{"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/mixed-order-spectral-clustering-for-networks","title":"Mixed-Order Spectral Clustering for Networks","arxiv_id":"1812.10140","date":"2018-12-25","proceeding":null,"authors":["Yan Ge","Haiping Lu","Pan Peng"],"abstract":"Clustering is fundamental for gaining insights from complex networks, and\nspectral clustering (SC) is a popular approach. Conventional SC focuses on\nsecond-order structures (e.g., edges connecting two nodes) without direct\nconsideration of higher-order structures (e.g., triangles and cliques). This\nhas motivated SC extensions that directly consider higher-order structures.\nHowever, both approaches are limited to considering a single order. This paper\nproposes a new Mixed-Order Spectral Clustering (MOSC) approach to model both\nsecond-order and third-order structures simultaneously, with two MOSC methods\ndeveloped based on Graph Laplacian (GL) and Random Walks (RW). MOSC-GL combines\nedge and triangle adjacency matrices, with theoretical performance guarantee.\nMOSC-RW combines first-order and second-order random walks for a probabilistic\ninterpretation. We automatically determine the mixing parameter based on cut\ncriteria or triangle density, and construct new structure-aware error metrics\nfor performance evaluation. Experiments on real-world networks show 1) the\nsuperior performance of two MOSC methods over existing SC methods, 2) the\neffectiveness of the mixing parameter determination strategy, and 3) insights\noffered by the structure-aware error metrics.","url_abs":"http://arxiv.org/abs/1812.10140v1","url_pdf":"http://arxiv.org/pdf/1812.10140v1.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":"mixed-order-spectral-clustering-for-networks","repo_url":"https://bitbucket.org/Yan_Sheffield/mosc","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"}],"methods":[{"method_slug":"spectral-clustering","method_name":"Spectral Clustering"}],"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}