[MRG] Partial Entropic FGW solvers (#702)

* merge

* new dev version

* first commit partial fgw

* complete tests + solve_gromov

* complete tests + solve_gromov

* release

* partial entropic fgw solvers

* add tests

* complete solve_gromov

* update

* fix solvers

* fix solvers

* fix solvers

* improve example and doc

* update readme

* reset solve_gromov behavior for unbalanced=none

* merge

* merge

---------

Co-authored-by: Rémi Flamary <[email protected]>

Author: cedricvincentcuaz

README.md

@@ -40,8 +40,7 @@ POT provides the following generic OT solvers (links to examples):
 * [Sampled solver of Gromov Wasserstein](https://pythonot.github.io/auto_examples/gromov/plot_gromov.html) for large-scale problem with any loss functions [33]
 * Non regularized [free support Wasserstein barycenters](https://pythonot.github.io/auto_examples/barycenters/plot_free_support_barycenter.html) [20].
 * [One dimensional Unbalanced OT](https://pythonot.github.io/auto_examples/unbalanced-partial/plot_UOT_1D.html) with KL relaxation and [barycenter](https://pythonot.github.io/auto_examples/unbalanced-partial/plot_UOT_barycenter_1D.html) [10, 25]. Also [exact unbalanced OT](https://pythonot.github.io/auto_examples/unbalanced-partial/plot_unbalanced_ot.html) with KL and quadratic regularization and the [regularization path of UOT](https://pythonot.github.io/auto_examples/unbalanced-partial/plot_regpath.html) [41]
-* [Partial Wasserstein and Gromov-Wasserstein](https://pythonot.github.io/auto_examples/unbalanced-partial/plot_partial_wass_and_gromov.html) (exact [29] and entropic [3]
-  formulations).
+* [Partial Wasserstein and Gromov-Wasserstein](https://pythonot.github.io/auto_examples/unbalanced-partial/plot_partial_wass_and_gromov.html) and [Partial Fused Gromov-Wasserstein](https://pythonot.github.io/auto_examples/gromov/plot_partial_fgw.html) (exact [29] and entropic [3] formulations).
 * [Sliced Wasserstein](https://pythonot.github.io/auto_examples/sliced-wasserstein/plot_variance.html) [31, 32] and Max-sliced Wasserstein [35] that can be used for gradient flows [36].
 * [Wasserstein distance on the circle](https://pythonot.github.io/auto_examples/plot_compute_wasserstein_circle.html) [44, 45]
 * [Spherical Sliced Wasserstein](https://pythonot.github.io/auto_examples/sliced-wasserstein/plot_variance_ssw.html) [46]

RELEASES.md

@@ -7,6 +7,7 @@
 - Added feature `grad=last_step` for `ot.solvers.solve` (PR #693)
 - Automatic PR labeling and release file update check (PR #704)
 - Reorganize sub-module `ot/lp/__init__.py` into separate files (PR #714)
+- Implement projected gradient descent solvers for entropic partial FGW (PR #702)
 - Fix documentation in the module `ot.gaussian` (PR #718)
 
 #### Closed issues

examples/gromov/plot_barycenter_fgw.py

@@ -91,7 +91,7 @@ def build_noisy_circular_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 = np.random.normal(mu, sigma, 1)[0]
         if with_noise:
             g.add_node(i, attr_name=math.sin((2 * i * math.pi / N)) + noise)
         else:
@@ -107,7 +107,7 @@ def build_noisy_circular_graph(
                 if i == N - 1:
                     g.add_edge(i, 1)
     g.add_edge(N, 0)
-    noise = float(np.random.normal(mu, sigma, 1))
+    noise = np.random.normal(mu, sigma, 1)[0]
     if with_noise:
         g.add_node(N, attr_name=math.sin((2 * N * math.pi / N)) + noise)
     else:
@@ -157,7 +157,7 @@ def graph_colors(nx_graph, vmin=0, vmax=7):
     plt.subplot(3, 3, i + 1)
     g = X0[i]
     pos = nx.kamada_kawai_layout(g)
-    nx.draw(
+    nx.draw_networkx(
         g,
         pos=pos,
         node_color=graph_colors(g, vmin=-1, vmax=1),
@@ -173,7 +173,7 @@ def graph_colors(nx_graph, vmin=0, vmax=7):
 
 # %% 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).todense()) for x in X0]
+Cs = [shortest_path(nx.adjacency_matrix(x).toarray()) 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(
@@ -199,7 +199,7 @@ def graph_colors(nx_graph, vmin=0, vmax=7):
 
 # %%
 pos = nx.kamada_kawai_layout(bary)
-nx.draw(
+nx.draw_networkx(
     bary, pos=pos, node_color=graph_colors(bary, vmin=-1, vmax=1), with_labels=False
 )
 plt.suptitle("Barycenter", fontsize=20)