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Volume 29, 2023
Article Number 19
Number of page(s) 36
Published online 07 March 2023
  1. M. Agueh and G. Carlier Barycenters in the Wasserstein space. SIAM J. Math. Anal. 43 (2011) 904–924. [CrossRef] [MathSciNet] [Google Scholar]
  2. J. Bigot and T. Klein Characterization of barycenters in the Wasserstein space by averaging optimal transport maps. ESAIM: PS 22 (2018) 35–57. [CrossRef] [EDP Sciences] [Google Scholar]
  3. D.P. Bourne and S.M. Roper Centroidal power diagrams, Lloyd’s algorithm, and applications to optimal location problems. SIAM J. Numer. Anal. 53 (2015) 2545–2569. [CrossRef] [MathSciNet] [Google Scholar]
  4. T. Cai, J. Cheng, B. Schmitzer and M. Thorpe The linearized Hellinger-Kantorovich distance. SIAM J. Imaging Sci. 15 (2022) 45–83. [CrossRef] [MathSciNet] [Google Scholar]
  5. K. Chaudhuri, S. Dasgupta, S. Kpotufe and U. von Luxburg Consistent procedures for cluster tree estimation and pruning. IEEE Trans. Inf. Theory 60 (2014) 7900–7912. [CrossRef] [Google Scholar]
  6. L. Chizat, G. Peyré, B. Schmitzer and F.-X. Vialard An interpolating distance between optimal transport and Fisher-Rao metrics. Found. Comp. Math. 18 (2018) 1–44. [CrossRef] [Google Scholar]
  7. L. Chizat, G. Peyré, B. Schmitzer and F.-X. Vialard Unbalanced optimal transport: dynamic and Kantorovich formulations. J. Funct. Anal. 274 (2018) 3090–3123. [CrossRef] [MathSciNet] [Google Scholar]
  8. N.-P. Chung and M.-N. Phung Barycenters in the Hellinger-Kantorovich space. Appl. Math. Optim. 84 (2021) 1791–1820. [CrossRef] [MathSciNet] [Google Scholar]
  9. L.C. Evans, Partial differential equations., Vol. 19 of Graduate Studies in Mathematics, 2nd edn. American Mathematical Society, Providence, RI (2010). [CrossRef] [Google Scholar]
  10. G. Friesecke, D. Matthes and B. Schmitzer Barycenters for the Hellinger-Kantorovich distance over Rd. SIAM J. Math. Anal. 53 (2021) 62–110. [CrossRef] [MathSciNet] [Google Scholar]
  11. W.W. Hager and H. Zhang, A new conjugate gradient method with guaranteed descent and an efficient line search. SIAM J. Optim. 16 (2005) 170–192. [CrossRef] [MathSciNet] [Google Scholar]
  12. S. Kondratyev, L. Monsaingeon and D. Vorotnikov, A new optimal transport distance on the space of finite Radon measures. Adv. Differ. Equ. 21 (2016) 1117–1164. [Google Scholar]
  13. V. Laschos and A. Mielke Geometric properties of cones with applications on the Hellinger-Kantorovich space, and a new distance on the space of probability measures. J. Funct. Anal. 276 (2019) 3529–3576. [CrossRef] [MathSciNet] [Google Scholar]
  14. M. Liero, A. Mielke and G. Savaré Optimal entropy-transport problems and a new Hellinger-Kantorovich distance between positive measures. Invent. Math. 211 (2018) 969–1117. [CrossRef] [MathSciNet] [Google Scholar]
  15. C.F. Olson Parallel algorithms for hierarchical clustering. Parallel Comput. 21 (1995) 1313–1325. [CrossRef] [MathSciNet] [Google Scholar]
  16. B. Pass Optimal transportation with infinitely many marginals. J. Funct. Anal. 264 (2013) 947–963. [CrossRef] [MathSciNet] [Google Scholar]
  17. G. Peyré and M. Cuturi Computational optimal transport. Found. Trends Mach. Learn. 11 (2019) 355–607. [CrossRef] [Google Scholar]
  18. F. Santambrogio, Optimal transport for applied mathematicians, vol. 87 of Progress in Nonlinear Differential Equations and Their Applications. Birkhäuser Boston (2015). [CrossRef] [Google Scholar]
  19. C. Villani, Optimal transport: old and new. Vol. 338 of Grundlehren der mathematischen Wissenschaften. Springer (2009). [CrossRef] [Google Scholar]

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