This article has an erratum: [https://doi.org/10.1051/cocv/2023018]
Volume 29, 2023
|Number of page(s)||36|
|Published online||07 March 2023|
Hellinger–Kantorovich barycenter between Dirac measures
Campus Institute Data Science, Göttingen University, Germany
2 Department of Computer Science, University of Verona, Italy
* Corresponding author: firstname.lastname@example.org
Accepted: 16 December 2022
The Hellinger-Kantorovich (HK) distance is an unbalanced extension of the Wasserstein-2 distance. It was shown recently that the HK barycenter exhibits a much more complex behaviour than the Wasserstein barycenter. Motivated by this observation we study the HK barycenter in more detail for the case where the input measures are an uncountable collection of Dirac measures, in particular the dependency on the length scale parameter of HK, the question whether the HK barycenter is discrete or continuous and the relation between the expected and the empirical barycenter. The analytical results are complemented with numerical experiments that demonstrate that the HK barycenter can provide a coarse-to-fine representation of an input pointcloud or measure.
Mathematics Subject Classification: 49K35 / 49M29 / 49Q22
Key words: optimal transport / unbalanced optimal transport / barycenter / data analysis
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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