{"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/exploring-and-measuring-non-linear","title":"Exploring and measuring non-linear correlations: Copulas, Lightspeed Transportation and Clustering","arxiv_id":"1610.09659","date":"2016-10-30","proceeding":null,"authors":["Gautier Marti","Sebastien Andler","Frank Nielsen","Philippe Donnat"],"abstract":"We propose a methodology to explore and measure the pairwise correlations\nthat exist between variables in a dataset. The methodology leverages copulas\nfor encoding dependence between two variables, state-of-the-art optimal\ntransport for providing a relevant geometry to the copulas, and clustering for\nsummarizing the main dependence patterns found between the variables. Some of\nthe clusters centers can be used to parameterize a novel dependence coefficient\nwhich can target or forget specific dependence patterns. Finally, we illustrate\nand benchmark the methodology on several datasets. Code and numerical\nexperiments are available online for reproducible research.","url_abs":"http://arxiv.org/abs/1610.09659v1","url_pdf":"http://arxiv.org/pdf/1610.09659v1.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":"exploring-and-measuring-non-linear","repo_url":"https://github.com/subhobrata/Courses_ML_DL3","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}