[38] Matt Kusner, Yu Sun, Nicholas Kolkin, and Kilian Weinberger. From word embeddings to document distances. In International conference on machine learning, pages 957-966. PMLR, 2015.
[39] Yann LeCun. The MNIST database of handwritten digits. http://yann.lecun.com/exdb/mnist/, 1998.
[40] Tianyi Lin, Zeyu Zheng, Elynn Chen, Marco Cuturi, and Michael I Jordan. On projection robust optimal transport: Sample complexity and model misspecification. In International Conference on Artificial Intelligence and Statistics, pages 262-270, 2021.
[41] Quentin Mérigot, Alex Delalande, and Frédéric Chazal. Quantitative stability of optimal transport maps and linearization of the 2-wasserstein space. In International Conference on Artificial Intelligence and Statistics, pages 3186-3196, 2020.
[42] Gaspard Monge. Mémoire sur la théorie des déblais et des remblais. Mem. Math. Phys. Acad. Royale Sci., pages 666-704, 1781.
[43] Caroline Moosmüller and Alexander Cloninger. Linear optimal transport embedding: Provable Wasserstein classification for certain rigid transformations and perturbations. Information and Inference: A Journal of the IMA, 12(1):363-389, 2023.
[44] Boris Muzellec and Marco Cuturi. Subspace detours: Building transport plans that are optimal on subspace projections. Advances in Neural Information Processing Systems, 32, 2019.
[45] Kimia Nadjahi, Alain Durmus, Lénaïc Chizat, Soheil Kolouri, Shahin Shahrampour, and Umut Simsekli. Statistical and topological properties of sliced probability divergences. Advances in Neural Information Processing Systems, 33, 2020.
[46] Kimia Nadjahi, Alain Durmus, Pierre E Jacob, Roland Badeau, and Umut Simsekli. Fast approximation of the sliced-wasserstein distance using concentration of random projections. Advances in Neural Information Processing Systems, 34:12411-12424, 2021.
[47] Luca Nenna and Brendan Pass. Transport type metrics on the space of probability measures involving singular base measures. Applied Mathematics & Optimization, 87(2):28, 2023.
[48] Peer Neubert and Peter Protzel. Compact watershed and preemptive slic: On improving trade-offs of superpixel segmentation algorithms. In 2014 22nd international conference on pattern recognition, pages 996-1001. IEEE, 2014.
[49] Khai Nguyen, Nhat Ho, Tung Pham, and Hung Bui. Distributional sliced-wasserstein and applications to generative modeling. In International Conference on Learning Representations, 2021.
[50] Khai Nguyen, Tongzheng Ren, Huy Nguyen, Litu Rout, Tan Nguyen, and Nhat Ho. Hierarchical sliced Wasserstein distance. arXiv preprint arXiv:2209.13570, 2022.
[51] Felix Otto. The geometry of dissipative evolution equations: the porous medium equation. Communications in Partial Differential Equations, 26(1-2):101-174, 2001.
[52] François-Pierre Paty and Marco Cuturi. Subspace robust Wasserstein distances. In International conference on machine learning, pages 5072-5081, 2019.
[53] Gabriel Peyre and Marco Cuturi. Computational optimal transport. Foundations and Trends in Machine Learning, 11(5-6):355–607, 2019.
[54] Martin Pincus. A monte carlo method for the approximate solution of certain types of constrained optimization problems. Operations research, 18(6):1225-1228, 1970.
[55] Julien Rabin, Sira Ferradans, and Nicolas Papadakis. Adaptive color transfer with relaxed optimal transport. In IEEE international conference on image processing (ICIP), pages 4852-4856, 2014.