.. _sphx_glr_auto_examples_plot_gromov.py:


==========================
Gromov-Wasserstein example
==========================

This example is designed to show how to use the Gromov-Wassertsein distance
computation in POT.



.. code-block:: python


    # Author: Erwan Vautier <erwan.vautier@gmail.com>
    #         Nicolas Courty <ncourty@irisa.fr>
    #
    # License: MIT License

    import scipy as sp
    import numpy as np
    import matplotlib.pylab as pl
    from mpl_toolkits.mplot3d import Axes3D  # noqa
    import ot








Sample two Gaussian distributions (2D and 3D)
 ---------------------------------------------

 The Gromov-Wasserstein distance allows to compute distances with samples that
 do not belong to the same metric space. For demonstration purpose, we sample
 two Gaussian distributions in 2- and 3-dimensional spaces.



.. code-block:: python



    n_samples = 30  # nb samples

    mu_s = np.array([0, 0])
    cov_s = np.array([[1, 0], [0, 1]])

    mu_t = np.array([4, 4, 4])
    cov_t = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])


    xs = ot.datasets.get_2D_samples_gauss(n_samples, mu_s, cov_s)
    P = sp.linalg.sqrtm(cov_t)
    xt = np.random.randn(n_samples, 3).dot(P) + mu_t








Plotting the distributions
--------------------------



.. code-block:: python



    fig = pl.figure()
    ax1 = fig.add_subplot(121)
    ax1.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
    ax2 = fig.add_subplot(122, projection='3d')
    ax2.scatter(xt[:, 0], xt[:, 1], xt[:, 2], color='r')
    pl.show()





.. image:: /auto_examples/images/sphx_glr_plot_gromov_001.png
    :align: center




Compute distance kernels, normalize them and then display
---------------------------------------------------------



.. code-block:: python



    C1 = sp.spatial.distance.cdist(xs, xs)
    C2 = sp.spatial.distance.cdist(xt, xt)

    C1 /= C1.max()
    C2 /= C2.max()

    pl.figure()
    pl.subplot(121)
    pl.imshow(C1)
    pl.subplot(122)
    pl.imshow(C2)
    pl.show()




.. image:: /auto_examples/images/sphx_glr_plot_gromov_002.png
    :align: center




Compute Gromov-Wasserstein plans and distance
---------------------------------------------



.. code-block:: python



    p = ot.unif(n_samples)
    q = ot.unif(n_samples)

    gw = ot.gromov_wasserstein(C1, C2, p, q, 'square_loss', epsilon=5e-4)
    gw_dist = ot.gromov_wasserstein2(C1, C2, p, q, 'square_loss', epsilon=5e-4)

    print('Gromov-Wasserstein distances between the distribution: ' + str(gw_dist))

    pl.figure()
    pl.imshow(gw, cmap='jet')
    pl.colorbar()
    pl.show()



.. image:: /auto_examples/images/sphx_glr_plot_gromov_003.png
    :align: center


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

 Out::

    Gromov-Wasserstein distances between the distribution: 0.225058076974


**Total running time of the script:** ( 0 minutes  4.070 seconds)



.. container:: sphx-glr-footer


  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

     :download:`Download Jupyter notebook: plot_gromov.ipynb <plot_gromov.ipynb>`

.. rst-class:: sphx-glr-signature

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