A spectral notion of Gromov-Wasserstein distance and related methods

DOI10.1016/j.acha.2010.09.005zbMath1219.53046OpenAlexW2037232171MaRDI QIDQ533501

Facundo Mémoli

Publication date: 3 May 2011

Published in: Applied and Computational Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.acha.2010.09.005

zbMATH Keywords

Laplace-Beltrami operatorheat kernelGromov-Hausdorff distancemass transportspectral methodsmetric geometryspectral invariantsdiffusion distanceGromov-Wasserstein distanceshape and data analysis

Mathematics Subject Classification ID

Computing methodologies for image processing (68U10) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Elliptic equations on manifolds, general theory (58J05) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (13)

Embedding Riemannian manifolds by the heat kernel of the connection Laplacian ⋮ Expected value of the one-dimensional earth mover's distance ⋮ Metric Curvatures Revisited: A Brief Overview ⋮ Distances Between Datasets ⋮ Local scales on curves and surfaces ⋮ Some properties of Gromov-Hausdorff distances ⋮ Diffusion maps for changing data ⋮ Learning shape metrics with Monte Carlo optimization ⋮ Diffusion pruning for rapidly and robustly selecting global correspondences using local isometry ⋮ Modelling convex shape priors and matching based on the Gromov-Wasserstein distance ⋮ The embedding dimension of Laplacian eigenfunction maps ⋮ A topological study of functional data and Fréchet functions of metric measure spaces ⋮ The Gromov-Wasserstein distance: a brief overview

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