A Wasserstein-type distance in the space of Gaussian Mixture Models
Résumé
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.
Mots clés
optimal transport
Wasserstein distance
Gaussian mixture model
multi-marginal optimal trans- port
barycenter
image processing applications
65K05
90C05
62-07
68Q25
68U10
68U05
68R10
multi-marginal optimal trans- 10 port
image processing applications 11 AMS subject classifications 65K10
68R10 12
image processing applications AMS subject classifications 65K10
Domaines
Optimisation et contrôle [math.OC]| Origine | Fichiers produits par l'(les) auteur(s) |
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