Barycenters for the Hellinger-Kantorovich Distance Over ℝd

@article{Friesecke2021BarycentersFT,
  title={Barycenters for the Hellinger-Kantorovich Distance Over ℝd},
  author={G. Friesecke and D. Matthes and Bernhard Schmitzer},
  journal={SIAM J. Math. Anal.},
  year={2021},
  volume={53},
  pages={62-110}
}
We study the barycenter of the Hellinger--Kantorovich metric over non-negative measures on compact, closed subsets of $\mathbb{R}^d$. The article establishes existence, uniqueness (under suitable assumptions) and equivalence between a `coupled-two-marginal' and a multi-marginal formulation. We analyze the HK barycenter between Dirac measures in detail, and find that it differs substantially from the Wasserstein barycenter by exhibiting a local `clustering' behaviour. 
3 Citations

Figures from this paper

The Linearized Hellinger--Kantorovich Distance
  • PDF
Weak Optimal Entropy Transport Problems
  • PDF

References

SHOWING 1-10 OF 34 REFERENCES
Barycenters in the Hellinger-Kantorovich space.
  • 2
  • PDF
Barycenters in the Wasserstein Space
  • 441
  • Highly Influential
  • PDF
Optimal Transport in Competition with Reaction: The Hellinger-Kantorovich Distance and Geodesic Curves
  • 83
  • PDF
Optimal Entropy-Transport problems and a new Hellinger–Kantorovich distance between positive measures
  • 137
  • Highly Influential
  • PDF
An Interpolating Distance Between Optimal Transport and Fisher–Rao Metrics
  • 124
  • PDF
Unbalanced Optimal Transport: Dynamic and Kantorovich Formulations
  • 54
Optimal maps for the multidimensional Monge-Kantorovich problem
  • 142
  • PDF
A new optimal transport distance on the space of finite Radon measures
  • 92
  • PDF
...
1
2
3
4
...