{"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/stochastic-block-models-are-a-discrete","title":"Stochastic Block Models are a Discrete Surface Tension","arxiv_id":"1806.02485","date":"2018-06-07","proceeding":null,"authors":["Zachary M. Boyd","Mason A. Porter","Andrea L. Bertozzi"],"abstract":"Networks, which represent agents and interactions between them, arise in\nmyriad applications throughout the sciences, engineering, and even the\nhumanities. To understand large-scale structure in a network, a common task is\nto cluster a network's nodes into sets called \"communities\", such that there\nare dense connections within communities but sparse connections between them. A\npopular and statistically principled method to perform such clustering is to\nuse a family of generative models known as stochastic block models (SBMs). In\nthis paper, we show that maximum likelihood estimation in an SBM is a network\nanalog of a well-known continuum surface-tension problem that arises from an\napplication in metallurgy. To illustrate the utility of this relationship, we\nimplement network analogs of three surface-tension algorithms, with which we\nsuccessfully recover planted community structure in synthetic networks and\nwhich yield fascinating insights on empirical networks that we construct from\nhyperspectral videos.","url_abs":"http://arxiv.org/abs/1806.02485v2","url_pdf":"http://arxiv.org/pdf/1806.02485v2.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":"stochastic-block-models-are-a-discrete","repo_url":"https://github.com/zboyd2/SBM-surface-tension","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"},{"task_slug":"video-semantic-segmentation","task_name":"Video Semantic Segmentation"}],"methods":[{"method_slug":"dense-connections","method_name":"Dense Connections"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}