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All issues Volume 30 (2024) ESAIM: COCV, 30 (2024) 78 References
Open Access
Issue
ESAIM: COCV
Volume 30, 2024
Article Number 78
Number of page(s) 21
DOI https://doi.org/10.1051/cocv/2024063
Published online 07 October 2024
  1. D. Alvarez-Melis and T. Jaakkola, Gromov–Wasserstein alignment of word embedding spaces, in Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing (2018) 1881–1890. [CrossRef] [Google Scholar]
  2. C. Bunne, D. Alvarez-Melis, A. Krause and S. Jegelka, Learning generative models across incomparable spaces, in International Conference on Machine Learning (2019) 851–861. [Google Scholar]
  3. S. Chowdhury, D. Miller and T. Needham, Quantized Gromov–Wasserstein, in Joint European Conference on Machine Learning and Knowledge Discovery in Databases. Springer (2021) 811–827. [Google Scholar]
  4. P. Demetci, R. Santorella, B. Sandstede, W.S. Noble and R. Singh, Scot: single-cell multi-omics alignment with optimal transport. J. Computat. Biol. 29 (2022) 3–18. [CrossRef] [Google Scholar]
  5. G. Peyré, M. Cuturi and J. Solomon, Gromov–Wasserstein averaging of kernel and distance matrices, in International Conference on Machine Learning (2016) 2664–2672. [Google Scholar]
  6. H. Xu, D. Luo, H. Zha and L.C. Duke, Gromov–Wasserstein learning for graph matching and node Embedding, in International Conference on Machine Learning (2019) 6932–6941. [Google Scholar]
  7. F. Mémoli and T. Needham, Distance distributions and inverse problems for metric measure spaces. Stud. Appl. Math. 149 (2022) 943–1001. [CrossRef] [MathSciNet] [Google Scholar]
  8. T. Dumont, T. Lacombe and F.-X. Vialard, On the existence of Monge maps for the Gromov–Wasserstein problem. Found. Computat. Math. (2024) 1–48. [Google Scholar]
  9. Y.H. Hur, W. Guo and T. Liang, Reversible Gromov–Monge sampler for simulation-based inference. SIAM J. Math. Data Sci. 6 (2024) 283–310. [CrossRef] [MathSciNet] [Google Scholar]
  10. A. Salmona, J. Delon and A. Desolneux, Gromov–Wasserstein distances between Gaussian distributions. J. Appl. Probab. 59 (2022) 1178–1198. [CrossRef] [MathSciNet] [Google Scholar]
  11. T. Vayer, A contribution to optimal transport on incomparable spaces. Preprint arXiv:2011.04447 (2020). [Google Scholar]
  12. Z. Zhang, Y. Mroueh, Z. Goldfeld and B. Sriperumbudur, Cycle consistent probability divergences across different spaces, in International Conference on Artificial Intelligence and Statistics. PMLR (2022) 7257–7285. [Google Scholar]
  13. G. Peyré and M. Cuturi, Computational optimal transport. Found. Trends Mach. Learn. 11 (2019) 355–607. [CrossRef] [Google Scholar]
  14. C. Villani, Optimal Transport: Old and New, Vol. 338. Springer Science & Business Media (2008). [Google Scholar]
  15. Y.H. Hur, W. Guo and T. Liang, Reversible Gromov–Monge sampler for simulation-based inference. Preprint arXiv:2109.14090v3 (2022). [Google Scholar]
  16. L. Ambrosio, Lecture notes on optimal transport problems, in Mathematical Aspects of Evolving Interfaces. Springer (2003) 1–52. [Google Scholar]
  17. A. Pratelli, On the equality between Monge’s infimum and Kantorovich’s minimum in optimal mass transportation, in Annales de l’Institut Henri Poincare (B) Probability and Statistics, Vol. 43. Elsevier (2007) 1–13. [CrossRef] [Google Scholar]
  18. K.-T. Sturm, The Space of Spaces: Curvature Bounds and Gradient Flows on the Space of Metric Measure Spaces, Vol. 290. Memoirs of the American Mathematical Society (2023). [Google Scholar]
  19. Y. Brenier, Polar factorization and monotone rearrangement of vector-valued functions. Commun. Pure Appl. Math. 44 (1991) 375–417. [Google Scholar]
  20. S. Chowdhury and F. Mémoli, Distances and isomorphism between networks: stability and convergence of network invariants. J. Appl. Computat. Topol. 7 (2022) 243–361. [Google Scholar]
  21. S. Chowdhury and T. Needham, Gromov–Wasserstein averaging in a Riemannian framework. preprint arXiv:1910.04308 (2019). [Google Scholar]
  22. K.-T. Sturm, On the geometry of metric measure spaces. Acta Mathematica 196 (2006) 65–131. [CrossRef] [MathSciNet] [Google Scholar]
  23. R. Al-Aifari, I. Daubechies and Y. Lipman, Continuous Procrustes distance between two surfaces. Commun. Pure Appl. Math. 66 (2013) 934–964. [CrossRef] [Google Scholar]
  24. D.M. Boyer, Y. Lipman, E. St Clair, J. Puente, B.A. Patel, T. Funkhouser, J. Jernvall and I. Daubechies, Algorithms to automatically quantify the geometric similarity of anatomical surfaces. Proc. Natl. Acad. Sci. U.S.A. (2011). [Google Scholar]
  25. S. Haker, L. Zhu, A. Tannenbaum and S. Angenent, Optimal mass transport for registration and warping. Int. J. Comput. Vis. 60 (2004) 225–240. [CrossRef] [Google Scholar]
  26. F. Mémoli, On the use of Gromov–Hausdorff distances for shape comparison, in Proceedings of Point Based Graphics (2007). [Google Scholar]
  27. S. Chen, S. Lim, F. Mémoli, Z. Wan and Y. Wang, Weisfeiler–Lehman meets Gromov–Wasserstein, in International Conference on Machine Learning. PMLR (2022) 3371–3416. [Google Scholar]
  28. S. Chowdhury and F. Mémoli, The Gromov–Wasserstein distance between networks and stable network invariants. Inform. Inference 8 (2019) 757–787. [CrossRef] [Google Scholar]
  29. S. Chowdhury, T. Needham, E. Semrad, B. Wang and Y. Zhou, Hypergraph co-optimal transport: Metric and categorical properties. J. Appl. Computat. Topol. (2023) 1–60. [Google Scholar]
  30. V. Titouan, I. Redko, R. Flamary and N. Courty, Co-optimal transport. Adv. Neural Inform. Process. Syst. 33 (2020) 17559–17570. [Google Scholar]
  31. H. Xu, D. Luo and L. Carin, Scalable Gromov–Wasserstein learning for graph partitioning and matching. Adv. Neural Inform. Process. Syst. 32 (2019). [Google Scholar]
  32. S. Chowdhury and T. Needham, Generalized spectral clustering via Gromov-Wasserstein learning, in International Conference on Artificial Intelligence and Statistics. PMLR (2021) 712–720. [Google Scholar]
  33. F. Mémoli, Gromov–Wasserstein distances and the metric approach to object matching. Found. Computat. Math. 11 (2011) 417–487. [CrossRef] [Google Scholar]
  34. F.W. Lawvere, Metric spaces, generalized logic, and closed categories. Rend. Semin. Maté. Fis. Milano 43 (1973) 135–166. [CrossRef] [Google Scholar]
  35. T. Vayer, R. Flamary, R. Tavenard, L. Chapel and N. Courty, Sliced Gromov–Wasserstein, in Advances in Neural Information Processing Systems (NeurIPS) (2019) 32. [Google Scholar]
  36. N. Bonneel, J. Rabin, G. Peyré and H. Pfister, Sliced and Radon Wasserstein barycenters of measures. J. Math. Imaging Vis. 51 (2015) 22–45. [CrossRef] [Google Scholar]
  37. R. Beinert, C. Heiss and G. Steidl, On assignment problems related to Gromov-Wasserstein distances on the real line. Preprint arXiv:2205.09006 (2022). [Google Scholar]
  38. W. Gangbo, The Monge mass transfer problem and its applications. Contemp. Math. 226 (1999) 79–104. [CrossRef] [Google Scholar]
  39. H.L. Royden, Real Analysis, Vol. 3. Macmillan, New York (1968). [Google Scholar]
  40. Y. Brenier and W. Gangbo, lp approximation of maps by diffeomorphisms. Calc. Variat. Part. Differ. Eq. 16 (2003) 147–164. [CrossRef] [Google Scholar]
  41. H. Maron and Y. Lipman, (Probably) concave graph matching. Adv. Neural Inform. Process. Syst. 31 (2018). [Google Scholar]
  42. D. Alvarez-Melis, S. Jegelka and T.S. Jaakkola, Towards optimal transport with global invariances, in The 22nd International Conference on Artificial Intelligence and Statistics. PMLR (2019) 1870–1879. [Google Scholar]
  43. H.P. Benson, Concave programming, in Encyclopedia of Optimization. Springer (2001) 315–319. [Google Scholar]
  44. F. Mémoli, Gromov–Hausdorff distances in Euclidean spaces, in IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops, 2008. CVPRW’08. IEEE (2008) 1–8. [Google Scholar]
  45. D. Burago, Y.D. Burago and S. Ivanov, A Course in Metric Geometry, Vol. 33. American Mathematical Society (2001). [Google Scholar]
  46. P. Alestalo, D.A. Trotsenko and J. Väisälä, Isometric approximation. Isr. J. Math. 125 (2001) 61–82. [CrossRef] [Google Scholar]
  47. S. Majhi, J. Vitter and C. Wenk, Approximating Gromov–Hausdorff distance in Euclidean space. Computat. Geom. 116 (2024) 102034. [CrossRef] [Google Scholar]

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