{"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/computing-kantorovich-wasserstein-distances-1","title":"Computing Kantorovich-Wasserstein Distances on $d$-dimensional histograms using $(d+1)$-partite graphs","arxiv_id":"1805.07416","date":"2018-05-18","proceeding":"NeurIPS 2018","authors":["Gennaro Auricchio","Federico Bassetti","Stefano Gualandi","Marco Veneroni"],"abstract":"This paper presents a novel method to compute the exact\nKantorovich-Wasserstein distance between a pair of $d$-dimensional histograms\nhaving $n$ bins each. We prove that this problem is equivalent to an\nuncapacitated minimum cost flow problem on a $(d+1)$-partite graph with\n$(d+1)n$ nodes and $dn^{\\frac{d+1}{d}}$ arcs, whenever the cost is separable\nalong the principal $d$-dimensional directions. We show numerically the\nbenefits of our approach by computing the Kantorovich-Wasserstein distance of\norder 2 among two sets of instances: gray scale images and $d$-dimensional\nbiomedical histograms. On these types of instances, our approach is competitive\nwith state-of-the-art optimal transport algorithms.","url_abs":"http://arxiv.org/abs/1805.07416v2","url_pdf":"http://arxiv.org/pdf/1805.07416v2.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":"computing-kantorovich-wasserstein-distances-1","repo_url":"https://github.com/stegua/dpartion-nips2018","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}