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
, Massively scalable Sinkhorn distances via the Nyström method, 2018.
Preprint repository arXiv achieves milestone million uploads, Physics Today, 2014. ,
Minimizing Flows for the Monge--Kantorovich Problem, SIAM Journal on Mathematical Analysis, vol.35, issue.1, pp.61-97, 2003. ,
Mineral resources of the San Rafael primitive area, California, 1966. ,
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
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
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
Wasserstein barycentric coordinates, ACM Transactions on Graphics, vol.35, issue.4, pp.1-10, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01303148
The Metric Nearness Problem, SIAM Journal on Matrix Analysis and Applications, vol.30, issue.1, pp.375-396, 2008. ,
Optimal Riemannian distances preventing mass transfer, Journal für die reine und angewandte Mathematik (Crelles Journal), vol.2004, issue.575, 2004. ,
Large Scale Online Learning of Image Similarity through Ranking, Pattern Recognition and Image Analysis, pp.11-14, 2009. ,
Scaling algorithms for unbalanced optimal transport problems, Mathematics of Computation, vol.87, issue.314, pp.2563-2609, 2018. ,
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 ,
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
Geodesics in heat, ACM Transactions on Graphics, vol.32, issue.5, pp.1-11, 2013. ,
Sinkhorn distances: Lightspeed computation of optimal transport, Advances in Neural Information Processing Systems, pp.2292-2300, 2013. ,
Ground metric learning, Machine Learning Research, vol.15, issue.1, pp.533-564, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-02366636
Fast computation of Wasserstein barycenters, International Conference on Machine Learning, pp.685-693, 2014. ,
Adversarial Semantic Alignment for Improved Image Captions, 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2019. ,
Estimating Matching Affinity Matrix under Low-Rank Constraints, SSRN Electronic Journal, 2016. ,
Computational Optimal Transport: Complexity by Accelerated Gradient Descent Is Better Than by Sinkhorn's Algorithm, 2018. ,
Learning with a Wasserstein Loss, Advances in Neural Information Processing Systems p, p.9, 2015. ,
, Learning Generative Models with Sinkhorn Divergences, 2017.
Preprint repository arXiv achieves milestone million uploads, Physics Today, 2014. ,
Algorithm 799: revolve, ACM Transactions on Mathematical Software, vol.26, issue.1, pp.19-45, 2000. ,
Evaluating Derivatives, Other Titles in Applied Mathematics. Society for Industrial and Applied Mathematics, 2008. ,
Semi-Supervised MarginBoost, Advances in Neural Information Processing Systems 14, pp.4862-4870, 2002. ,
, Non-linear Metric Learning. Neural Information Processing Systems (NIPS) p, p.9, 2012.
Metric Learning: A Survey, Foundations and Trends® in Machine Learning, vol.5, issue.4, pp.287-364, 2013. ,
A Numerical Algorithm forL2Semi-Discrete Optimal Transport in 3D, ESAIM: Mathematical Modelling and Numerical Analysis, vol.49, issue.6, pp.1693-1715, 2015. ,
Learning to Match via Inverse Optimal Transport, Journal of Machine Learning Research, p.37, 2019. ,
Visual Sensitivities to Color Differences in Daylight*, Journal of the Optical Society of America, vol.32, issue.5, p.247, 1942. ,
A Convexity Principle for Interacting Gases, Advances in Mathematics, vol.128, issue.1, pp.153-179, 1997. ,
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
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
, Automatic differentiation in PyTorch, p.4, 2017.
Interpolated Discretized Embedding of Single Vectors and Vector Pairs for Classification, Metric Learning and Distance Approximation, 2016. ,
Computational Optimal Transport, 2019. ,
A metric for distributions with applications to image databases, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271), p.23 ,
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. ,
Gradient flows, Optimal Transport for Applied Mathematicians, pp.285-323, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01365905
Optimal-Transport Analysis of Single-Cell Gene Expression Identifies Developmental Trajectories in Reprogramming, Cell, vol.176, issue.4, pp.928-943.e22, 2019. ,
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
Graph Signal Representation with Wasserstein Barycenters, ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2019. ,
Convolutional wasserstein distances, ACM Transactions on Graphics, vol.34, issue.4, pp.1-11, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01188953
Inverse Optimal Transport, SIAM Journal on Applied Mathematics, vol.80, issue.1, pp.599-619, 2020. ,
Large Margin Component Analysis, Advances in Neural Information Processing Systems 19, vol.8, 2007. ,
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. ,
Supervised Earth Mover?s Distance Learning and Its Computer Vision Applications, Computer Vision ? ECCV 2012, vol.7572, pp.442-455, 2012. ,
Implicit Online Learning with Kernels, Advances in Neural Information Processing Systems 19, p.9, 2007. ,
Max-margin classification of incomplete data, Advances in Neural Information Processing Systems 19, 2007. ,
Fast solvers and efficient implementations for distance metric learning, Proceedings of the 25th international conference on Machine learning - ICML '08, pp.1160-1167, 2008. ,
Distance Metric Learning with Application to Clustering with Side-Information, Advances in Neural Information Processing Systems, p.8, 2003. ,
Multi-Level Metric Learning via Smoothed Wasserstein Distance, Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence, pp.2919-2925, 2018. ,
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
Chi-Squared Distance Metric Learning for Histogram Data, Mathematical Problems in Engineering, vol.2015, pp.1-12, 2015. ,
Simultaneous Ground Metric Learning and Matrix Factorization with Earth Mover's Distance, 2014 22nd International Conference on Pattern Recognition, pp.3690-3695, 2014. ,