT/blob/master/notebooks/plot_barycenter_fgw.ipynb)
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* [1D optimal transport](https://github.com/PythonOT/POT/blob/master/notebooks/plot_OT_1D.ipynb)
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* [OT Ground Loss](https://github.com/PythonOT/POT/blob/master/notebooks/plot_OT_L1_vs_L2.ipynb)
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* [Multiple EMD computation](https://github.com/PythonOT/POT/blob/master/notebooks/plot_compute_emd.ipynb)
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* [2D optimal transport on empirical distributions](https://github.com/PythonOT/POT/blob/master/notebooks/plot_OT_2D_samples.ipynb)
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* [1D Wasserstein barycenter](https://github.com/PythonOT/POT/blob/master/notebooks/plot_barycenter_1D.ipynb)
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* [OT with user provided regularization](https://github.com/PythonOT/POT/blob/master/notebooks/plot_optim_OTreg.ipynb)
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* [Domain adaptation with optimal transport](https://github.com/PythonOT/POT/blob/master/notebooks/plot_otda_d2.ipynb)
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* [Color transfer in images](https://github.com/PythonOT/POT/blob/master/notebooks/plot_otda_color_images.ipynb)
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* [OT mapping estimation for domain adaptation](https://github.com/PythonOT/POT/blob/master/notebooks/plot_otda_mapping.ipynb)
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* [OT mapping estimation for color transfer in images](https://github.com/PythonOT/POT/blob/master/notebooks/plot_otda_mapping_colors_images.ipynb)
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* [Wasserstein Discriminant Analysis](https://github.com/PythonOT/POT/blob/master/notebooks/plot_WDA.ipynb)
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* [Gromov Wasserstein](https://github.com/PythonOT/POT/blob/master/notebooks/plot_gromov.ipynb)
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* [Gromov Wasserstein Barycenter](https://github.com/PythonOT/POT/blob/master/notebooks/plot_gromov_barycenter.ipynb)
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* [Fused Gromov Wasserstein](https://github.com/PythonOT/POT/blob/master/notebooks/plot_fgw.ipynb)
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* [Fused Gromov Wasserstein Barycenter](https://github.com/PythonOT/POT/blob/master/notebooks/plot_barycenter_fgw.ipynb)
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You can also see the notebooks with [Jupyter nbviewer](https://nbviewer.jupyter.org/github/rflamary/POT/tree/master/notebooks/).
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You can also see the notebooks with [Jupyter nbviewer](https://nbviewer.jupyter.org/github/PythonOT/POT/tree/master/notebooks/).
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## Acknowledgements
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* [Hicham Janati](https://hichamjanati.github.io/) (Unbalanced OT)
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* [Romain Tavenard](https://rtavenar.github.io/) (1d Wasserstein)
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* [Mokhtar Z. Alaya](http://mzalaya.github.io/) (Screenkhorn)
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* [Ievgen Redko](https://ievred.github.io/)
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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):
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[28] Caffarelli, L. A., McCann, R. J. (2020). [Free boundaries in optimal transport and Monge-Ampere obstacle problems](http://www.math.toronto.edu/~mccann/papers/annals2010.pdf), Annals of mathematics, 673-730.
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[29] Chapel, L., Alaya, M., Gasso, G. (2019). [Partial Gromov-Wasserstein with Applications on Positive-Unlabeled Learning](https://arxiv.org/abs/2002.08276), arXiv preprint arXiv:2002.08276.
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[29] Chapel, L., Alaya, M., Gasso, G. (2019). [Partial Gromov-Wasserstein with Applications on Positive-Unlabeled Learning](https://arxiv.org/abs/2002.08276), arXiv preprint arXiv:2002.08276.
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[30] Flamary R., Courty N., Tuia D., Rakotomamonjy A. (2014). [Optimal transport with Laplacian regularization: Applications to domain adaptation and shape matching](https://remi.flamary.com/biblio/flamary2014optlaplace.pdf), NIPS Workshop on Optimal Transport and Machine Learning OTML, 2014.

‎examples/plot_otda_laplacian.py

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# -*- coding: utf-8 -*-
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"""
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======================================================
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OT with Laplacian regularization for domain adaptation
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======================================================
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This example introduces a domain adaptation in a 2D setting and OTDA
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approach with Laplacian regularization.
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"""
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# Authors: Ievgen Redko <[email protected]>
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# License: MIT License
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import matplotlib.pylab as pl
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import ot
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##############################################################################
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# Generate data
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# -------------
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n_source_samples = 150
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n_target_samples = 150
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Xs, ys = ot.datasets.make_data_classif('3gauss', n_source_samples)
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Xt, yt = ot.datasets.make_data_classif('3gauss2', n_target_samples)
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##############################################################################
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# Instantiate the different transport algorithms and fit them
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# -----------------------------------------------------------
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# EMD Transport
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ot_emd = ot.da.EMDTransport()
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ot_emd.fit(Xs=Xs, Xt=Xt)
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# Sinkhorn Transport
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ot_sinkhorn = ot.da.SinkhornTransport(reg_e=.01)
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ot_sinkhorn.fit(Xs=Xs, Xt=Xt)
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# EMD Transport with Laplacian regularization
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ot_emd_laplace = ot.da.EMDLaplaceTransport(reg_lap=100, reg_src=1)
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ot_emd_laplace.fit(Xs=Xs, Xt=Xt)
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# transport source samples onto target samples
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transp_Xs_emd = ot_emd.transform(Xs=Xs)
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transp_Xs_sinkhorn = ot_sinkhorn.transform(Xs=Xs)
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transp_Xs_emd_laplace = ot_emd_laplace.transform(Xs=Xs)
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##############################################################################
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# Fig 1 : plots source and target samples
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# ---------------------------------------
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pl.figure(1, figsize=(10, 5))
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pl.subplot(1, 2, 1)
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pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples')
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pl.xticks([])
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pl.yticks([])
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pl.legend(loc=0)
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pl.title('Source samples')
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pl.subplot(1, 2, 2)
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pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples')
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pl.xticks([])
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pl.yticks([])
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pl.legend(loc=0)
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pl.title('Target samples')
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pl.tight_layout()
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##############################################################################
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# Fig 2 : plot optimal couplings and transported samples
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# ------------------------------------------------------
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param_img = {'interpolation': 'nearest'}
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pl.figure(2, figsize=(15, 8))
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pl.subplot(2, 3, 1)
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pl.imshow(ot_emd.coupling_, **param_img)
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pl.xticks([])
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pl.yticks([])
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pl.title('Optimal coupling\nEMDTransport')
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pl.figure(2, figsize=(15, 8))
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pl.subplot(2, 3, 2)
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pl.imshow(ot_sinkhorn.coupling_, **param_img)
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pl.xticks([])
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pl.yticks([])
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pl.title('Optimal coupling\nSinkhornTransport')
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pl.subplot(2, 3, 3)
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pl.imshow(ot_emd_laplace.coupling_, **param_img)
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pl.xticks([])
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pl.yticks([])
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pl.title('Optimal coupling\nEMDLaplaceTransport')
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pl.subplot(2, 3, 4)
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pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',
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label='Target samples', alpha=0.3)
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pl.scatter(transp_Xs_emd[:, 0], transp_Xs_emd[:, 1], c=ys,
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marker='+', label='Transp samples', s=30)
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pl.xticks([])
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pl.yticks([])
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pl.title('Transported samples\nEmdTransport')
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pl.legend(loc="lower left")
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pl.subplot(2, 3, 5)
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pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',
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label='Target samples', alpha=0.3)
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pl.scatter(transp_Xs_sinkhorn[:, 0], transp_Xs_sinkhorn[:, 1], c=ys,
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marker='+', label='Transp samples', s=30)
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pl.xticks([])
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pl.yticks([])
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pl.title('Transported samples\nSinkhornTransport')
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pl.subplot(2, 3, 6)
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pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',
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label='Target samples', alpha=0.3)
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pl.scatter(transp_Xs_emd_laplace[:, 0], transp_Xs_emd_laplace[:, 1], c=ys,
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marker='+', label='Transp samples', s=30)
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pl.xticks([])
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pl.yticks([])
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pl.title('Transported samples\nEMDLaplaceTransport')
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pl.tight_layout()
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pl.show()

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