Results 11 to 20 of about 4,469 (193)
Alignment of density maps in Wasserstein distance. [PDF]
Biol ImagingAbstract In this article, we propose an algorithm for aligning three-dimensional objects when represented as density maps, motivated by applications in cryogenic electron microscopy. The algorithm is based on minimizing the 1-Wasserstein distance between the density maps after a rigid transformation.
Singer A, Yang R.
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The Gromov–Wasserstein Distance: A Brief Overview [PDF]
Axioms, 2014 We recall the construction of the Gromov–Wasserstein distance and concentrate on quantitative aspects of the definition.
Facundo Mémoli
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On the computation of the infinity Wasserstein distance and the Wasserstein Projection Problem
Journal of Computational and Applied MathematicsComputing the infinity Wasserstein distance and retrieving projections of a probability measure onto a closed subset of probability measures are critical sub-problems in various applied fields. However, the practical applicability of these objects is limited by two factors: either the associated quantities are computationally prohibitive or there is a ...
Gabriele Loli, Gennaro Auricchio
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Quantum Wasserstein distance based on an optimization over separable states [PDF]
Quantum, 2023 We define the quantum Wasserstein distance such that the optimization of the coupling is carried out over bipartite separable states rather than bipartite quantum states in general, and examine its properties. Surprisingly, we find that the self-distance
Géza Tóth, József Pitrik
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Wasserstein distance to independence models [PDF]
Journal of Symbolic Computation, 2021 An independence model for discrete random variables is a Segre-Veronese variety in a probability simplex. Any metric on the set of joint states of the random variables induces a Wasserstein metric on the probability simplex. The unit ball of this polyhedral norm is dual to the Lipschitz polytope.
Türkü Özlüm Çelik +4 more
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Asymptotics of Smoothed Wasserstein Distances [PDF]
Potential Analysis, 2021 We investigate contraction of the Wasserstein distances on $\mathbb{R}^d$ under Gaussian smoothing. It is well known that the heat semigroup is exponentially contractive with respect to the Wasserstein distances on manifolds of positive curvature; however, on flat Euclidean space---where the heat semigroup corresponds to smoothing the measures by ...
Hong-Bin Chen, Jonathan Niles-Weed
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Federated Wasserstein Distance
CoRR, 2023 We introduce a principled way of computing the Wasserstein distance between two distributions in a federated manner. Namely, we show how to estimate the Wasserstein distance between two samples stored and kept on different devices/clients whilst a central entity/server orchestrates the computations (again, without having access to the samples).
Alain Rakotomamonjy +2 more
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On Properties of the Generalized Wasserstein Distance [PDF]
Archive for Rational Mechanics and Analysis, 2016 The Wasserstein distances $W_p$ ($p\geq 1$), defined in terms of solution to the Monge-Kantorovich problem, are known to be a useful tool to investigate transport equations. In particular, the Benamou-Brenier formula characterizes the square of the Wasserstein distance $W_2$ as the infimum of the kinetic energy, or action functional, of all vector ...
Piccoli, Benedetto, Rossi, Francesco
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The Ultrametric Gromov–Wasserstein Distance
Discrete & Computational Geometry, 2023 In this paper, we investigate compact ultrametric measure spaces which form a subset $\mathcal{U}^w$ of the collection of all metric measure spaces $\mathcal{M}^w$. Similar as for the ultrametric Gromov-Hausdorff distance on the collection of ultrametric spaces $\mathcal{U}$, we define ultrametric versions of two metrics on $\mathcal{U}^w$, namely of ...
Facundo Mémoli +3 more
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Entropy-Regularized Optimal Transport on Multivariate Normal and q-normal Distributions
Entropy, 2021 The distance and divergence of the probability measures play a central role in statistics, machine learning, and many other related fields. The Wasserstein distance has received much attention in recent years because of its distinctions from other ...
Qijun Tong, Kei Kobayashi
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