.. only:: html .. note:: :class: sphx-glr-download-link-note Click :ref:`here ` to download the full example code .. rst-class:: sphx-glr-example-title .. _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:: default # Author: Titouan Vayer # # 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 --------- We create two 1D random measures .. code-block:: default 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:: default 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, 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, y=1) pl.yticks(()) pl.tight_layout() pl.show() .. image:: /auto_examples/images/sphx_glr_plot_fgw_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out Out: .. code-block:: none /home/circleci/project/examples/plot_fgw.py:73: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. pl.show() Create structure matrices and across-feature distance matrix --------- .. code-block:: default 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:: default 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_002.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out Out: .. code-block:: none /home/circleci/project/examples/plot_fgw.py:128: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. pl.show() Compute FGW/GW --------- .. code-block:: default 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: .. code-block:: none It. |Loss |Relative loss|Absolute loss ------------------------------------------------ 0|4.734412e+01|0.000000e+00|0.000000e+00 1|2.508254e+01|8.875326e-01|2.226158e+01 2|2.189327e+01|1.456740e-01|3.189279e+00 3|2.189327e+01|0.000000e+00|0.000000e+00 Elapsed time : 0.0013608932495117188 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:: default 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_003.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out Out: .. code-block:: none /home/circleci/project/examples/plot_fgw.py:173: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure. pl.show() .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 0.514 seconds) .. _sphx_glr_download_auto_examples_plot_fgw.py: .. only :: html .. container:: sphx-glr-footer :class: sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_fgw.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_fgw.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_