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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>`_
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