.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        Click :ref:`here <sphx_glr_download_auto_examples_plot_otda_d2.py>`     to download the full example code
    .. rst-class:: sphx-glr-example-title

    .. _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:: default


    # 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:: default


    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:: default


    # 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:: default


    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
    :class: sphx-glr-single-img





Fig 2 : plots optimal couplings for the different methods
---------------------------------------------------------


.. code-block:: default

    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_002.png
    :class: sphx-glr-single-img





Fig 3 : plot transported samples
--------------------------------


.. code-block:: default


    # 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_003.png
    :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

    /home/circleci/project/examples/plot_otda_d2.py:172: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure.
      pl.show()





.. rst-class:: sphx-glr-timing

   **Total running time of the script:** ( 0 minutes  7.594 seconds)


.. _sphx_glr_download_auto_examples_plot_otda_d2.py:


.. only :: html

 .. container:: sphx-glr-footer
    :class: sphx-glr-footer-example



  .. container:: sphx-glr-download sphx-glr-download-python

     :download:`Download Python source code: plot_otda_d2.py <plot_otda_d2.py>`



  .. container:: sphx-glr-download sphx-glr-download-jupyter

     :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.github.io>`_