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Gromov–Wasserstein distances between Gaussian distributions
Journal of Applied Probability, 2022 AbstractGromov–Wasserstein distances were proposed a few years ago to compare distributions which do not lie in the same space. In particular, they offer an interesting alternative to the Wasserstein distances for comparing probability measures living on Euclidean spaces of different dimensions. We focus on the Gromov–Wasserstein distance with a ground
Salmona, Antoine +2 more
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Shape Analysis with Hyperbolic Wasserstein Distance. [PDF]
Proc IEEE Comput Soc Conf Comput Vis Pattern Recognit, 2016 Shape space is an active research field in computer vision study. The shape distance defined in a shape space may provide a simple and refined index to represent a unique shape. Wasserstein distance defines a Riemannian metric for the Wasserstein space. It intrinsically measures the similarities between shapes and is robust to image noise.
Shi J, Zhang W, Wang Y.
europepmc +4 more sources
Free complete Wasserstein algebras [PDF]
Logical Methods in Computer Science, 2018 We present an algebraic account of the Wasserstein distances $W_p$ on complete metric spaces, for $p \geq 1$. This is part of a program of a quantitative algebraic theory of effects in programming languages.
Radu Mardare +2 more
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On a Linear Gromov–Wasserstein Distance
IEEE Transactions on Image Processing, 2022 Gromov-Wasserstein distances are generalization of Wasserstein distances, which are invariant under distance preserving transformations. Although a simplified version of optimal transport in Wasserstein spaces, called linear optimal transport (LOT), was successfully used in practice, there does not exist a notion of linear Gromov-Wasserstein distances ...
Florian Beier +2 more
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Federated Wasserstein Distance
, 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).
Rakotomamonjy, Alain +2 more
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Generalized Wasserstein distance and its application to transport equations with source [PDF]
, 2012 In this article, we generalize the Wasserstein distance to measures with different masses. We study the properties of such distance. In particular, we show that it metrizes weak convergence for tight sequences.
A. Figalli +17 more
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Big Data and Cognitive Computing, 2022 Large retail companies routinely gather huge amounts of customer data, which are to be analyzed at a low granularity. To enable this analysis, several Key Performance Indicators (KPIs), acquired for each customer through different channels are associated
Andrea Ponti +4 more
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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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NeuroImage, 2023 Persistent homology offers a powerful tool for extracting hidden topological signals from brain networks. It captures the evolution of topological structures across multiple scales, known as filtrations, thereby revealing topological features that ...
Moo K. Chung +9 more
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Tanaka Theorem for Inelastic Maxwell Models [PDF]
, 2006 We show that the Euclidean Wasserstein distance is contractive for inelastic homogeneous Boltzmann kinetic equations in the Maxwellian approximation and its associated Kac-like caricature.
A. Pulvirenti +29 more
core +4 more sources