diff options
Diffstat (limited to 'docs/source/auto_examples/plot_gromov.rst')
| -rw-r--r-- | docs/source/auto_examples/plot_gromov.rst | 204 |
1 files changed, 119 insertions, 85 deletions
diff --git a/docs/source/auto_examples/plot_gromov.rst b/docs/source/auto_examples/plot_gromov.rst index 65cf4e4..131861f 100644 --- a/docs/source/auto_examples/plot_gromov.rst +++ b/docs/source/auto_examples/plot_gromov.rst @@ -14,75 +14,72 @@ 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
-
-
+ # 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.
+ + + +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
-
-
+ 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
---------------------------
+ + + +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()
-
-
+ + + 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() + @@ -92,28 +89,28 @@ Plotting the distributions -Compute distance kernels, normalize them and then display
----------------------------------------------------------
+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()
-
+ + + 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() + @@ -123,27 +120,39 @@ Compute distance kernels, normalize them and then display -Compute Gromov-Wasserstein plans and distance
----------------------------------------------
+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()
+ + 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() @@ -155,14 +164,36 @@ Compute Gromov-Wasserstein plans and distance Out:: - Gromov-Wasserstein distances between the distribution: 0.225058076974 + It. |Loss |Delta loss + -------------------------------- + 0|4.517558e-02|0.000000e+00 + 1|2.563483e-02|-7.622736e-01 + 2|2.443903e-02|-4.892972e-02 + 3|2.231600e-02|-9.513496e-02 + 4|1.676188e-02|-3.313541e-01 + 5|1.464792e-02|-1.443180e-01 + 6|1.454315e-02|-7.204526e-03 + 7|1.454142e-02|-1.185811e-04 + 8|1.454141e-02|-1.190466e-06 + 9|1.454141e-02|-1.190512e-08 + 10|1.454141e-02|-1.190520e-10 + It. |Err + ------------------- + 0|6.743761e-02| + 10|5.477003e-04| + 20|2.461503e-08| + 30|1.205155e-11| + Gromov-Wasserstein distances: 0.014541405718693563 + Entropic Gromov-Wasserstein distances: 0.015800739725237274 + +**Total running time of the script:** ( 0 minutes 1.448 seconds) -**Total running time of the script:** ( 0 minutes 4.070 seconds) +.. only :: html -.. container:: sphx-glr-footer + .. container:: sphx-glr-footer .. container:: sphx-glr-download @@ -175,6 +206,9 @@ Compute Gromov-Wasserstein plans and distance :download:`Download Jupyter notebook: plot_gromov.ipynb <plot_gromov.ipynb>` -.. rst-class:: sphx-glr-signature - `Generated by Sphinx-Gallery <http://sphinx-gallery.readthedocs.io>`_ +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_ |