.. _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 # Nicolas Courty # # 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 ` .. container:: sphx-glr-download :download:`Download Jupyter notebook: plot_gromov.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_