.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/gromov/plot_fgw.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_gromov_plot_fgw.py: ============================== Plot Fused-Gromov-Wasserstein ============================== This example first illustrates the computation of FGW for 1D measures estimated using a Conditional Gradient solver [24]. [24] Vayer Titouan, Chapel Laetitia, Flamary Rémi, Tavenard Romain and Courty Nicolas "Optimal Transport for structured data with application on graphs" International Conference on Machine Learning (ICML). 2019. .. GENERATED FROM PYTHON SOURCE LINES 15-28 .. code-block:: Python # Author: Titouan Vayer # # License: MIT License # sphinx_gallery_thumbnail_number = 3 import matplotlib.pyplot as pl import numpy as np import ot from ot.gromov import gromov_wasserstein, fused_gromov_wasserstein .. GENERATED FROM PYTHON SOURCE LINES 29-31 Generate data ------------- .. GENERATED FROM PYTHON SOURCE LINES 31-54 .. 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) .. GENERATED FROM PYTHON SOURCE LINES 55-57 Plot data --------- .. GENERATED FROM PYTHON SOURCE LINES 57-78 .. code-block:: Python # plot the distributions pl.figure(1, (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-sg:: /auto_examples/gromov/images/sphx_glr_plot_fgw_001.png :alt: $\mu=\sum_i \delta_{x_i,a_i}$, $\nu=\sum_j \delta_{y_j,b_j}$ :srcset: /auto_examples/gromov/images/sphx_glr_plot_fgw_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 79-81 Create structure matrices and across-feature distance matrix ------------------------------------------------------------ .. GENERATED FROM PYTHON SOURCE LINES 81-90 .. 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) .. GENERATED FROM PYTHON SOURCE LINES 91-93 Plot matrices ------------- .. GENERATED FROM PYTHON SOURCE LINES 93-131 .. code-block:: Python cmap = 'Reds' pl.figure(2, (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.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-sg:: /auto_examples/gromov/images/sphx_glr_plot_fgw_002.png :alt: $C_1$, $C_2$, $M_{AB}$ :srcset: /auto_examples/gromov/images/sphx_glr_plot_fgw_002.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 132-134 Compute FGW/GW -------------- .. GENERATED FROM PYTHON SOURCE LINES 134-145 .. 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 .. 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|1.622743e-16|3.552714e-15 Elapsed time : 0.0015797615051269531 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 .. GENERATED FROM PYTHON SOURCE LINES 146-148 Visualize transport matrices ---------------------------- .. GENERATED FROM PYTHON SOURCE LINES 148-174 .. code-block:: Python # visu OT matrix cmap = 'Blues' fs = 15 pl.figure(3, (13, 5)) pl.clf() pl.subplot(1, 3, 1) pl.imshow(Got, cmap=cmap, interpolation='nearest') 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-sg:: /auto_examples/gromov/images/sphx_glr_plot_fgw_003.png :alt: Wasserstein ($M$ only), Gromov ($C_1,C_2$ only), FGW ($M+C_1,C_2$) :srcset: /auto_examples/gromov/images/sphx_glr_plot_fgw_003.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.663 seconds) .. _sphx_glr_download_auto_examples_gromov_plot_fgw.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_fgw.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_fgw.py ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_