{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-wasserstein-type-distance-in-the-space-of","title":"A Wasserstein-type distance in the space of Gaussian Mixture Models","arxiv_id":"1907.05254","date":"2019-07-11","proceeding":null,"authors":["Julie Delon","Agnes 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.","url_abs":"http://arxiv.org/abs/1907.05254v4","url_pdf":"http://arxiv.org/pdf/1907.05254v4.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"a-wasserstein-type-distance-in-the-space-of","repo_url":"https://github.com/judelo/gmmot","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"a-wasserstein-type-distance-in-the-space-of","repo_url":"https://github.com/rflamary/POT","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1907.05254","atlas_url":"https://app.syntology.ai/?focus=1907.05254","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}