code review1

5 files changed, 204 insertions, 54 deletions

diff --git a/examples/plot_barycenter_fgw.py b/examples/plot_barycenter_fgw.py
index 9eea036..e4be447 100644
--- a/examples/plot_barycenter_fgw.py
+++ b/examples/plot_barycenter_fgw.py
@@ -125,7 +125,11 @@ def graph_colors(nx_graph, vmin=0, vmax=7):
         colors.append(val_map[node])
     return colors
 
-#%% create dataset
+##############################################################################
+# Generate data
+# -------------
+
+#%% circular 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.
 
@@ -135,7 +139,11 @@ 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))
 
-#%% Plot dataset
+##############################################################################
+# Plot data
+# ---------
+
+#%% Plot graphs
 
 plt.figure(figsize=(8, 10))
 for i in range(len(X0)):
@@ -146,9 +154,11 @@ for i in range(len(X0)):
 plt.suptitle('Dataset of noisy graphs. Color indicates the label', fontsize=20)
 plt.show()
 
+##############################################################################
+# Barycenter computation
+# ----------------------
 
-#%%
-# We compute the barycenter using FGW. Structure matrices are computed using the shortest_path distance in the graph
+#%% 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]
@@ -156,14 +166,16 @@ Ys = [np.array([v for (k, v) in nx.get_node_attributes(x, 'attr_name').items()])
 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)
 
-#%%
+##############################################################################
+# Plot Barycenter
+# -------------------------
+
+#%% Create the barycenter
 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]))
+for i, v in enumerate(A.ravel()):
+    bary.add_node(i, attr_name=v)
 
 #%%
 pos = nx.kamada_kawai_layout(bary)
diff --git a/examples/plot_fgw.py b/examples/plot_fgw.py
index ae3c487..43efc94 100644
--- a/examples/plot_fgw.py
+++ b/examples/plot_fgw.py
@@ -22,12 +22,16 @@ 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
-n2 = 30
-sig = 1
-sig2 = 0.1
+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)
 
@@ -43,6 +47,10 @@ yt = yt[::-1, :]
 p = ot.unif(n)
 q = ot.unif(n2)
 
+##############################################################################
+# Plot data
+# ---------
+
 #%% plot the distributions
 
 pl.close(10)
@@ -64,15 +72,22 @@ 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).T
+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)
@@ -112,6 +127,9 @@ pl.tight_layout()
 ax3.set_aspect('auto')
 pl.show()
 
+##############################################################################
+# Compute FGW/GW
+# ---------
 
 #%% Computing FGW and GW
 alpha = 1e-3
@@ -123,6 +141,10 @@ 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
diff --git a/ot/gromov.py b/ot/gromov.py
index 5a57dc8..53349b7 100644
--- a/ot/gromov.py
+++ b/ot/gromov.py
@@ -10,6 +10,7 @@ Gromov-Wasserstein transport method
 #         Nicolas Courty <ncourty@irisa.fr>

 #         Rémi Flamary <remi.flamary@unice.fr>

 #         Titouan Vayer <titouan.vayer@irisa.fr>

+#

 # License: MIT License

 

 import numpy as np

@@ -351,9 +352,9 @@ def gromov_wasserstein(C1, C2, p, q, loss_fun, log=False, armijo=False, **kwargs
         return cg(p, q, 0, 1, f, df, G0, armijo=armijo, C1=C1, C2=C2, constC=constC, **kwargs)

 

 

-def fused_gromov_wasserstein(M, C1, C2, p, q, loss_fun='square_loss', alpha=0.5, armijo=False, **kwargs):

+def fused_gromov_wasserstein(M, C1, C2, p, q, loss_fun='square_loss', alpha=0.5, armijo=False, log=False, **kwargs):

     """

-    Computes the FGW distance between two graphs see [3]

+    Computes the FGW transport between two graphs see [24]

     .. math::

         \gamma = arg\min_\gamma (1-\alpha)*<\gamma,M>_F + alpha* \sum_{i,j,k,l} L(C1_{i,k},C2_{j,l})*T_{i,j}*T_{k,l}

         s.t. \gamma 1 = p

@@ -377,7 +378,7 @@ def fused_gromov_wasserstein(M, C1, C2, p, q, loss_fun='square_loss', alpha=0.5,
          distribution in the source space

     q :  ndarray, shape (nt,)

          distribution in the target space

-    loss_fun :  string,optionnal

+    loss_fun :  string,optional

         loss function used for the solver

     max_iter : int, optional

         Max number of iterations

@@ -416,7 +417,86 @@ def fused_gromov_wasserstein(M, C1, C2, p, q, loss_fun='square_loss', alpha=0.5,
     def df(G):

         return gwggrad(constC, hC1, hC2, G)

 

-    return cg(p, q, M, alpha, f, df, G0, armijo=armijo, C1=C1, C2=C2, constC=constC, **kwargs)

+    if log:

+        res, log = cg(p, q, M, alpha, f, df, G0, armijo=armijo, C1=C1, C2=C2, constC=constC, log=True, **kwargs)

+        log['fgw_dist'] = log['loss'][::-1][0]

+        return res, log

+    else:

+        return cg(p, q, M, alpha, f, df, G0, armijo=armijo, C1=C1, C2=C2, constC=constC, **kwargs)

+

+

+def fused_gromov_wasserstein2(M, C1, C2, p, q, loss_fun='square_loss', alpha=0.5, armijo=False, log=False, **kwargs):

+    """

+    Computes the FGW distance between two graphs see [24]

+    .. math::

+        \gamma = arg\min_\gamma (1-\alpha)*<\gamma,M>_F + alpha* \sum_{i,j,k,l} L(C1_{i,k},C2_{j,l})*T_{i,j}*T_{k,l}

+        s.t. \gamma 1 = p

+             \gamma^T 1= q

+             \gamma\geq 0

+    where :

+    - M is the (ns,nt) metric cost matrix

+    - :math:`f` is the regularization term ( and df is its gradient)

+    - a and b are source and target weights (sum to 1)

+    - L is a loss function to account for the misfit between the similarity matrices

+    The algorithm used for solving the problem is conditional gradient as discussed in  [1]_

+    Parameters

+    ----------

+    M  : ndarray, shape (ns, nt)

+         Metric cost matrix between features across domains

+    C1 : ndarray, shape (ns, ns)

+         Metric cost matrix respresentative of the structure in the source space

+    C2 : ndarray, shape (nt, nt)

+         Metric cost matrix espresentative of the structure in the target space

+    p :  ndarray, shape (ns,)

+         distribution in the source space

+    q :  ndarray, shape (nt,)

+         distribution in the target space

+    loss_fun :  string,optional

+        loss function used for the solver

+    max_iter : int, optional

+        Max number of iterations

+    tol : float, optional

+        Stop threshold on error (>0)

+    verbose : bool, optional

+        Print information along iterations

+    log : bool, optional

+        record log if True

+    armijo : bool, optional

+        If True the steps of the line-search is found via an armijo research. Else closed form is used.

+        If there is convergence issues use False.

+    **kwargs : dict

+        parameters can be directly pased to the ot.optim.cg solver

+    Returns

+    -------

+    gamma : (ns x nt) ndarray

+        Optimal transportation matrix for the given parameters

+    log : dict

+        log dictionary return only if log==True in parameters

+    References

+    ----------

+    .. [24] 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.

+    """

+

+    constC, hC1, hC2 = init_matrix(C1, C2, p, q, loss_fun)

+

+    G0 = p[:, None] * q[None, :]

+

+    def f(G):

+        return gwloss(constC, hC1, hC2, G)

+

+    def df(G):

+        return gwggrad(constC, hC1, hC2, G)

+

+    res, log = cg(p, q, M, alpha, f, df, G0, armijo=armijo, C1=C1, C2=C2, constC=constC, log=True, **kwargs)

+    if log:

+        log['fgw_dist'] = log['loss'][::-1][0]

+        log['T'] = res

+        return log['fgw_dist'], log

+    else:

+        return log['fgw_dist']

 

 

 def gromov_wasserstein2(C1, C2, p, q, loss_fun, log=False, armijo=False, **kwargs):

@@ -889,7 +969,7 @@ def gromov_barycenters(N, Cs, ps, p, lambdas, loss_fun,
 

 def fgw_barycenters(N, Ys, Cs, ps, lambdas, alpha, fixed_structure=False, fixed_features=False,

                     p=None, loss_fun='square_loss', max_iter=100, tol=1e-9,

-                    verbose=False, log=True, init_C=None, init_X=None):

+                    verbose=False, log=False, init_C=None, init_X=None):

     """

     Compute the fgw barycenter as presented eq (5) in [24].

     ----------

@@ -919,7 +999,8 @@ def fgw_barycenters(N, Ys, Cs, ps, lambdas, alpha, fixed_structure=False, fixed_
         Barycenters' features

     C : ndarray, shape (N,N)

         Barycenters' structure matrix

-    log_:

+    log_: dictionary

+        Only returned when log=True

         T : list of (N,ns) transport matrices

         Ms : all distance matrices between the feature of the barycenter and the other features dist(X,Ys) shape (N,ns)

     References

@@ -1015,14 +1096,13 @@ def fgw_barycenters(N, Ys, Cs, ps, lambdas, alpha, fixed_structure=False, fixed_
         T = [fused_gromov_wasserstein((1 - alpha) * Ms[s], C, Cs[s], p, ps[s], loss_fun, alpha, numItermax=max_iter, stopThr=1e-5, verbose=verbose) for s in range(S)]

 

         # T is N,ns

-

-        log_['Ts_iter'].append(T)

         err_feature = np.linalg.norm(X - Xprev.reshape(N, d))

         err_structure = np.linalg.norm(C - Cprev)

 

         if log:

             log_['err_feature'].append(err_feature)

             log_['err_structure'].append(err_structure)

+            log_['Ts_iter'].append(T)

 

         if verbose:

             if cpt % 200 == 0:

@@ -1032,11 +1112,15 @@ def fgw_barycenters(N, Ys, Cs, ps, lambdas, alpha, fixed_structure=False, fixed_
             print('{:5d}|{:8e}|'.format(cpt, err_feature))

 

         cpt += 1

-    log_['T'] = T  # from target to Ys

-    log_['p'] = p

-    log_['Ms'] = Ms  # Ms are N,ns

+    if log:

+        log_['T'] = T  # from target to Ys

+        log_['p'] = p

+        log_['Ms'] = Ms  # Ms are N,ns

 

-    return X, C, log_

+    if log:

+        return X, C, log_

+    else:

+        return X, C

 

 

 def update_sructure_matrix(p, lambdas, T, Cs):

diff --git a/ot/optim.py b/ot/optim.py
index 7d103e2..4d428d9 100644
--- a/ot/optim.py
+++ b/ot/optim.py
@@ -5,6 +5,7 @@ Optimization algorithms for OT
 
 # Author: Remi Flamary <remi.flamary@unice.fr>
 #         Titouan Vayer <titouan.vayer@irisa.fr>
+#
 # License: MIT License
 
 import numpy as np
@@ -88,20 +89,20 @@ def do_linesearch(cost, G, deltaG, Mi, f_val,
         Cost matrix of the linearized transport problem. Corresponds to the gradient of the cost
     f_val :  float
         Value of the cost at G
-    armijo : bool, optionnal
+    armijo : bool, optional
             If True the steps of the line-search is found via an armijo research. Else closed form is used.
             If there is convergence issues use False.
-    C1 : ndarray (ns,ns), optionnal
+    C1 : ndarray (ns,ns), optional
         Structure matrix in the source domain. Only used when armijo=False
-    C2 : ndarray (nt,nt), optionnal
+    C2 : ndarray (nt,nt), optional
         Structure matrix in the target domain. Only used when armijo=False
-    reg : float, optionnal
+    reg : float, optional
           Regularization parameter. Only used when armijo=False
     Gc : ndarray (ns,nt)
         Optimal map found by linearization in the FW algorithm. Only used when armijo=False
     constC : ndarray (ns,nt)
              Constant for the gromov cost. See [24]. Only used when armijo=False
-    M : ndarray (ns,nt), optionnal
+    M : ndarray (ns,nt), optional
         Cost matrix between the features. Only used when armijo=False
     Returns
     -------
@@ -223,9 +224,9 @@ def cg(a, b, M, reg, f, df, G0=None, numItermax=200,
     it = 0
 
     if verbose:
-        print('{:5s}|{:12s}|{:8s}'.format(
-            'It.', 'Loss', 'Delta loss') + '\n' + '-' * 32)
-        print('{:5d}|{:8e}|{:8e}'.format(it, f_val, 0))
+        print('{:5s}|{:12s}|{:8s}|{:8s}'.format(
+            'It.', 'Loss', 'Relative loss', 'Absolute loss') + '\n' + '-' * 48)
+        print('{:5d}|{:8e}|{:8e}|{:8e}'.format(it, f_val, 0, 0))
 
     while loop:
 
@@ -261,8 +262,8 @@ def cg(a, b, M, reg, f, df, G0=None, numItermax=200,
 
         if verbose:
             if it % 20 == 0:
-                print('{:5s}|{:12s}|{:8s}'.format(
-                    'It.', 'Loss', 'Relative variation loss', 'Absolute variation loss') + '\n' + '-' * 32)
+                print('{:5s}|{:12s}|{:8s}|{:8s}'.format(
+                    'It.', 'Loss', 'Relative loss', 'Absolute loss') + '\n' + '-' * 48)
             print('{:5d}|{:8e}|{:8e}|{:8e}'.format(it, f_val, relative_delta_fval, abs_delta_fval))
 
     if log:
@@ -363,9 +364,9 @@ def gcg(a, b, M, reg1, reg2, f, df, G0=None, numItermax=10,
     it = 0
 
     if verbose:
-        print('{:5s}|{:12s}|{:8s}'.format(
-            'It.', 'Loss', 'Delta loss') + '\n' + '-' * 32)
-        print('{:5d}|{:8e}|{:8e}'.format(it, f_val, 0))
+        print('{:5s}|{:12s}|{:8s}|{:8s}'.format(
+            'It.', 'Loss', 'Relative loss', 'Absolute loss') + '\n' + '-' * 48)
+        print('{:5d}|{:8e}|{:8e}|{:8e}'.format(it, f_val, 0, 0))
 
     while loop:
 
@@ -402,8 +403,8 @@ def gcg(a, b, M, reg1, reg2, f, df, G0=None, numItermax=10,
 
         if verbose:
             if it % 20 == 0:
-                print('{:5s}|{:12s}|{:8s}'.format(
-                    'It.', 'Loss', 'Relative variation loss', 'Absolute variation loss') + '\n' + '-' * 32)
+                print('{:5s}|{:12s}|{:8s}|{:8s}'.format(
+                    'It.', 'Loss', 'Relative loss', 'Absolute loss') + '\n' + '-' * 48)
             print('{:5d}|{:8e}|{:8e}|{:8e}'.format(it, f_val, relative_delta_fval, abs_delta_fval))
 
     if log:
diff --git a/test/test_gromov.py b/test/test_gromov.py
index cd180d4..ec85abf 100644
--- a/test/test_gromov.py
+++ b/test/test_gromov.py
@@ -2,6 +2,7 @@
 

 # Author: Erwan Vautier <erwan.vautier@gmail.com>

 #         Nicolas Courty <ncourty@irisa.fr>

+#         Titouan Vayer <titouan.vayer@irisa.fr>

 #

 # License: MIT License

 

@@ -10,6 +11,8 @@ import ot
 

 

 def test_gromov():

+    np.random.seed(42)

+

     n_samples = 50  # nb samples

 

     mu_s = np.array([0, 0])

@@ -36,6 +39,11 @@ def test_gromov():
     np.testing.assert_allclose(

         q, G.sum(0), atol=1e-04)  # cf convergence gromov

 

+    Id = (1 / n_samples) * np.eye(n_samples, n_samples)

+

+    np.testing.assert_allclose(

+        G, np.flipud(Id), atol=1e-04)

+

     gw, log = ot.gromov.gromov_wasserstein2(C1, C2, p, q, 'kl_loss', log=True)

 

     G = log['T']

@@ -50,6 +58,8 @@ def test_gromov():
 

 

 def test_entropic_gromov():

+    np.random.seed(42)

+

     n_samples = 50  # nb samples

 

     mu_s = np.array([0, 0])

@@ -92,6 +102,7 @@ def test_entropic_gromov():
 

 

 def test_gromov_barycenter():

+    np.random.seed(42)

 

     ns = 50

     nt = 60

@@ -120,7 +131,7 @@ def test_gromov_barycenter():
 

 

 def test_gromov_entropic_barycenter():

-

+    np.random.seed(42)

     ns = 50

     nt = 60

 

@@ -148,6 +159,8 @@ def test_gromov_entropic_barycenter():
 

 

 def test_fgw():

+    np.random.seed(42)

+

     n_samples = 50  # nb samples

 

     mu_s = np.array([0, 0])

@@ -180,8 +193,26 @@ def test_fgw():
     np.testing.assert_allclose(

         q, G.sum(0), atol=1e-04)  # cf convergence fgw

 

+    Id = (1 / n_samples) * np.eye(n_samples, n_samples)

+

+    np.testing.assert_allclose(

+        G, np.flipud(Id), atol=1e-04)  # cf convergence gromov

+

+    fgw, log = ot.gromov.fused_gromov_wasserstein2(M, C1, C2, p, q, 'square_loss', alpha=0.5, log=True)

+

+    G = log['T']

+

+    np.testing.assert_allclose(fgw, 0, atol=1e-1, rtol=1e-1)

+

+    # check constratints

+    np.testing.assert_allclose(

+        p, G.sum(1), atol=1e-04)  # cf convergence gromov

+    np.testing.assert_allclose(

+        q, G.sum(0), atol=1e-04)  # cf convergence gromov

+

 

 def test_fgw_barycenter():

+    np.random.seed(42)

 

     ns = 50

     nt = 60

@@ -196,28 +227,28 @@ def test_fgw_barycenter():
     C2 = ot.dist(Xt)

 

     n_samples = 3

-    X, C, log = ot.gromov.fgw_barycenters(n_samples, [ys, yt], [C1, C2], [ot.unif(ns), ot.unif(nt)], [.5, .5], 0.5,

-                                          fixed_structure=False, fixed_features=False,

-                                          p=ot.unif(n_samples), loss_fun='square_loss',

-                                          max_iter=100, tol=1e-3)

+    X, C = ot.gromov.fgw_barycenters(n_samples, [ys, yt], [C1, C2], [ot.unif(ns), ot.unif(nt)], [.5, .5], 0.5,

+                                     fixed_structure=False, fixed_features=False,

+                                     p=ot.unif(n_samples), loss_fun='square_loss',

+                                     max_iter=100, tol=1e-3)

     np.testing.assert_allclose(C.shape, (n_samples, n_samples))

     np.testing.assert_allclose(X.shape, (n_samples, ys.shape[1]))

 

     xalea = np.random.randn(n_samples, 2)

     init_C = ot.dist(xalea, xalea)

 

-    X, C, log = ot.gromov.fgw_barycenters(n_samples, [ys, yt], [C1, C2], ps=[ot.unif(ns), ot.unif(nt)], lambdas=[.5, .5], alpha=0.5,

-                                          fixed_structure=True, init_C=init_C, fixed_features=False,

-                                          p=ot.unif(n_samples), loss_fun='square_loss',

-                                          max_iter=100, tol=1e-3)

+    X, C = ot.gromov.fgw_barycenters(n_samples, [ys, yt], [C1, C2], ps=[ot.unif(ns), ot.unif(nt)], lambdas=[.5, .5], alpha=0.5,

+                                     fixed_structure=True, init_C=init_C, fixed_features=False,

+                                     p=ot.unif(n_samples), loss_fun='square_loss',

+                                     max_iter=100, tol=1e-3)

     np.testing.assert_allclose(C.shape, (n_samples, n_samples))

     np.testing.assert_allclose(X.shape, (n_samples, ys.shape[1]))

 

     init_X = np.random.randn(n_samples, ys.shape[1])

 

-    X, C, log = ot.gromov.fgw_barycenters(n_samples, [ys, yt], [C1, C2], [ot.unif(ns), ot.unif(nt)], [.5, .5], 0.5,

-                                          fixed_structure=False, fixed_features=True, init_X=init_X,

-                                          p=ot.unif(n_samples), loss_fun='square_loss',

-                                          max_iter=100, tol=1e-3)

+    X, C = ot.gromov.fgw_barycenters(n_samples, [ys, yt], [C1, C2], [ot.unif(ns), ot.unif(nt)], [.5, .5], 0.5,

+                                     fixed_structure=False, fixed_features=True, init_X=init_X,

+                                     p=ot.unif(n_samples), loss_fun='square_loss',

+                                     max_iter=100, tol=1e-3)

     np.testing.assert_allclose(C.shape, (n_samples, n_samples))

     np.testing.assert_allclose(X.shape, (n_samples, ys.shape[1]))