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diff --git a/docs/source/auto_examples/plot_fgw.rst b/docs/source/auto_examples/plot_fgw.rst deleted file mode 100644 index aec725d..0000000 --- a/docs/source/auto_examples/plot_fgw.rst +++ /dev/null @@ -1,297 +0,0 @@ - - -.. _sphx_glr_auto_examples_plot_fgw.py: - - -============================== -Plot Fused-gromov-Wasserstein -============================== - -This example illustrates the computation of FGW for 1D measures[18]. - -.. [18] Vayer Titouan, Chapel Laetitia, Flamary R{'e}mi, Tavenard Romain - and Courty Nicolas - "Optimal Transport for structured data with application on graphs" - International Conference on Machine Learning (ICML). 2019. - - - - -.. code-block:: python - - - # Author: Titouan Vayer <titouan.vayer@irisa.fr> - # - # License: MIT License - - import matplotlib.pyplot as pl - import numpy as np - import ot - from ot.gromov import gromov_wasserstein, fused_gromov_wasserstein - - - - - - - -Generate data ---------- - - - -.. code-block:: python - - - #%% parameters - # We create two 1D random measures - n = 20 # number of points in the first distribution - n2 = 30 # number of points in the second distribution - sig = 1 # std of first distribution - sig2 = 0.1 # std of second distribution - - np.random.seed(0) - - phi = np.arange(n)[:, None] - xs = phi + sig * np.random.randn(n, 1) - ys = np.vstack((np.ones((n // 2, 1)), 0 * np.ones((n // 2, 1)))) + sig2 * np.random.randn(n, 1) - - phi2 = np.arange(n2)[:, None] - xt = phi2 + sig * np.random.randn(n2, 1) - yt = np.vstack((np.ones((n2 // 2, 1)), 0 * np.ones((n2 // 2, 1)))) + sig2 * np.random.randn(n2, 1) - yt = yt[::-1, :] - - p = ot.unif(n) - q = ot.unif(n2) - - - - - - - -Plot data ---------- - - - -.. code-block:: python - - - #%% plot the distributions - - pl.close(10) - pl.figure(10, (7, 7)) - - pl.subplot(2, 1, 1) - - pl.scatter(ys, xs, c=phi, s=70) - pl.ylabel('Feature value a', fontsize=20) - pl.title('$\mu=\sum_i \delta_{x_i,a_i}$', fontsize=25, usetex=True, y=1) - pl.xticks(()) - pl.yticks(()) - pl.subplot(2, 1, 2) - pl.scatter(yt, xt, c=phi2, s=70) - pl.xlabel('coordinates x/y', fontsize=25) - pl.ylabel('Feature value b', fontsize=20) - pl.title('$\\nu=\sum_j \delta_{y_j,b_j}$', fontsize=25, usetex=True, y=1) - pl.yticks(()) - pl.tight_layout() - pl.show() - - - - -.. image:: /auto_examples/images/sphx_glr_plot_fgw_010.png - :align: center - - - - -Create structure matrices and across-feature distance matrix ---------- - - - -.. code-block:: python - - - #%% Structure matrices and across-features distance matrix - C1 = ot.dist(xs) - C2 = ot.dist(xt) - M = ot.dist(ys, yt) - w1 = ot.unif(C1.shape[0]) - w2 = ot.unif(C2.shape[0]) - Got = ot.emd([], [], M) - - - - - - - -Plot matrices ---------- - - - -.. code-block:: python - - - #%% - cmap = 'Reds' - pl.close(10) - pl.figure(10, (5, 5)) - fs = 15 - l_x = [0, 5, 10, 15] - l_y = [0, 5, 10, 15, 20, 25] - gs = pl.GridSpec(5, 5) - - ax1 = pl.subplot(gs[3:, :2]) - - pl.imshow(C1, cmap=cmap, interpolation='nearest') - pl.title("$C_1$", fontsize=fs) - pl.xlabel("$k$", fontsize=fs) - pl.ylabel("$i$", fontsize=fs) - pl.xticks(l_x) - pl.yticks(l_x) - - ax2 = pl.subplot(gs[:3, 2:]) - - pl.imshow(C2, cmap=cmap, interpolation='nearest') - pl.title("$C_2$", fontsize=fs) - pl.ylabel("$l$", fontsize=fs) - #pl.ylabel("$l$",fontsize=fs) - pl.xticks(()) - pl.yticks(l_y) - ax2.set_aspect('auto') - - ax3 = pl.subplot(gs[3:, 2:], sharex=ax2, sharey=ax1) - pl.imshow(M, cmap=cmap, interpolation='nearest') - pl.yticks(l_x) - pl.xticks(l_y) - pl.ylabel("$i$", fontsize=fs) - pl.title("$M_{AB}$", fontsize=fs) - pl.xlabel("$j$", fontsize=fs) - pl.tight_layout() - ax3.set_aspect('auto') - pl.show() - - - - -.. image:: /auto_examples/images/sphx_glr_plot_fgw_011.png - :align: center - - - - -Compute FGW/GW ---------- - - - -.. code-block:: python - - - #%% Computing FGW and GW - alpha = 1e-3 - - ot.tic() - Gwg, logw = fused_gromov_wasserstein(M, C1, C2, p, q, loss_fun='square_loss', alpha=alpha, verbose=True, log=True) - ot.toc() - - #%reload_ext WGW - Gg, log = gromov_wasserstein(C1, C2, p, q, loss_fun='square_loss', verbose=True, log=True) - - - - - -.. rst-class:: sphx-glr-script-out - - Out:: - - It. |Loss |Relative loss|Absolute loss - ------------------------------------------------ - 0|4.734462e+01|0.000000e+00|0.000000e+00 - 1|2.508258e+01|8.875498e-01|2.226204e+01 - 2|2.189329e+01|1.456747e-01|3.189297e+00 - 3|2.189329e+01|0.000000e+00|0.000000e+00 - Elapsed time : 0.0016989707946777344 s - It. |Loss |Relative loss|Absolute loss - ------------------------------------------------ - 0|4.683978e+04|0.000000e+00|0.000000e+00 - 1|3.860061e+04|2.134468e-01|8.239175e+03 - 2|2.182948e+04|7.682787e-01|1.677113e+04 - 3|2.182948e+04|0.000000e+00|0.000000e+00 - - -Visualize transport matrices ---------- - - - -.. code-block:: python - - - #%% visu OT matrix - cmap = 'Blues' - fs = 15 - pl.figure(2, (13, 5)) - pl.clf() - pl.subplot(1, 3, 1) - pl.imshow(Got, cmap=cmap, interpolation='nearest') - #pl.xlabel("$y$",fontsize=fs) - pl.ylabel("$i$", fontsize=fs) - pl.xticks(()) - - pl.title('Wasserstein ($M$ only)') - - pl.subplot(1, 3, 2) - pl.imshow(Gg, cmap=cmap, interpolation='nearest') - pl.title('Gromov ($C_1,C_2$ only)') - pl.xticks(()) - pl.subplot(1, 3, 3) - pl.imshow(Gwg, cmap=cmap, interpolation='nearest') - pl.title('FGW ($M+C_1,C_2$)') - - pl.xlabel("$j$", fontsize=fs) - pl.ylabel("$i$", fontsize=fs) - - pl.tight_layout() - pl.show() - - - -.. image:: /auto_examples/images/sphx_glr_plot_fgw_004.png - :align: center - - - - -**Total running time of the script:** ( 0 minutes 1.468 seconds) - - - -.. only :: html - - .. container:: sphx-glr-footer - - - .. container:: sphx-glr-download - - :download:`Download Python source code: plot_fgw.py <plot_fgw.py>` - - - - .. container:: sphx-glr-download - - :download:`Download Jupyter notebook: plot_fgw.ipynb <plot_fgw.ipynb>` - - -.. only:: html - - .. rst-class:: sphx-glr-signature - - `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_ |