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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.
.. rst-class:: sphx-glr-horizontal
*
.. image:: /auto_examples/images/sphx_glr_plot_gromov_001.png
:scale: 47
*
.. image:: /auto_examples/images/sphx_glr_plot_gromov_002.png
:scale: 47
.. rst-class:: sphx-glr-script-out
Out::
It. |Loss |Delta loss
--------------------------------
0|4.042674e-02|0.000000e+00
1|2.432476e-02|-6.619583e-01
2|2.170023e-02|-1.209448e-01
3|1.941223e-02|-1.178640e-01
4|1.823606e-02|-6.449667e-02
5|1.446641e-02|-2.605800e-01
6|1.184011e-02|-2.218140e-01
7|1.173274e-02|-9.150805e-03
8|1.173127e-02|-1.253458e-04
9|1.173126e-02|-1.256842e-06
10|1.173126e-02|-1.256876e-08
11|1.173126e-02|-1.256885e-10
It. |Err
-------------------
0|7.034302e-02|
10|1.044218e-03|
20|5.426783e-08|
30|3.532029e-12|
Gromov-Wasserstein distances: 0.0117312557987
Entropic Gromov-Wasserstein distances: 0.0101639418389
|
.. 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.
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
# --------------------------
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()
#
# Compute distance kernels, normalize them and then display
# ---------------------------------------------------------
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()
#
# Compute Gromov-Wasserstein plans and distance
# ---------------------------------------------
p = ot.unif(n_samples)
q = ot.unif(n_samples)
gw0, log0 = ot.gromov.gromov_wasserstein(
C1, C2, p, q, 'square_loss', verbose=True, log=True)
gw, log = ot.gromov.entropic_gromov_wasserstein(
C1, C2, p, q, 'square_loss', epsilon=5e-4, log=True, verbose=True)
print('Gromov-Wasserstein distances: ' + str(log0['gw_dist']))
print('Entropic Gromov-Wasserstein distances: ' + str(log['gw_dist']))
pl.figure(1, (10, 5))
pl.subplot(1, 2, 1)
pl.imshow(gw0, cmap='jet')
pl.title('Gromov Wasserstein')
pl.subplot(1, 2, 2)
pl.imshow(gw, cmap='jet')
pl.title('Entropic Gromov Wasserstein')
pl.show()
**Total running time of the script:** ( 0 minutes 1.465 seconds)
.. only :: html
.. 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>`
.. only:: html
.. rst-class:: sphx-glr-signature
`Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_
|
