path: root/docs/source/auto_examples/plot_partial_wass_and_gromov.rst

.. only:: html

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

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

    .. _sphx_glr_auto_examples_plot_partial_wass_and_gromov.py:


==================================================
Partial Wasserstein and Gromov-Wasserstein example
==================================================

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


.. code-block:: default


    # Author: Laetitia Chapel <laetitia.chapel@irisa.fr>
    # License: MIT License

    # necessary for 3d plot even if not used
    from mpl_toolkits.mplot3d import Axes3D  # noqa
    import scipy as sp
    import numpy as np
    import matplotlib.pylab as pl
    import ot









Sample two 2D Gaussian distributions and plot them
--------------------------------------------------

For demonstration purpose, we sample two Gaussian distributions in 2-d
spaces and add some random noise.


.. code-block:: default



    n_samples = 20  # nb samples (gaussian)
    n_noise = 20  # nb of samples (noise)

    mu = np.array([0, 0])
    cov = np.array([[1, 0], [0, 2]])

    xs = ot.datasets.make_2D_samples_gauss(n_samples, mu, cov)
    xs = np.append(xs, (np.random.rand(n_noise, 2) + 1) * 4).reshape((-1, 2))
    xt = ot.datasets.make_2D_samples_gauss(n_samples, mu, cov)
    xt = np.append(xt, (np.random.rand(n_noise, 2) + 1) * -3).reshape((-1, 2))

    M = sp.spatial.distance.cdist(xs, xt)

    fig = pl.figure()
    ax1 = fig.add_subplot(131)
    ax1.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
    ax2 = fig.add_subplot(132)
    ax2.scatter(xt[:, 0], xt[:, 1], color='r')
    ax3 = fig.add_subplot(133)
    ax3.imshow(M)
    pl.show()




.. image:: /auto_examples/images/sphx_glr_plot_partial_wass_and_gromov_001.png
    :class: sphx-glr-single-img


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

 Out:

 .. code-block:: none

    /home/rflamary/PYTHON/POT/examples/plot_partial_wass_and_gromov.py:51: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure.
      pl.show()




Compute partial Wasserstein plans and distance
----------------------------------------------


.. code-block:: default


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

    w0, log0 = ot.partial.partial_wasserstein(p, q, M, m=0.5, log=True)
    w, log = ot.partial.entropic_partial_wasserstein(p, q, M, reg=0.1, m=0.5,
                                                     log=True)

    print('Partial Wasserstein distance (m = 0.5): ' + str(log0['partial_w_dist']))
    print('Entropic partial Wasserstein distance (m = 0.5): ' +
          str(log['partial_w_dist']))

    pl.figure(1, (10, 5))
    pl.subplot(1, 2, 1)
    pl.imshow(w0, cmap='jet')
    pl.title('Partial Wasserstein')
    pl.subplot(1, 2, 2)
    pl.imshow(w, cmap='jet')
    pl.title('Entropic partial Wasserstein')
    pl.show()





.. image:: /auto_examples/images/sphx_glr_plot_partial_wass_and_gromov_002.png
    :class: sphx-glr-single-img


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

 Out:

 .. code-block:: none

    Partial Wasserstein distance (m = 0.5): 0.507323938973194
    Entropic partial Wasserstein distance (m = 0.5): 0.5205305886057896
    /home/rflamary/PYTHON/POT/examples/plot_partial_wass_and_gromov.py:76: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure.
      pl.show()




Sample one 2D and 3D Gaussian distributions and plot them
---------------------------------------------------------

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:: default


    n_samples = 20  # nb samples
    n_noise = 10  # nb of samples (noise)

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

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

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


    xs = ot.datasets.make_2D_samples_gauss(n_samples, mu_s, cov_s)
    xs = np.concatenate((xs, ((np.random.rand(n_noise, 2) + 1) * 4)), axis=0)
    P = sp.linalg.sqrtm(cov_t)
    xt = np.random.randn(n_samples, 3).dot(P) + mu_t
    xt = np.concatenate((xt, ((np.random.rand(n_noise, 3) + 1) * 10)), axis=0)

    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_partial_wass_and_gromov_003.png
    :class: sphx-glr-single-img


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

 Out:

 .. code-block:: none

    /home/rflamary/PYTHON/POT/examples/plot_partial_wass_and_gromov.py:112: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure.
      pl.show()




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


.. code-block:: default


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

    # transport 100% of the mass
    print('-----m = 1')
    m = 1
    res0, log0 = ot.partial.partial_gromov_wasserstein(C1, C2, p, q, m=m, log=True)
    res, log = ot.partial.entropic_partial_gromov_wasserstein(C1, C2, p, q, 10,
                                                              m=m, log=True)

    print('Wasserstein distance (m = 1): ' + str(log0['partial_gw_dist']))
    print('Entropic Wasserstein distance (m = 1): ' + str(log['partial_gw_dist']))

    pl.figure(1, (10, 5))
    pl.title("mass to be transported m = 1")
    pl.subplot(1, 2, 1)
    pl.imshow(res0, cmap='jet')
    pl.title('Wasserstein')
    pl.subplot(1, 2, 2)
    pl.imshow(res, cmap='jet')
    pl.title('Entropic Wasserstein')
    pl.show()

    # transport 2/3 of the mass
    print('-----m = 2/3')
    m = 2 / 3
    res0, log0 = ot.partial.partial_gromov_wasserstein(C1, C2, p, q, m=m, log=True)
    res, log = ot.partial.entropic_partial_gromov_wasserstein(C1, C2, p, q, 10,
                                                              m=m, log=True)

    print('Partial Wasserstein distance (m = 2/3): ' +
          str(log0['partial_gw_dist']))
    print('Entropic partial Wasserstein distance (m = 2/3): ' +
          str(log['partial_gw_dist']))

    pl.figure(1, (10, 5))
    pl.title("mass to be transported m = 2/3")
    pl.subplot(1, 2, 1)
    pl.imshow(res0, cmap='jet')
    pl.title('Partial Wasserstein')
    pl.subplot(1, 2, 2)
    pl.imshow(res, cmap='jet')
    pl.title('Entropic partial Wasserstein')
    pl.show()



.. image:: /auto_examples/images/sphx_glr_plot_partial_wass_and_gromov_004.png
    :class: sphx-glr-single-img


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

 Out:

 .. code-block:: none

    -----m = 1
    Wasserstein distance (m = 1): 63.65368600872179
    Entropic Wasserstein distance (m = 1): 65.23659085946916
    /home/rflamary/PYTHON/POT/examples/plot_partial_wass_and_gromov.py:141: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure.
      pl.show()
    -----m = 2/3
    Partial Wasserstein distance (m = 2/3): 0.23235485397666825
    Entropic partial Wasserstein distance (m = 2/3): 1.4645434781619244
    /home/rflamary/PYTHON/POT/examples/plot_partial_wass_and_gromov.py:157: MatplotlibDeprecationWarning: Adding an axes using the same arguments as a previous axes currently reuses the earlier instance.  In a future version, a new instance will always be created and returned.  Meanwhile, this warning can be suppressed, and the future behavior ensured, by passing a unique label to each axes instance.
      pl.subplot(1, 2, 1)
    /home/rflamary/PYTHON/POT/examples/plot_partial_wass_and_gromov.py:160: MatplotlibDeprecationWarning: Adding an axes using the same arguments as a previous axes currently reuses the earlier instance.  In a future version, a new instance will always be created and returned.  Meanwhile, this warning can be suppressed, and the future behavior ensured, by passing a unique label to each axes instance.
      pl.subplot(1, 2, 2)
    /home/rflamary/PYTHON/POT/examples/plot_partial_wass_and_gromov.py:163: 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  1.543 seconds)


.. _sphx_glr_download_auto_examples_plot_partial_wass_and_gromov.py:


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