Reame +pep8

Author: tvayer

README.md

@@ -222,3 +222,17 @@ 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] Genevay, A., Cuturi, M., Peyré, G. & Bach, F. (2016) [Stochastic Optimization for Large-scale Optimal Transport](https://arxiv.org/abs/1605.08527). Advances in Neural Information Processing Systems (2016).
+
+[19] Seguy, V., Bhushan Damodaran, B., Flamary, R., Courty, N., Rolet, A.& Blondel, M. [Large-scale Optimal Transport and Mapping Estimation](https://arxiv.org/pdf/1711.02283.pdf). International Conference on Learning Representation (2018)
+
+[20] Cuturi, M. and Doucet, A. (2014) [Fast Computation of Wasserstein Barycenters](http://proceedings.mlr.press/v32/cuturi14.html). International Conference in Machine Learning
+
+[21] Solomon, J., De Goes, F., Peyré, G., Cuturi, M., Butscher, A., Nguyen, A. & Guibas, L. (2015). [Convolutional wasserstein distances: Efficient optimal transportation on geometric domains](https://dl.acm.org/citation.cfm?id=2766963). ACM Transactions on Graphics (TOG), 34(4), 66.
+
+[22] J. Altschuler, J.Weed, P. Rigollet, (2017) [Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration](https://papers.nips.cc/paper/6792-near-linear-time-approximation-algorithms-for-optimal-transport-via-sinkhorn-iteration.pdf), Advances in Neural Information Processing Systems (NIPS) 31
+
+[23] Aude, G., Peyré, G., Cuturi, M., [Learning Generative Models with Sinkhorn Divergences](https://arxiv.org/abs/1706.00292), Proceedings of the Twenty-First International Conference on Artficial Intelligence and Statistics, (AISTATS) 21, 2018
+
+[24] 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_barycenter_fgw.py

@@ -30,10 +30,11 @@
 from ot.gromov import fgw_barycenters
 #%% Graph functions
 
-def find_thresh(C,inf=0.5,sup=3,step=10):
+
+def find_thresh(C, inf=0.5, sup=3, step=10):
     """ Trick to find the adequate thresholds from where value of the C matrix are considered close enough to say that nodes are connected
-        Tthe threshold is found by a linesearch between values "inf" and "sup" with "step" thresholds tested. 
-        The optimal threshold is the one which minimizes the reconstruction error between the shortest_path matrix coming from the thresholded adjency matrix 
+        Tthe threshold is found by a linesearch between values "inf" and "sup" with "step" thresholds tested.
+        The optimal threshold is the one which minimizes the reconstruction error between the shortest_path matrix coming from the thresholded adjency matrix
         and the original matrix.
     Parameters
     ----------
@@ -43,21 +44,22 @@ def find_thresh(C,inf=0.5,sup=3,step=10):
           The beginning of the linesearch
     sup : float
           The end of the linesearch
-    step : integer 
-            Number of thresholds tested        
+    step : integer
+            Number of thresholds tested
     """
-    dist=[]
-    search=np.linspace(inf,sup,step)
+    dist = []
+    search = np.linspace(inf, sup, step)
     for thresh in search:
-        Cprime=sp_to_adjency(C,0,thresh)
-        SC=shortest_path(Cprime,method='D')
-        SC[SC==float('inf')]=100
-        dist.append(np.linalg.norm(SC-C))
-    return search[np.argmin(dist)],dist
-
-def sp_to_adjency(C,threshinf=0.2,threshsup=1.8):
-    """ Thresholds the structure matrix in order to compute an adjency matrix. 
-    All values between threshinf and threshsup are considered representing connected nodes and set to 1. Else are set to 0    
+        Cprime = sp_to_adjency(C, 0, thresh)
+        SC = shortest_path(Cprime, method='D')
+        SC[SC == float('inf')] = 100
+        dist.append(np.linalg.norm(SC - C))
+    return search[np.argmin(dist)], dist
+
+
+def sp_to_adjency(C, threshinf=0.2, threshsup=1.8):
+    """ Thresholds the structure matrix in order to compute an adjency matrix.
+    All values between threshinf and threshsup are considered representing connected nodes and set to 1. Else are set to 0
     Parameters
     ----------
     C : ndarray, shape (n_nodes,n_nodes)
@@ -71,102 +73,100 @@ def sp_to_adjency(C,threshinf=0.2,threshsup=1.8):
     C : ndarray, shape (n_nodes,n_nodes)
         The threshold matrix. Each element is in {0,1}
     """
-    H=np.zeros_like(C)
-    np.fill_diagonal(H,np.diagonal(C))
-    C=C-H
-    C=np.minimum(np.maximum(C,threshinf),threshsup)
-    C[C==threshsup]=0
-    C[C!=0]=1   
-    
-    return C 
-
-def build_noisy_circular_graph(N=20,mu=0,sigma=0.3,with_noise=False,structure_noise=False,p=None):
+    H = np.zeros_like(C)
+    np.fill_diagonal(H, np.diagonal(C))
+    C = C - H
+    C = np.minimum(np.maximum(C, threshinf), threshsup)
+    C[C == threshsup] = 0
+    C[C != 0] = 1
+
+    return C
+
+
+def build_noisy_circular_graph(N=20, mu=0, sigma=0.3, with_noise=False, structure_noise=False, p=None):
     """ Create a noisy circular graph
     """
-    g=nx.Graph()
+    g = nx.Graph()
     g.add_nodes_from(list(range(N)))
     for i in range(N):
-        noise=float(np.random.normal(mu,sigma,1))
+        noise = float(np.random.normal(mu, sigma, 1))
         if with_noise:
-            g.add_node(i,attr_name=math.sin((2*i*math.pi/N))+noise)
+            g.add_node(i, attr_name=math.sin((2 * i * math.pi / N)) + noise)
         else:
-            g.add_node(i,attr_name=math.sin(2*i*math.pi/N))
-        g.add_edge(i,i+1)
+            g.add_node(i, attr_name=math.sin(2 * i * math.pi / N))
+        g.add_edge(i, i + 1)
         if structure_noise:
-            randomint=np.random.randint(0,p)
-            if randomint==0:
-                if i<=N-3:
-                    g.add_edge(i,i+2)
-                if i==N-2:
-                    g.add_edge(i,0)
-                if i==N-1:
-                    g.add_edge(i,1)
-    g.add_edge(N,0)
-    noise=float(np.random.normal(mu,sigma,1))
+            randomint = np.random.randint(0, p)
+            if randomint == 0:
+                if i <= N - 3:
+                    g.add_edge(i, i + 2)
+                if i == N - 2:
+                    g.add_edge(i, 0)
+                if i == N - 1:
+                    g.add_edge(i, 1)
+    g.add_edge(N, 0)
+    noise = float(np.random.normal(mu, sigma, 1))
     if with_noise:
-        g.add_node(N,attr_name=math.sin((2*N*math.pi/N))+noise)
+        g.add_node(N, attr_name=math.sin((2 * N * math.pi / N)) + noise)
     else:
-        g.add_node(N,attr_name=math.sin(2*N*math.pi/N))
+        g.add_node(N, attr_name=math.sin(2 * N * math.pi / N))
     return g
 
-def graph_colors(nx_graph,vmin=0,vmax=7):
-    cnorm = mcol.Normalize(vmin=vmin,vmax=vmax)
-    cpick = cm.ScalarMappable(norm=cnorm,cmap='viridis')
+
+def graph_colors(nx_graph, vmin=0, vmax=7):
+    cnorm = mcol.Normalize(vmin=vmin, vmax=vmax)
+    cpick = cm.ScalarMappable(norm=cnorm, cmap='viridis')
     cpick.set_array([])
     val_map = {}
-    for k,v in nx.get_node_attributes(nx_graph,'attr_name').items():
-        val_map[k]=cpick.to_rgba(v)
-    colors=[]
+    for k, v in nx.get_node_attributes(nx_graph, 'attr_name').items():
+        val_map[k] = cpick.to_rgba(v)
+    colors = []
     for node in nx_graph.nodes():
         colors.append(val_map[node])
     return colors
-    
+
 #%% create dataset
 # We build a dataset of noisy circular graphs.
 # Noise is added on the structures by random connections and on the features by gaussian noise.
 
+
 np.random.seed(30)
-X0=[]
+X0 = []
 for k in range(9):
-    X0.append(build_noisy_circular_graph(np.random.randint(15,25),with_noise=True,structure_noise=True,p=3))
-    
+    X0.append(build_noisy_circular_graph(np.random.randint(15, 25), with_noise=True, structure_noise=True, p=3))
+
 #%% Plot dataset
 
-plt.figure(figsize=(8,10))
+plt.figure(figsize=(8, 10))
 for i in range(len(X0)):
-    plt.subplot(3,3,i+1)
-    g=X0[i]
-    pos=nx.kamada_kawai_layout(g)
-    nx.draw(g,pos=pos,node_color = graph_colors(g,vmin=-1,vmax=1),with_labels=False,node_size=100)
-plt.suptitle('Dataset of noisy graphs. Color indicates the label',fontsize=20)
+    plt.subplot(3, 3, i + 1)
+    g = X0[i]
+    pos = nx.kamada_kawai_layout(g)
+    nx.draw(g, pos=pos, node_color=graph_colors(g, vmin=-1, vmax=1), with_labels=False, node_size=100)
+plt.suptitle('Dataset of noisy graphs. Color indicates the label', fontsize=20)
 plt.show()
 
 
-
 #%%
 # We compute the barycenter using FGW. Structure matrices are computed using the shortest_path distance in the graph
 # Features distances are the euclidean distances
-Cs=[shortest_path(nx.adjacency_matrix(x)) for x in X0]
-ps=[np.ones(len(x.nodes()))/len(x.nodes()) for x in X0]
-Ys=[np.array([v for (k,v) in nx.get_node_attributes(x,'attr_name').items()]).reshape(-1,1) for x in X0]
-lambdas=np.array([np.ones(len(Ys))/len(Ys)]).ravel()
-sizebary=15 # we choose a barycenter with 15 nodes
+Cs = [shortest_path(nx.adjacency_matrix(x)) for x in X0]
+ps = [np.ones(len(x.nodes())) / len(x.nodes()) for x in X0]
+Ys = [np.array([v for (k, v) in nx.get_node_attributes(x, 'attr_name').items()]).reshape(-1, 1) for x in X0]
+lambdas = np.array([np.ones(len(Ys)) / len(Ys)]).ravel()
+sizebary = 15  # we choose a barycenter with 15 nodes
 
 #%%
 
-A,C,log=fgw_barycenters(sizebary,Ys,Cs,ps,lambdas,alpha=0.95)
+A, C, log = fgw_barycenters(sizebary, Ys, Cs, ps, lambdas, alpha=0.95)
 
 #%%
-bary=nx.from_numpy_matrix(sp_to_adjency(C,threshinf=0,threshsup=find_thresh(C,sup=100,step=100)[0]))
+bary = nx.from_numpy_matrix(sp_to_adjency(C, threshinf=0, threshsup=find_thresh(C, sup=100, step=100)[0]))
 for i in range(len(A.ravel())):
-    bary.add_node(i,attr_name=float(A.ravel()[i]))
- 
+    bary.add_node(i, attr_name=float(A.ravel()[i]))
+
 #%%
 pos = nx.kamada_kawai_layout(bary)
-nx.draw(bary,pos=pos,node_color = graph_colors(bary,vmin=-1,vmax=1),with_labels=False)
-plt.suptitle('Barycenter',fontsize=20)
+nx.draw(bary, pos=pos, node_color=graph_colors(bary, vmin=-1, vmax=1), with_labels=False)
+plt.suptitle('Barycenter', fontsize=20)
 plt.show()
-
-
-
-