A Wasserstein-Type Distance in the Space of Gaussian Mixture Models
Julie Delon, Agnès Desolneux
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.
Topics & Concepts
MathematicsGaussianType (biology)Space (punctuation)Set (abstract data type)Simple (philosophy)Mathematical optimizationApplied mathematicsAlgorithmComputer sciencePhysicsProgramming languageEcologyPhilosophyOperating systemBiologyQuantum mechanicsEpistemologyMarkov Chains and Monte Carlo MethodsPoint processes and geometric inequalitiesStatistical Methods and Inference