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-# -*- coding: utf-8 -*-
-"""
-==============================
-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.
-
-"""
-
-# 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
-# ---------
-
-#%% 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
-# ---------
-
-#%% 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()
-
-##############################################################################
-# Create structure matrices and across-feature distance matrix
-# ---------
-
-#%% 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
-# ---------
-
-#%%
-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()
-
-##############################################################################
-# Compute FGW/GW
-# ---------
-
-#%% 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)
-
-##############################################################################
-# Visualize transport matrices
-# ---------
-
-#%% 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()