{"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/fused-gromov-wasserstein-distance-for","title":"Fused Gromov-Wasserstein distance for structured objects: theoretical foundations and mathematical properties","arxiv_id":"1811.02834","date":"2018-11-07","proceeding":null,"authors":["Titouan Vayer","Laetita Chapel","Rémi Flamary","Romain Tavenard","Nicolas Courty"],"abstract":"Optimal transport theory has recently found many applications in machine\nlearning thanks to its capacity for comparing various machine learning objects\nconsidered as distributions. The Kantorovitch formulation, leading to the\nWasserstein distance, focuses on the features of the elements of the objects\nbut treat them independently, whereas the Gromov-Wasserstein distance focuses\nonly on the relations between the elements, depicting the structure of the\nobject, yet discarding its features.\n  In this paper we propose to extend these distances in order to encode\nsimultaneously both the feature and structure informations, resulting in the\nFused Gromov-Wasserstein distance. We develop the mathematical framework for\nthis novel distance, prove its metric and interpolation properties and provide\na concentration result for the convergence of finite samples. We also\nillustrate and interpret its use in various contexts where structured objects\nare involved.","url_abs":"http://arxiv.org/abs/1811.02834v1","url_pdf":"http://arxiv.org/pdf/1811.02834v1.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":"abstracts"},"code_links":[{"paper_slug":"fused-gromov-wasserstein-distance-for","repo_url":"https://github.com/PythonOT/POT","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"machine-learning","task_name":"BIG-bench Machine Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1811.02834","atlas_url":"https://app.syntology.ai/?focus=1811.02834","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}