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Optimal transport (OT) has become exceedingly popular in machine learning, data science, and computer vision.
On a problem of monge
Leonid V Kantorovich · 1948
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A relationship between arbitrary positive matrices and doubly stochastic matrices
Richard Sinkhorn · 1964
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A new polynomial-time algorithm for linear programming
Narendra Karmarkar · 1984
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A faster strongly polynomial minimum cost flow algorithm
James Orlin · 1988
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Least-squares estimation of transformation parameters between two point patterns
Shinji Umeyama · 1991
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Method for registration of 3-d shapes
Paul J Besl and Neil D McKay · 1992
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Object modelling by registration of multiple range images
Yang Chen and Gérard Medioni · 1992
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Perspectives of Monge properties in optimization
R. E. Burkhard, B. Klinz, and R. Rudolf · 1996
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Extended Kantorovich norms: a tool for optimization
Kevin Guittet · 2002
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An extension of the icp algorithm considering scale factor
Shaoyi Du, Nanning Zheng, Shihui Ying, Qubo You, and Yang Wu · 2007
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Optimal transport: old and new
Cedric Villani · 2009
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Free boundaries in optimal transport and monge-ampere obstacle problems
Luis A Caffarelli and Robert J McCann · 2010
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The optimal partial transport problem
Alessio Figalli · 2010
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A new transportation distance between non-negative measures, with applications to gradients flows with dirichlet boundary conditions
Alessio Figalli and Nicola Gigli · 2010
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Computer vision: algorithms and applications
Richard Szeliski · 2010
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Wasserstein barycenter and its application to texture mixing
Julien Rabin, Gabriel Peyré, Julie Delon, and Marc Bernot · 2011
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Sinkhorn distances: Lightspeed computation of optimal transport
Marco Cuturi · 2013
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Domain adaptation with regularized optimal transport
Nicolas Courty, Rémi Flamary, and Devis Tuia · 2014
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Regularized discrete optimal transport
Sira Ferradans, Nicolas Papadakis, Gabriel Peyré, and Jean-François Aujol · 2014
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Imaging with kantorovich–rubinstein discrepancy
Jan Lellmann, Dirk A Lorenz, Carola Schonlieb, and Tuomo Valkonen · 2014
Cited alongside, same era.
Generalized wasserstein distance and its application to transport equations with source
Benedetto Piccoli and Francesco Rossi · 2014
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Wasserstein propagation for semi-supervised learning
Justin Solomon, Raif Rustamov, Leonidas Guibas, and Adrian Butscher · 2014
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Iterative bregman projections for regularized transportation problems
Jean-David Benamou, Guillaume Carlier, Marco Cuturi, Luca Nenna, and Gabriel Peyré · 2015
Cited alongside, same era.
Sliced and Radon Wasserstein barycenters of measures
Nicolas Bonneel, Julien Rabin, Gabriel Peyré, and Hanspeter Pfister · 2015
Cited alongside, same era.
Learning with a Wasserstein loss
Charlie Frogner, Chiyuan Zhang, Hossein Mobahi, Mauricio Araya, and Tomaso A Poggio · 2015
An interpolating distance between optimal transport and Fisher–Rao metrics
Lenaic Chizat, Gabriel Peyré, Bernhard Schmitzer, and François-Xavier Vialard · 2018
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Scaling algorithms for unbalanced optimal transport problems
Lenaic Chizat, Gabriel Peyré, Bernhard Schmitzer, and François-Xavier Vialard · 2018
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Unbalanced optimal transport: Dynamic and Kantorovich formulations
Lenaic Chizat, Gabriel Peyré, Bernhard Schmitzer, and François-Xavier Vialard · 2018
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Optimal entropy-transport problems and a new Hellinger–Kantorovich distance between positive measures
Matthias Liero, Alexander Mielke, and Giuseppe Savare · 2018
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SPOT: sliced partial optimal transport
Nicolas Bonneel and David Coeurjolly · 2019
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Max-sliced wasserstein distance and its use for gans
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Cited alongside, same era.
The radon cumulative distribution transform and its application to image classification
Soheil Kolouri, Se Rim Park, and Gustavo K Rohde · 2015
Cited alongside, same era.
Optimal Transport for Applied Mathematicians
Filippo Santambrogio · 2015
Cited alongside, same era.
Convolutional Wasserstein distances: Efficient optimal transportation on geometric domains
Justin Solomon, Fernando De Goes, Gabriel Peyré, Marco Cuturi, Adrian Butscher, Andy Nguyen, Tao Du, and Leonidas Guibas · 2015
Cited alongside, same era.
Stochastic optimization for large-scale optimal transport
Aude Genevay, Marco Cuturi, Gabriel Peyré, and Francis Bach · 2016
Cited alongside, same era.
Sliced wasserstein kernels for probability distributions
Soheil Kolouri, Yang Zou, and Gustavo K Rohde · 2016
Cited alongside, same era.
Wasserstein training of restricted Boltzmann machines
Grégoire Montavon, Klaus-Robert Müller, and Marco Cuturi · 2016
Cited alongside, same era.
Ishan Deshpande, Yuan-Ting Hu, Ruoyu Sun, Ayis Pyrros, Nasir Siddiqui, Sanmi Koyejo, Zhizhen Zhao, David Forsyth, and Alexander G Schwing · 2019
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Unnormalized optimal transport
Wilfrid Gangbo, Wuchen Li, Stanley Osher, and Michael Puthawala · 2019
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Generalized sliced Wasserstein distances
Soheil Kolouri, Kimia Nadjahi, Umut Simsekli, Roland Badeau, and Gustavo Rohde · 2019
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Tree-sliced variants of wasserstein distances
Tam Le, Makoto Yamada, Kenji Fukumizu, and Marco Cuturi · 2019
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Wasserstein GAN with quadratic transport cost
Huidong Liu, Xianfeng Gu, and Dimitris Samaras · 2019
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Sliced-wasserstein flows: Nonparametric generative modeling via optimal transport and diffusions
Antoine Liutkus, Umut Simsekli, Szymon Majewski, Alain Durmus, and Fabian-Robert Stöter · 2019
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Computational optimal transport: With applications to data science
Gabriel Peyré, Marco Cuturi, et al · 2019
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Fast and robust comparison of probability measures in heterogeneous spaces
Ryoma Sato, Marco Cuturi, Makoto Yamada, and Hisashi Kashima · 2020
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Unbalanced minibatch optimal transport; applications to domain adaptation
Kilian Fatras, Thibault Séjourné, Rémi Flamary, and Nicolas Courty · 2021
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Pot: Python optimal transport
Rémi Flamary, Nicolas Courty, Alexandre Gramfort, Mokhtar Z. Alaya, Aurélie Boisbunon, Stanislas Chambon, Laetitia Chapel, Adrien Corenflos, Kilian Fatras, Nemo Fournier, Léo Gautheron, Nathalie T.H. Gayraud, Hicham Janati, Alain Rakotomamonjy, Ievgen Redko, Antoine Rolet, Antony Schutz, Vivien Seguy, Danica J. Sutherland, Romain Tavenard, Alexander Tong, and Titouan Vayer · 2021
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A comprehensive survey on point cloud registration
Xiaoshui Huang, Guofeng Mei, Jian Zhang, and Rana Abbas · 2021
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Generalized unnormalized optimal transport and its fast algorithms
Wonjun Lee, Rongjie Lai, Wuchen Li, and Stanley Osher · 2021
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Kantorovich–rubinstein distance and barycenter for finitely supported measures: Foundations and algorithms
Florian Heinemann, Marcel Klatt, and Axel Munk · 2023
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