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diff --git a/docs/source/auto_examples/plot_gromov.rst b/docs/source/auto_examples/plot_gromov.rst new file mode 100644 index 0000000..3ed4e11 --- /dev/null +++ b/docs/source/auto_examples/plot_gromov.rst @@ -0,0 +1,214 @@ + + +.. _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.make_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) + + 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() + + + +.. image:: /auto_examples/images/sphx_glr_plot_gromov_003.png + :align: center + + +.. rst-class:: sphx-glr-script-out + + Out:: + + It. |Loss |Delta loss + -------------------------------- + 0|4.328711e-02|0.000000e+00 + 1|2.281369e-02|-8.974178e-01 + 2|1.843659e-02|-2.374139e-01 + 3|1.602820e-02|-1.502598e-01 + 4|1.353712e-02|-1.840179e-01 + 5|1.285687e-02|-5.290977e-02 + 6|1.284537e-02|-8.952931e-04 + 7|1.284525e-02|-8.989584e-06 + 8|1.284525e-02|-8.989950e-08 + 9|1.284525e-02|-8.989949e-10 + It. |Err + ------------------- + 0|7.263293e-02| + 10|1.737784e-02| + 20|7.783978e-03| + 30|3.399419e-07| + 40|3.751207e-11| + Gromov-Wasserstein distances: 0.012845252089244688 + Entropic Gromov-Wasserstein distances: 0.013543882352191079 + + +**Total running time of the script:** ( 0 minutes 1.916 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>`_ |