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

2019/07/11 by Julie Delon, Agnès Desolneux, Delon, Julie +1 · 14 citations
Environmental Science · Mathematics · #FOS: Mathematics #Heavy Metal Exposure and Toxicity #Markov Chains and Monte Carlo Methods #Optimization and Control (math.OC) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1907.05254

openalex publication_date 2019/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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