M. Agueh and G. Carlier, Barycenters in the Wasserstein Space, SIAM Journal on Mathematical Analysis, vol.43, issue.2, pp.904-924, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00637399

J. Altschuler, F. Bach, A. Rudi, and J. Weed, Massively scalable Sinkhorn distances via the Nyström method, 2018.

J. Altschuler, J. Weed, and P. Rigollet, Preprint repository arXiv achieves milestone million uploads, Physics Today, 2014.

S. Angenent, S. Haker, and A. Tannenbaum, Minimizing Flows for the Monge--Kantorovich Problem, SIAM Journal on Mathematical Analysis, vol.35, issue.1, pp.61-97, 2003.

A. Bellet, A. Habrard, and M. Sebban, Mineral resources of the San Rafael primitive area, California, 1966.

J. D. Benamou, G. Carlier, M. Cuturi, L. Nenna, and G. Peyré, Iterative Bregman Projections for Regularized Transportation Problems, SIAM Journal on Scientific Computing, vol.37, issue.2, pp.A1111-A1138, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01096124

F. Benmansour, G. Carlier, G. Peyré, and F. Santambrogio, Derivatives with respect to metrics and applications: subgradient marching algorithm, Numerische Mathematik, vol.116, issue.3, pp.357-381, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00360971

F. Benmansour, G. Carlier, G. Peyré, and F. Santambrogio, Derivatives with respect to metrics and applications: subgradient marching algorithm, Numerische Mathematik, vol.116, issue.3, pp.357-381, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00360971

N. Bonneel, G. Peyré, and M. Cuturi, Wasserstein barycentric coordinates, ACM Transactions on Graphics, vol.35, issue.4, pp.1-10, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01303148

J. Brickell, I. S. Dhillon, S. Sra, and J. A. Tropp, The Metric Nearness Problem, SIAM Journal on Matrix Analysis and Applications, vol.30, issue.1, pp.375-396, 2008.

G. Buttazzo, A. Davini, I. Fragalà, and F. Macià, Optimal Riemannian distances preventing mass transfer, Journal für die reine und angewandte Mathematik (Crelles Journal), vol.2004, issue.575, 2004.

G. Chechik, V. Sharma, U. Shalit, and S. Bengio, Large Scale Online Learning of Image Similarity through Ranking, Pattern Recognition and Image Analysis, pp.11-14, 2009.

L. Chizat, G. Peyré, B. Schmitzer, and F. X. Vialard, Scaling algorithms for unbalanced optimal transport problems, Mathematics of Computation, vol.87, issue.314, pp.2563-2609, 2018.

S. Chopra, R. Hadsell, and Y. Lecun, Learning a Similarity Metric Discriminatively, with Application to Face Verification, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05), vol.1, pp.539-546

N. Courty, R. Flamary, D. Tuia, and A. Rakotomamonjy, Optimal Transport for Domain Adaptation, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.39, issue.9, pp.1853-1865, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01377220

K. Crane, C. Weischedel, and M. Wardetzky, Geodesics in heat, ACM Transactions on Graphics, vol.32, issue.5, pp.1-11, 2013.

M. Cuturi, Sinkhorn distances: Lightspeed computation of optimal transport, Advances in Neural Information Processing Systems, pp.2292-2300, 2013.

M. Cuturi and D. Avis, Ground metric learning, Machine Learning Research, vol.15, issue.1, pp.533-564, 2014.
URL : https://hal.archives-ouvertes.fr/hal-02366636

M. Cuturi and A. Doucet, Fast computation of Wasserstein barycenters, International Conference on Machine Learning, pp.685-693, 2014.

P. Dognin, I. Melnyk, Y. Mroueh, J. Ross, and T. Sercu, Adversarial Semantic Alignment for Improved Image Captions, 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2019.

A. Dupuy, A. Galichon, and Y. Sun, Estimating Matching Affinity Matrix under Low-Rank Constraints, SSRN Electronic Journal, 2016.

P. Dvurechensky, A. Gasnikov, and A. Kroshnin, Computational Optimal Transport: Complexity by Accelerated Gradient Descent Is Better Than by Sinkhorn's Algorithm, 2018.

C. Frogner, C. Zhang, H. Mobahi, M. Araya, and T. A. Poggio, Learning with a Wasserstein Loss, Advances in Neural Information Processing Systems p, p.9, 2015.

A. Genevay, G. Peyré, and M. Cuturi, Learning Generative Models with Sinkhorn Divergences, 2017.

S. Gerber and M. Maggioni, Preprint repository arXiv achieves milestone million uploads, Physics Today, 2014.

A. Griewank and A. Walther, Algorithm 799: revolve, ACM Transactions on Mathematical Software, vol.26, issue.1, pp.19-45, 2000.

A. Griewank and A. Walther, Evaluating Derivatives, Other Titles in Applied Mathematics. Society for Industrial and Applied Mathematics, 2008.

G. Huang, C. Guo, M. J. Kusner, Y. Sun, F. Sha et al., Semi-Supervised MarginBoost, Advances in Neural Information Processing Systems 14, pp.4862-4870, 2002.

D. Kedem, S. Tyree, F. Sha, G. R. Lanckriet, and K. Q. Weinberger, Non-linear Metric Learning. Neural Information Processing Systems (NIPS) p, p.9, 2012.

B. Kulis, Metric Learning: A Survey, Foundations and Trends® in Machine Learning, vol.5, issue.4, pp.287-364, 2013.

B. Lévy, A Numerical Algorithm forL2Semi-Discrete Optimal Transport in 3D, ESAIM: Mathematical Modelling and Numerical Analysis, vol.49, issue.6, pp.1693-1715, 2015.

R. Li, X. Ye, H. Zhou, and H. Zha, Learning to Match via Inverse Optimal Transport, Journal of Machine Learning Research, p.37, 2019.

D. L. Macadam, Visual Sensitivities to Color Differences in Daylight*, Journal of the Optical Society of America, vol.32, issue.5, p.247, 1942.

R. J. Mccann, A Convexity Principle for Interacting Gases, Advances in Mathematics, vol.128, issue.1, pp.153-179, 1997.

J. M. Mirebeau and J. Dreo, Automatic Differentiation of Non-holonomic Fast Marching for Computing Most Threatening Trajectories Under Sensors Surveillance, Lecture Notes in Computer Science, pp.791-800, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01503607

N. Papadakis, G. Peyré, and E. Oudet, Optimal Transport with Proximal Splitting, SIAM Journal on Imaging Sciences, vol.7, issue.1, pp.212-238, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00918460

A. Paszke, S. Gross, S. Chintala, G. Chanan, E. Yang et al., Automatic differentiation in PyTorch, p.4, 2017.

O. Pele and Y. Ben-aliz, Interpolated Discretized Embedding of Single Vectors and Vector Pairs for Classification, Metric Learning and Distance Approximation, 2016.

G. Peyré and M. Cuturi, Computational Optimal Transport, 2019.

Y. Rubner, C. Tomasi, and L. J. Guibas, A metric for distributions with applications to image databases, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271), p.23

R. Sandler and M. Lindenbaum, Nonnegative Matrix Factorization with Earth Mover's Distance Metric for Image Analysis, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.33, issue.8, pp.1590-1602, 2011.

F. Santambrogio, Gradient flows, Optimal Transport for Applied Mathematicians, pp.285-323, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01365905

G. Schiebinger, J. Shu, M. Tabaka, B. Cleary, V. Subramanian et al., Optimal-Transport Analysis of Single-Cell Gene Expression Identifies Developmental Trajectories in Reprogramming, Cell, vol.176, issue.4, pp.928-943.e22, 2019.

M. A. Schmitz, M. Heitz, N. Bonneel, F. Ngolè, D. Coeurjolly et al., Wasserstein Dictionary Learning: Optimal Transport-Based Unsupervised Nonlinear Dictionary Learning, SIAM Journal on Imaging Sciences, vol.11, issue.1, pp.643-678, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01717943

E. Simou and P. Frossard, Graph Signal Representation with Wasserstein Barycenters, ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2019.

J. Solomon, F. De-goes, G. Peyré, M. Cuturi, A. Butscher et al., Convolutional wasserstein distances, ACM Transactions on Graphics, vol.34, issue.4, pp.1-11, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01188953

A. M. Stuart and M. T. Wolfram, Inverse Optimal Transport, SIAM Journal on Applied Mathematics, vol.80, issue.1, pp.599-619, 2020.

L. Torresani and K. C. Lee, Large Margin Component Analysis, Advances in Neural Information Processing Systems 19, vol.8, 2007.

S. R. Varadhan, On the behavior of the fundamental solution of the heat equation with variable coefficients, Communications on Pure and Applied Mathematics, vol.20, issue.2, pp.431-455, 2010.

F. Wang and L. J. Guibas, Supervised Earth Mover?s Distance Learning and Its Computer Vision Applications, Computer Vision ? ECCV 2012, vol.7572, pp.442-455, 2012.

J. Wang, H. T. Do, A. Woznica, and A. Kalousis, Implicit Online Learning with Kernels, Advances in Neural Information Processing Systems 19, p.9, 2007.

K. Q. Weinberger, J. Blitzer, and L. K. Saul, Max-margin classification of incomplete data, Advances in Neural Information Processing Systems 19, 2007.

K. Q. Weinberger and L. K. Saul, Fast solvers and efficient implementations for distance metric learning, Proceedings of the 25th international conference on Machine learning - ICML '08, pp.1160-1167, 2008.

E. P. Xing, M. I. Jordan, S. J. Russell, and A. Y. Ng, Distance Metric Learning with Application to Clustering with Side-Information, Advances in Neural Information Processing Systems, p.8, 2003.

J. Xu, L. Luo, C. Deng, and H. Huang, Multi-Level Metric Learning via Smoothed Wasserstein Distance, Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence, pp.2919-2925, 2018.

F. Yang and L. D. Cohen, Geodesic Distance and Curves Through Isotropic and Anisotropic Heat Equations on Images and Surfaces, Journal of Mathematical Imaging and Vision, vol.55, issue.2, pp.210-228, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01415017

W. Yang, L. Xu, X. Chen, F. Zheng, and Y. Liu, Chi-Squared Distance Metric Learning for Histogram Data, Mathematical Problems in Engineering, vol.2015, pp.1-12, 2015.

G. Zen, E. Ricci, and N. Sebe, Simultaneous Ground Metric Learning and Matrix Factorization with Earth Mover's Distance, 2014 22nd International Conference on Pattern Recognition, pp.3690-3695, 2014.