Add to ORKGOn the set of all metric measure spaces, we have two important metrics, the box metric and the observable metric, both introduced by M. Gromov. We obtain the representation of these metrics by using transport plan. In addition, we prove the existence of optimal transport plans of these metrics.Comment: 22 page
We introduce the setting of extended metric–topological measure spaces as a general “Wiener like” fr...
Abstract: We introduce a new optimal transport distance between nonnegative finite Radon measures wi...
We introduce a new class of distances between nonnegative Radon measures on the euclidean space. The...
Erbar M, Rumpf M, Schmitzer B, Simon S. Computation of optimal transport on discrete metric measure ...
Inspired by the recent theory of Entropy-Transport problems and by the $\mathbf{D}$-distance of Stur...
In this article, we define the transport dimension of probability measures on $\mathbb{R}^m...
The numerous logistics problems occurring in power train and transport industry lead to wear of vehi...
We propose a novel approach for comparing distributions whose supports do not necessarily lie on the...
papers [2, 3, 1]. We explain, in the setting of discrete spaces, the definition of optimal transport...
We introduce the setting of extended metric\u2013topological measure spaces as a general \u201cWiene...
Applications in data science, shape analysis and object classification frequently require comparison...
An optimal transport path may be viewed as a geodesic in the space of probability measures ...
Let (X,d,m) be a proper, non-branching, metric measure space. We show existence and uniqueness of op...
In applications in computer graphics and computational anatomy, one seeks a measure-preserving map f...
This article presents a new class of "optimal transportation"-like distances between arbitrary posit...
We introduce the setting of extended metric–topological measure spaces as a general “Wiener like” fr...
Abstract: We introduce a new optimal transport distance between nonnegative finite Radon measures wi...
We introduce a new class of distances between nonnegative Radon measures on the euclidean space. The...
Erbar M, Rumpf M, Schmitzer B, Simon S. Computation of optimal transport on discrete metric measure ...
Inspired by the recent theory of Entropy-Transport problems and by the $\mathbf{D}$-distance of Stur...
In this article, we define the transport dimension of probability measures on $\mathbb{R}^m...
The numerous logistics problems occurring in power train and transport industry lead to wear of vehi...
We propose a novel approach for comparing distributions whose supports do not necessarily lie on the...
papers [2, 3, 1]. We explain, in the setting of discrete spaces, the definition of optimal transport...
We introduce the setting of extended metric\u2013topological measure spaces as a general \u201cWiene...
Applications in data science, shape analysis and object classification frequently require comparison...
An optimal transport path may be viewed as a geodesic in the space of probability measures ...
Let (X,d,m) be a proper, non-branching, metric measure space. We show existence and uniqueness of op...
In applications in computer graphics and computational anatomy, one seeks a measure-preserving map f...
This article presents a new class of "optimal transportation"-like distances between arbitrary posit...
We introduce the setting of extended metric–topological measure spaces as a general “Wiener like” fr...
Abstract: We introduce a new optimal transport distance between nonnegative finite Radon measures wi...
We introduce a new class of distances between nonnegative Radon measures on the euclidean space. The...