A Wasserstein-type distance in the space of Gaussian Mixture Models

DOI10.1137/19M1301047arXiv1907.05254MaRDI QIDQ6321938

Publication date: 11 July 2019

Abstract: In this paper we introduce a Wasserstein-type distance on the set of Gaussian mixture models. This distance is defined by restricting the set of possible coupling measures in the optimal transport problem to Gaussian mixture models. We derive a very simple discrete formulation for this distance, which makes it suitable for high dimensional problems. We also study the corresponding multi-marginal and barycenter formulations. We show some properties of this Wasserstein-type distance, and we illustrate its practical use with some examples in image processing.

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Numerical mathematical programming methods (65K05) Numerical optimization and variational techniques (65K10) Computing methodologies for image processing (68U10) Linear programming (90C05) Graph theory (including graph drawing) in computer science (68R10) Computer graphics; computational geometry (digital and algorithmic aspects) (68U05)

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