FGW+gromov changes

Author: tvayer

README.md

@@ -219,3 +219,5 @@ You can also post bug reports and feature requests in Github issues. Make sure t
 [16] Agueh, M., & Carlier, G. (2011). [Barycenters in the Wasserstein space](https://hal.archives-ouvertes.fr/hal-00637399/document). SIAM Journal on Mathematical Analysis, 43(2), 904-924.
 
 [17] Blondel, M., Seguy, V., & Rolet, A. (2018). [Smooth and Sparse Optimal Transport](https://arxiv.org/abs/1710.06276). Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics (AISTATS).
+
+[18] Vayer, T., Chapel, L., Flamary, R., Tavenard, R. and Courty, N. (2019). [Optimal Transport for structured data with application on graphs](http://proceedings.mlr.press/v97/titouan19a.html) Proceedings of the 36th International Conference on Machine Learning (ICML).

examples/plot_fgw.py

@@ -0,0 +1,152 @@
+#!/usr/bin/env python3
+# -*- 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
+
+#%% parameters
+# We create two 1D random measures 
+n=20
+n2=30
+sig=1
+sig2=0.1
+
+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 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()
+
+
+#%% Structure matrices and across-features distance matrix
+C1=ot.dist(xs)
+C2=ot.dist(xt).T
+M=ot.dist(ys,yt)
+w1=ot.unif(C1.shape[0])
+w2=ot.unif(C2.shape[0])
+Got=ot.emd([],[],M)
+
+#%%
+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()
+
+
+#%% 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)
+    
+#%% 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()

ot/bregman.py

@@ -5,7 +5,7 @@
 
 # Author: Remi Flamary <remi.flamary@unice.fr>
 #         Nicolas Courty <ncourty@irisa.fr>
-#
+#         Titouan Vayer <titouan.vayer@irisa.fr>
 # License: MIT License
 
 import numpy as np