Derives MSIP algorithm from MMD gradient flows for weighted quantization, extending mean shift and relating to preconditioned gradient descent and Lloyd's clustering.
A new optimal transport distance on the space of finite Radon measures
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
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.
verdicts
UNVERDICTED 2representative citing papers
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
-
Weighted quantization using MMD: From mean field to mean shift via gradient flows
Derives MSIP algorithm from MMD gradient flows for weighted quantization, extending mean shift and relating to preconditioned gradient descent and Lloyd's clustering.
-
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.