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-
-
-.. _sphx_glr_auto_examples_plot_otda_d2.py:
-
-
-===================================================
-OT for domain adaptation on empirical distributions
-===================================================
-
-This example introduces a domain adaptation in a 2D setting. It explicits
-the problem of domain adaptation and introduces some optimal transport
-approaches to solve it.
-
-Quantities such as optimal couplings, greater coupling coefficients and
-transported samples are represented in order to give a visual understanding
-of what the transport methods are doing.
-
-
-
-.. code-block:: python
-
-
- # Authors: Remi Flamary <remi.flamary@unice.fr>
- # Stanislas Chambon <stan.chambon@gmail.com>
- #
- # License: MIT License
-
- import matplotlib.pylab as pl
- import ot
- import ot.plot
-
-
-
-
-
-
-
-generate data
--------------
-
-
-
-.. code-block:: python
-
-
- n_samples_source = 150
- n_samples_target = 150
-
- Xs, ys = ot.datasets.make_data_classif('3gauss', n_samples_source)
- Xt, yt = ot.datasets.make_data_classif('3gauss2', n_samples_target)
-
- # Cost matrix
- M = ot.dist(Xs, Xt, metric='sqeuclidean')
-
-
-
-
-
-
-
-
-Instantiate the different transport algorithms and fit them
------------------------------------------------------------
-
-
-
-.. code-block:: python
-
-
- # EMD Transport
- ot_emd = ot.da.EMDTransport()
- ot_emd.fit(Xs=Xs, Xt=Xt)
-
- # Sinkhorn Transport
- ot_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1)
- ot_sinkhorn.fit(Xs=Xs, Xt=Xt)
-
- # Sinkhorn Transport with Group lasso regularization
- ot_lpl1 = ot.da.SinkhornLpl1Transport(reg_e=1e-1, reg_cl=1e0)
- ot_lpl1.fit(Xs=Xs, ys=ys, Xt=Xt)
-
- # transport source samples onto target samples
- transp_Xs_emd = ot_emd.transform(Xs=Xs)
- transp_Xs_sinkhorn = ot_sinkhorn.transform(Xs=Xs)
- transp_Xs_lpl1 = ot_lpl1.transform(Xs=Xs)
-
-
-
-
-
-
-
-
-Fig 1 : plots source and target samples + matrix of pairwise distance
----------------------------------------------------------------------
-
-
-
-.. code-block:: python
-
-
- pl.figure(1, figsize=(10, 10))
- pl.subplot(2, 2, 1)
- pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples')
- pl.xticks([])
- pl.yticks([])
- pl.legend(loc=0)
- pl.title('Source samples')
-
- pl.subplot(2, 2, 2)
- pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples')
- pl.xticks([])
- pl.yticks([])
- pl.legend(loc=0)
- pl.title('Target samples')
-
- pl.subplot(2, 2, 3)
- pl.imshow(M, interpolation='nearest')
- pl.xticks([])
- pl.yticks([])
- pl.title('Matrix of pairwise distances')
- pl.tight_layout()
-
-
-
-
-
-.. image:: /auto_examples/images/sphx_glr_plot_otda_d2_001.png
- :align: center
-
-
-
-
-Fig 2 : plots optimal couplings for the different methods
----------------------------------------------------------
-
-
-
-.. code-block:: python
-
- pl.figure(2, figsize=(10, 6))
-
- pl.subplot(2, 3, 1)
- pl.imshow(ot_emd.coupling_, interpolation='nearest')
- pl.xticks([])
- pl.yticks([])
- pl.title('Optimal coupling\nEMDTransport')
-
- pl.subplot(2, 3, 2)
- pl.imshow(ot_sinkhorn.coupling_, interpolation='nearest')
- pl.xticks([])
- pl.yticks([])
- pl.title('Optimal coupling\nSinkhornTransport')
-
- pl.subplot(2, 3, 3)
- pl.imshow(ot_lpl1.coupling_, interpolation='nearest')
- pl.xticks([])
- pl.yticks([])
- pl.title('Optimal coupling\nSinkhornLpl1Transport')
-
- pl.subplot(2, 3, 4)
- ot.plot.plot2D_samples_mat(Xs, Xt, ot_emd.coupling_, c=[.5, .5, 1])
- pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples')
- pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples')
- pl.xticks([])
- pl.yticks([])
- pl.title('Main coupling coefficients\nEMDTransport')
-
- pl.subplot(2, 3, 5)
- ot.plot.plot2D_samples_mat(Xs, Xt, ot_sinkhorn.coupling_, c=[.5, .5, 1])
- pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples')
- pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples')
- pl.xticks([])
- pl.yticks([])
- pl.title('Main coupling coefficients\nSinkhornTransport')
-
- pl.subplot(2, 3, 6)
- ot.plot.plot2D_samples_mat(Xs, Xt, ot_lpl1.coupling_, c=[.5, .5, 1])
- pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples')
- pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples')
- pl.xticks([])
- pl.yticks([])
- pl.title('Main coupling coefficients\nSinkhornLpl1Transport')
- pl.tight_layout()
-
-
-
-
-
-.. image:: /auto_examples/images/sphx_glr_plot_otda_d2_003.png
- :align: center
-
-
-
-
-Fig 3 : plot transported samples
---------------------------------
-
-
-
-.. code-block:: python
-
-
- # display transported samples
- pl.figure(4, figsize=(10, 4))
- pl.subplot(1, 3, 1)
- pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',
- label='Target samples', alpha=0.5)
- pl.scatter(transp_Xs_emd[:, 0], transp_Xs_emd[:, 1], c=ys,
- marker='+', label='Transp samples', s=30)
- pl.title('Transported samples\nEmdTransport')
- pl.legend(loc=0)
- pl.xticks([])
- pl.yticks([])
-
- pl.subplot(1, 3, 2)
- pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',
- label='Target samples', alpha=0.5)
- pl.scatter(transp_Xs_sinkhorn[:, 0], transp_Xs_sinkhorn[:, 1], c=ys,
- marker='+', label='Transp samples', s=30)
- pl.title('Transported samples\nSinkhornTransport')
- pl.xticks([])
- pl.yticks([])
-
- pl.subplot(1, 3, 3)
- pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',
- label='Target samples', alpha=0.5)
- pl.scatter(transp_Xs_lpl1[:, 0], transp_Xs_lpl1[:, 1], c=ys,
- marker='+', label='Transp samples', s=30)
- pl.title('Transported samples\nSinkhornLpl1Transport')
- pl.xticks([])
- pl.yticks([])
-
- pl.tight_layout()
- pl.show()
-
-
-
-.. image:: /auto_examples/images/sphx_glr_plot_otda_d2_006.png
- :align: center
-
-
-
-
-**Total running time of the script:** ( 0 minutes 35.515 seconds)
-
-
-
-.. only :: html
-
- .. container:: sphx-glr-footer
-
-
- .. container:: sphx-glr-download
-
- :download:`Download Python source code: plot_otda_d2.py <plot_otda_d2.py>`
-
-
-
- .. container:: sphx-glr-download
-
- :download:`Download Jupyter notebook: plot_otda_d2.ipynb <plot_otda_d2.ipynb>`
-
-
-.. only:: html
-
- .. rst-class:: sphx-glr-signature
-
- `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_