{"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/constrained-fractional-set-programs-and-their","title":"Constrained fractional set programs and their application in local clustering and community detection","arxiv_id":"1306.3409","date":"2013-06-14","proceeding":null,"authors":["Thomas Bühler","Syama Sundar Rangapuram","Simon Setzer","Matthias Hein"],"abstract":"The (constrained) minimization of a ratio of set functions is a problem\nfrequently occurring in clustering and community detection. As these\noptimization problems are typically NP-hard, one uses convex or spectral\nrelaxations in practice. While these relaxations can be solved globally\noptimally, they are often too loose and thus lead to results far away from the\noptimum. In this paper we show that every constrained minimization problem of a\nratio of non-negative set functions allows a tight relaxation into an\nunconstrained continuous optimization problem. This result leads to a flexible\nframework for solving constrained problems in network analysis. While a\nglobally optimal solution for the resulting non-convex problem cannot be\nguaranteed, we outperform the loose convex or spectral relaxations by a large\nmargin on constrained local clustering problems.","url_abs":"http://arxiv.org/abs/1306.3409v1","url_pdf":"http://arxiv.org/pdf/1306.3409v1.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":"constrained-fractional-set-programs-and-their","repo_url":"https://github.com/tbuehler/CFSP","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"},{"task_slug":"community-detection","task_name":"Community Detection"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}