diff options
author | Rémi Flamary <remi.flamary@gmail.com> | 2018-02-16 15:04:04 +0100 |
---|---|---|
committer | Rémi Flamary <remi.flamary@gmail.com> | 2018-02-16 15:04:04 +0100 |
commit | ee19d423adc85a960c9a46e4f81c370196805dbf (patch) | |
tree | 1c0bc21a605d0097616c26cfdb846fc744ed43a0 /docs/source/auto_examples/plot_gromov.rst | |
parent | efdbf9e4fe9295fb1bec893e8aaa9102537cb7f5 (diff) |
update notebooks
Diffstat (limited to 'docs/source/auto_examples/plot_gromov.rst')
-rw-r--r-- | docs/source/auto_examples/plot_gromov.rst | 206 |
1 files changed, 106 insertions, 100 deletions
diff --git a/docs/source/auto_examples/plot_gromov.rst b/docs/source/auto_examples/plot_gromov.rst index 65cf4e4..ad29f7a 100644 --- a/docs/source/auto_examples/plot_gromov.rst +++ b/docs/source/auto_examples/plot_gromov.rst @@ -12,157 +12,160 @@ 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
-
-
+.. rst-class:: sphx-glr-horizontal + * + .. image:: /auto_examples/images/sphx_glr_plot_gromov_001.png + :scale: 47 + * -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.
+ .. image:: /auto_examples/images/sphx_glr_plot_gromov_002.png + :scale: 47 +.. rst-class:: sphx-glr-script-out -.. 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
-
-
+ 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 +| -Plotting the distributions
---------------------------
+.. code-block:: python -.. code-block:: python + # Author: Erwan Vautier <erwan.vautier@gmail.com> + # Nicolas Courty <ncourty@irisa.fr> + # + # License: MIT License -
-
- 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()
-
-
+ 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. -.. image:: /auto_examples/images/sphx_glr_plot_gromov_001.png - :align: center + 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]]) -Compute distance kernels, normalize them and then display
----------------------------------------------------------
+ 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 -.. code-block:: python + # + # Plotting the distributions + # -------------------------- -
-
- 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()
-
+ 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_002.png - :align: center + # + # 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() -Compute Gromov-Wasserstein plans and distance
----------------------------------------------
+ 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) -.. code-block:: python + gw0, log0 = ot.gromov.gromov_wasserstein( + C1, C2, p, q, 'square_loss', verbose=True, log=True) -
-
- 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()
+ 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'])) -.. image:: /auto_examples/images/sphx_glr_plot_gromov_003.png - :align: center + pl.figure(1, (10, 5)) -.. rst-class:: sphx-glr-script-out + pl.subplot(1, 2, 1) + pl.imshow(gw0, cmap='jet') + pl.title('Gromov Wasserstein') - Out:: + pl.subplot(1, 2, 2) + pl.imshow(gw, cmap='jet') + pl.title('Entropic Gromov Wasserstein') - Gromov-Wasserstein distances between the distribution: 0.225058076974 + pl.show() +**Total running time of the script:** ( 0 minutes 1.465 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 +178,9 @@ 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>`_ |