R. K. Ahuja, T. L. Magnanti, and J. B. Orlin, Network Flows: Theory, Algorithms and Applications, 1993.
DOI : 10.21236/ADA594171

I. Alabdulmohsin, X. Gao, and X. Zhang, Support vector machines with indefinite kernels, Asian Conference on Machine Learning (ACML), pp.32-47, 2014.

S. Amari and H. Nagaoka, Methods of Information Geometry, volume 191 of Translations of Mathematical Monographs, 2000.

M. Arjovsky, S. Chintala, L. Bottou, and G. Wasserstein, , 2017.

H. H. Bauschke and A. S. Lewis, Dykstra's algorithm with Bregman projections: A convergence proof. Optimization, pp.409-427, 2000.

J. 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.1111-1138, 2015.
DOI : 10.1137/141000439
URL : https://hal.archives-ouvertes.fr/hal-01096124

E. Bernton, P. E. Jacob, M. Gerber, and C. P. Robert, Inference in generative models using the Wasserstein distance, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01517550

J. Bigot, R. Gouet, T. Klein, and A. López, Geodesic PCA in the Wasserstein space, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01978864

M. Blondel, V. Seguy, and A. Rolet, Smooth and sparse optimal transport, 2017.

N. Bonneel, M. Van-de-panne, S. Paris, and W. Heidrich, Displacement interpolation using lagrangian mass transport, ACM Transactions on Graphics, vol.30158, issue.6, pp.1-15812, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00763270

O. Bousquet, S. Gelly, I. Tolstikhin, C. Simon-gabriel, and B. Schölkopf, From optimal transport to generative modeling: the VEGAN cookbook, 2017.

E. Cazelles, V. Seguy, J. Bigot, M. Cuturi, and N. Papadakis, Geodesic PCA versus Log-PCA of Histograms in the Wasserstein Space, SIAM Journal on Scientific Computing, vol.40, issue.2, 2017.
DOI : 10.1137/17M1143459
URL : https://hal.archives-ouvertes.fr/hal-01581699

R. Cominetti and J. San-martín, Asymptotic analysis of the exponential penalty trajectory in linear programming, Mathematical Programming, vol.27, issue.2, pp.1-3169, 1994.
DOI : 10.1007/BF01582220

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, 2015.
DOI : 10.1109/TPAMI.2016.2615921
URL : https://hal.archives-ouvertes.fr/hal-01103073

M. Cuturi, Sinkhorn distances: Lightspeed computation of optimal transport, International Conference on Neural Information Processing Systems (NIPS), pp.2292-2300, 2013.

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

M. Cuturi and G. Peyré, A Smoothed Dual Approach for Variational Wasserstein Problems, SIAM Journal on Imaging Sciences, vol.9, issue.1, pp.320-343, 2016.
DOI : 10.1137/15M1032600
URL : https://hal.archives-ouvertes.fr/hal-01188954

A. Dessein, N. Papadakis, and C. Deledalle, Parameter estimation in finite mixture models by regularized optimal transport: A unified framework for hard and soft clustering, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01635325

I. S. Dhillon and J. A. Tropp, Matrix Nearness Problems with Bregman Divergences, SIAM Journal on Matrix Analysis and Applications, vol.29, issue.4, pp.1120-1146, 2007.
DOI : 10.1137/060649021

S. Ferradans, N. Papadakis, G. Peyré, and J. Aujol, Regularized Discrete Optimal Transport, SIAM Journal on Imaging Sciences, vol.7, issue.3, pp.1853-1882, 2014.
DOI : 10.1137/130929886
URL : https://hal.archives-ouvertes.fr/hal-00797078

C. Frogner, C. Zhang, H. Mobahi, M. Araya-polo, and T. Poggio, Learning with a Wasserstein loss, International Conference on Neural Information Processing Systems (NIPS), pp.2053-2061, 2015.

A. Galichon and B. Salanié, Cupid???s Invisible Hand: Social Surplus and Identification in Matching Models, SSRN Electronic Journal, p.1804623, 2015.
DOI : 10.2139/ssrn.1804623

A. Genevay, G. Peyré, and M. Cuturi, GAN and VAE from an optimal transport point of view, 2017.

K. Grauman and T. Darrell, Fast contour matching using approximate Earth mover's distance, Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004., pp.220-227, 2004.
DOI : 10.1109/CVPR.2004.1315035

J. Gudmundsson, O. Klein, C. Knauer, and M. Smid, Small Manhattan networks and algorithmic applications for the earth mover's distance, European Workshop on Computational Geometry (EuroCG), pp.174-177, 2007.

B. Haasdonk, Feature space interpretation of SVMs with indefinite kernels, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.27, issue.4, pp.482-492, 2005.
DOI : 10.1109/TPAMI.2005.78

M. , A review of matrix scaling and Sinkhorn's normal form for matrices and positive maps, 2016.

P. Indyk and N. Thaper, Fast image retrieval via embeddings, International Workshop on Statistical and Computational Theories of Vision, 2003.

S. Kurras, Symmetric iterative proportional fitting, International Conference on Artificial Intelligence and Statistics (AISTATS), pp.526-534, 2015.

H. Lin and C. Lin, A study on sigmoid kernels for SVM and the training of non-PSD kernels by SMO-type methods, 2003.

H. Ling and K. Okada, An Efficient Earth Mover's Distance Algorithm for Robust Histogram Comparison, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.29, issue.5, pp.840-853, 2007.
DOI : 10.1109/TPAMI.2007.1058

A. Mesaros, T. Heittola, and T. Virtanen, TUT database for acoustic scene classification and sound event detection, 2016 24th European Signal Processing Conference (EUSIPCO), pp.1128-1132, 2016.
DOI : 10.1109/EUSIPCO.2016.7760424

G. Montavon, K. Müller, and M. Cuturi, Wasserstein training of restricted Boltzmann machines, International Conference on Neural Information Processing Systems (NIPS), pp.3718-3726, 2016.

B. Muzellec, R. Nock, G. Patrini, and F. Nielsen, Tsallis regularized optimal transport and ecological inference, AAAI Conference on Artificial Intelligence (AAAI), pp.2387-2393, 2018.

A. Naor and G. Schechtman, Planar Earthmover Is Not in $L_1$, SIAM Journal on Computing, vol.37, issue.3, pp.804-826, 2007.
DOI : 10.1137/05064206X

A. M. Oberman and Y. Ruan, An efficient linear programming method for optimal transportation, 2015.

O. Pele and M. Werman, A Linear Time Histogram Metric for Improved SIFT Matching, European Conference on Computer Vision (ECCV), pp.495-508, 2008.
DOI : 10.1109/CVPR.1997.609451

O. Pele and M. Werman, Fast and robust Earth Mover's Distances, 2009 IEEE 12th International Conference on Computer Vision, pp.460-467, 2009.
DOI : 10.1109/ICCV.2009.5459199

J. Rabin, J. Delon, and Y. Gousseau, A Statistical Approach to the Matching of Local Features, SIAM Journal on Imaging Sciences, vol.2, issue.3, pp.931-958, 2009.
DOI : 10.1137/090751359
URL : https://hal.archives-ouvertes.fr/hal-00168285

A. Rolet, M. Cuturi, and G. Peyré, Fast dictionary learning with a smoothed Wasserstein loss, International Conference on Artificial Intelligence and Statistics (AISTATS), pp.630-638, 2016.

Y. Rubner, C. Tomasi, and L. J. Guibas, The earth mover's distance as a metric for image retrieval, International Journal of Computer Vision, vol.40, issue.2, pp.99-121, 2000.
DOI : 10.1023/A:1026543900054

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.
DOI : 10.1137/17M1140431
URL : https://hal.archives-ouvertes.fr/hal-01717943

B. Schmitzer, A Sparse Multiscale Algorithm for Dense Optimal Transport, Journal of Mathematical Imaging and Vision, vol.101, issue.3, pp.238-259, 2016.
DOI : 10.1007/s11263-012-0566-z
URL : https://hal.archives-ouvertes.fr/hal-01385274

B. Schmitzer, Stabilized sparse scaling algorithms for entropy regularized transport problems, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01385251

V. Seguy and M. Cuturi, Principal geodesic analysis for probability measures under the optimal transport metric, International Conference on Neural Information Processing Systems (NIPS), pp.3312-3320, 2015.

F. Sha, Y. Lin, L. K. Saul, and D. D. Lee, Multiplicative Updates for Nonnegative Quadratic Programming, Neural Computation, vol.39, issue.8, pp.2004-2031, 2007.
DOI : 10.1080/10556780512331318182

S. Shirdhonkar and D. W. Jacobs, Approximate earth mover's distance in linear time, IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp.1-8, 2008.

R. Sinkhorn and P. Knopp, Concerning nonnegative matrices and doubly stochastic matrices, Pacific Journal of Mathematics, vol.21, issue.2, pp.343-348, 1967.
DOI : 10.2140/pjm.1967.21.343

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.1-6611, 2015.
DOI : 10.1145/563858.563893
URL : https://hal.archives-ouvertes.fr/hal-01188953

J. Solomon, R. M. Rustamov, L. Guibas, and A. Butscher, Wasserstein propagation for semi-supervised learning, International Conference on Machine Learning (ICML), pp.306-314, 2014.

A. Thibault, L. Chizat, C. Dossal, and N. Papadakis, Overrelaxed sinkhorn-knopp algorithm for regularized optimal transport, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01629985

L. Thorlund-petersen, Global convergence of Newton?s method on an interval, Mathematical Methods of Operations Research (ZOR), vol.59, issue.1, pp.91-110, 2004.
DOI : 10.1007/s001860300304

P. Tseng, Dual coordinate ascent methods for non-strictly convex minimization, Mathematical Programming, pp.231-247, 1993.
DOI : 10.1007/BF01581245

C. Villani, Optimal Transport: Old and New, Comprehensive Studies in Mathematics, vol.338, 2009.
DOI : 10.1007/978-3-540-71050-9

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.
DOI : 10.1109/ICPR.2014.634