update barycenter demo

Author: rflamary

examples/Demo_1D_barycenter.ipynb

@@ -58,7 +58,7 @@
 
 # True Group lasso regularization
 reg=1e-1
-eta=1e0
+eta=2e0
 da_l1l2=ot.da.OTDA_l1l2()
 da_l1l2.fit(xs,ys,xt,reg=reg,eta=eta,numItermax=20,verbose=True)
 xstgl=da_l1l2.interp()

examples/demo_OTDA_classes.py

@@ -9,7 +9,9 @@
 import matplotlib.pylab as pl
 import ot
 
-
+from mpl_toolkits.mplot3d import Axes3D
+from matplotlib.collections import PolyCollection
+from matplotlib.colors import colorConverter
 
 #%% parameters
 
@@ -19,8 +21,8 @@
 x=np.arange(n,dtype=np.float64)
 
 # Gaussian distributions
-a1=ot.datasets.get_1D_gauss(n,m=20,s=20) # m= mean, s= std
-a2=ot.datasets.get_1D_gauss(n,m=60,s=60)
+a1=ot.datasets.get_1D_gauss(n,m=20,s=5) # m= mean, s= std
+a2=ot.datasets.get_1D_gauss(n,m=60,s=8)
 
 # creating matrix A containing all distributions
 A=np.vstack((a1,a2)).T
@@ -39,12 +41,15 @@
 
 #%% barycenter computation
 
+alpha=0.2 # 0<=alpha<=1
+weights=np.array([1-alpha,alpha])
+
 # l2bary
-bary_l2=A.mean(1)
+bary_l2=A.dot(weights)
 
 # wasserstein
 reg=1e-3
-bary_wass=ot.bregman.barycenter(A,M,reg)
+bary_wass=ot.bregman.barycenter(A,M,reg,weights)
 
 pl.figure(2)
 pl.clf()
@@ -58,3 +63,74 @@
 pl.plot(x,bary_wass,'g',label='Wasserstein')
 pl.legend()
 pl.title('Barycenters')
+
+
+#%% barycenter interpolation
+
+nbalpha=11
+alphalist=np.linspace(0,1,nbalpha)
+
+
+B_l2=np.zeros((n,nbalpha))
+
+B_wass=np.copy(B_l2)
+
+for i in range(0,nbalpha):
+    alpha=alphalist[i]
+    weights=np.array([1-alpha,alpha])
+    B_l2[:,i]=A.dot(weights)
+    B_wass[:,i]=ot.bregman.barycenter(A,M,reg,weights)
+
+#%% plot interpolation
+
+pl.figure(3,(10,5))
+
+#pl.subplot(1,2,1)
+cmap=pl.cm.get_cmap('viridis')
+verts = []
+zs = alphalist
+for i,z in enumerate(zs):
+    ys = B_l2[:,i]
+    verts.append(list(zip(x, ys)))
+
+ax = pl.gcf().gca(projection='3d')
+
+poly = PolyCollection(verts,facecolors=[cmap(a) for a in alphalist])
+poly.set_alpha(0.7)
+ax.add_collection3d(poly, zs=zs, zdir='y')
+
+ax.set_xlabel('x')
+ax.set_xlim3d(0, n)
+ax.set_ylabel('$\\alpha$')
+ax.set_ylim3d(0,1)
+ax.set_zlabel('')
+ax.set_zlim3d(0, B_l2.max()*1.01)
+pl.title('Barycenter interpolation with l2')
+
+pl.show()
+
+pl.figure(4,(10,5))
+
+#pl.subplot(1,2,1)
+cmap=pl.cm.get_cmap('viridis')
+verts = []
+zs = alphalist
+for i,z in enumerate(zs):
+    ys = B_wass[:,i]
+    verts.append(list(zip(x, ys)))
+
+ax = pl.gcf().gca(projection='3d')
+
+poly = PolyCollection(verts,facecolors=[cmap(a) for a in alphalist])
+poly.set_alpha(0.7)
+ax.add_collection3d(poly, zs=zs, zdir='y')
+
+ax.set_xlabel('x')
+ax.set_xlim3d(0, n)
+ax.set_ylabel('$\\alpha$')
+ax.set_ylim3d(0,1)
+ax.set_zlabel('')
+ax.set_zlim3d(0, B_l2.max()*1.01)
+pl.title('Barycenter interpolation with Wasserstein')
+
+pl.show()

examples/demo_barycenter_1D.py

@@ -128,4 +128,4 @@ def get_data_classif(dataset,n,nz=.5,theta=0,**kwargs):
         y=0
         print("unknown dataset")
 
-    return x,y.astype(int)
+    return x,y