{"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/generalized-sliced-wasserstein-distances","title":"Generalized Sliced Wasserstein Distances","arxiv_id":"1902.00434","date":"2019-02-01","proceeding":"NeurIPS 2019 12","authors":["Soheil Kolouri","Kimia Nadjahi","Umut Simsekli","Roland Badeau","Gustavo K. Rohde"],"abstract":"The Wasserstein distance and its variations, e.g., the sliced-Wasserstein\n(SW) distance, have recently drawn attention from the machine learning\ncommunity. The SW distance, specifically, was shown to have similar properties\nto the Wasserstein distance, while being much simpler to compute, and is\ntherefore used in various applications including generative modeling and\ngeneral supervised/unsupervised learning. In this paper, we first clarify the\nmathematical connection between the SW distance and the Radon transform. We\nthen utilize the generalized Radon transform to define a new family of\ndistances for probability measures, which we call generalized\nsliced-Wasserstein (GSW) distances. We also show that, similar to the SW\ndistance, the GSW distance can be extended to a maximum GSW (max-GSW) distance.\nWe then provide the conditions under which GSW and max-GSW distances are indeed\ndistances. Finally, we compare the numerical performance of the proposed\ndistances on several generative modeling tasks, including SW flows and SW\nauto-encoders.","url_abs":"http://arxiv.org/abs/1902.00434v1","url_pdf":"http://arxiv.org/pdf/1902.00434v1.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":"generalized-sliced-wasserstein-distances","repo_url":"https://github.com/kimiandj/gsw","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1902.00434","atlas_url":"https://app.syntology.ai/?focus=1902.00434","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}