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+
+
+.. _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
+
+    `Generated by Sphinx-Gallery <http://sphinx-gallery.readthedocs.io>`_