[WIP] quantized gromov wasserstein solver (#603)

* first commit : quantized gromov wasserstein solver

* start setting up tests

* fix build OT for all backends - nb: concatenation procedure is less efficient for numpy and torch

* dealing with edge cases

* fix pep8

* updates + start setting exemple

* updates + start setting exemple

* updating code + exemple + test + docs

* fix sklearn imports

* fix

* setting up new API for qGW

* fix pep8

* tests

* update qFGW plots

* update qFGW plots

* up tests

* update example

* merge master

* complete tests

---------

Co-authored-by: Rémi Flamary <remi.flamary@gmail.com>

Author: cedricvincentcuaz

CONTRIBUTORS.md

@@ -41,7 +41,7 @@ The contributors to this library are:
 * [Tanguy Kerdoncuff](https://hv0nnus.github.io/) (Sampled Gromov Wasserstein)
 * [Minhui Huang](https://mhhuang95.github.io) (Projection Robust Wasserstein Distance)
 * [Nathan Cassereau](https://github.com/ncassereau-idris) (Backends)
-* [Cédric Vincent-Cuaz](https://github.com/cedricvincentcuaz) (Graph Dictionary Learning, FGW, semi-relaxed FGW)
+* [Cédric Vincent-Cuaz](https://github.com/cedricvincentcuaz) (Graph Dictionary Learning, FGW, semi-relaxed FGW, quantized FGW)
 * [Eloi Tanguy](https://github.com/eloitanguy) (Generalized Wasserstein Barycenters)
 * [Camille Le Coz](https://www.linkedin.com/in/camille-le-coz-8593b91a1/) (EMD2 debug)
 * [Eduardo Fernandes Montesuma](https://eddardd.github.io/my-personal-blog/) (Free support sinkhorn barycenter)

README.md

@@ -47,6 +47,7 @@ POT provides the following generic OT solvers (links to examples):
 * [Spherical Sliced Wasserstein](https://pythonot.github.io/auto_examples/sliced-wasserstein/plot_variance_ssw.html) [46]
 * [Graph Dictionary Learning solvers](https://pythonot.github.io/auto_examples/gromov/plot_gromov_wasserstein_dictionary_learning.html) [38].
 * [Semi-relaxed (Fused) Gromov-Wasserstein divergences](https://pythonot.github.io/auto_examples/gromov/plot_semirelaxed_fgw.html) (exact and regularized [48]).
+* [Quantized (Fused) Gromov-Wasserstein distances](https://pythonot.github.io/auto_examples/gromov/plot_quantized_gromov_wasserstein.html) [68].
 * [Efficient Discrete Multi Marginal Optimal Transport Regularization](https://pythonot.github.io/auto_examples/others/plot_demd_gradient_minimize.html) [50].
 * [Several backends](https://pythonot.github.io/quickstart.html#solving-ot-with-multiple-backends) for easy use of POT with  [Pytorch](https://pytorch.org/)/[jax](https://github.com/google/jax)/[Numpy](https://numpy.org/)/[Cupy](https://cupy.dev/)/[Tensorflow](https://www.tensorflow.org/) arrays.
 * Smooth Strongly Convex Nearest Brenier Potentials [58], with an extension to bounding potentials using [59].
@@ -358,4 +359,6 @@ distances between Gaussian distributions](https://hal.science/hal-03197398v2/fil
 
 [66] Pooladian, Aram-Alexandre, and Jonathan Niles-Weed. [Entropic estimation of optimal transport maps](https://arxiv.org/pdf/2109.12004.pdf). arXiv preprint arXiv:2109.12004 (2021).
 
-[67] Scetbon, M., Peyré, G. & Cuturi, M. (2022). [Linear-Time GromovWasserstein Distances using Low Rank Couplings and Costs](https://proceedings.mlr.press/v162/scetbon22b/scetbon22b.pdf). In International Conference on Machine Learning (ICML), 2022.
+[67] Scetbon, M., Peyré, G. & Cuturi, M. (2022). [Linear-Time Gromov-Wasserstein Distances using Low Rank Couplings and Costs](https://proceedings.mlr.press/v162/scetbon22b/scetbon22b.pdf). In International Conference on Machine Learning (ICML), 2022.
+
+[68] Chowdhury, S., Miller, D., & Needham, T. (2021). [Quantized gromov-wasserstein](https://link.springer.com/chapter/10.1007/978-3-030-86523-8_49). ECML PKDD 2021. Springer International Publishing.

RELEASES.md

@@ -3,6 +3,7 @@
 ## 0.9.4dev
 
 #### New features
++ New quantized FGW solvers `ot.gromov.quantized_fused_gromov_wasserstein`, `ot.gromov.quantized_fused_gromov_wasserstein_samples` and `ot.gromov.quantized_fused_gromov_wasserstein_partitioned` (PR #603)
 + `ot.gromov._gw.solve_gromov_linesearch` now has an argument to specify if the matrices are symmetric in which case the computation can be done faster (PR #607).
 + Continuous entropic mapping (PR #613)
 + New general unbalanced solvers for `ot.solve` and BFGS solver and illustrative example (PR #620)