Constructive isometry of tangent spaces along lifted geodesics equates local HK Riemannian geometry with Wasserstein geometry on the cone, enabling approximation of HK parallel transport.
A new optimal transport distance on the space of finite Radon measures
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We introduce a new optimal transport distance between nonnegative finite Radon measures with possibly different masses. The construction is based on non-conservative continuity equations and a corresponding modified Benamou-Brenier formula. We establish various topological and geometrical properties of the resulting metric space, derive some formal Riemannian structure, and develop differential calculus following F. Otto's approach. Finally, we apply these ideas to identify an ideal free distribution model of population dynamics as a gradient flow and obtain new long-time convergence results.
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UNVERDICTED 3representative citing papers
Derives MSIP algorithm from MMD gradient flows for weighted quantization, extending mean shift and relating to preconditioned gradient descent and Lloyd's clustering.
MUST-FM is a simulation-free multiscale supervised framework that scales unbalanced optimal transport flow matching for trajectory inference in single-cell data by exploiting hierarchical structure and transition priors.
citing papers explorer
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On the Differential-Geometric Equivalence of Hellinger-Kantorovich and Cone-Wasserstein Spaces
Constructive isometry of tangent spaces along lifted geodesics equates local HK Riemannian geometry with Wasserstein geometry on the cone, enabling approximation of HK parallel transport.
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Multiscale Supervised Unbalanced Optimal Transport Flow Matching
MUST-FM is a simulation-free multiscale supervised framework that scales unbalanced optimal transport flow matching for trajectory inference in single-cell data by exploiting hierarchical structure and transition priors.