{"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/path-based-spectral-clustering-guarantees","title":"Path-Based Spectral Clustering: Guarantees, Robustness to Outliers, and Fast Algorithms","arxiv_id":"1712.06206","date":"2017-12-17","proceeding":null,"authors":["Anna Little","Mauro Maggioni","James M. Murphy"],"abstract":"We consider the problem of clustering with the longest-leg path distance\n(LLPD) metric, which is informative for elongated and irregularly shaped\nclusters. We prove finite-sample guarantees on the performance of clustering\nwith respect to this metric when random samples are drawn from multiple\nintrinsically low-dimensional clusters in high-dimensional space, in the\npresence of a large number of high-dimensional outliers. By combining these\nresults with spectral clustering with respect to LLPD, we provide conditions\nunder which the Laplacian eigengap statistic correctly determines the number of\nclusters for a large class of data sets, and prove guarantees on the labeling\naccuracy of the proposed algorithm. Our methods are quite general and provide\nperformance guarantees for spectral clustering with any ultrametric. We also\nintroduce an efficient, easy to implement approximation algorithm for the LLPD\nbased on a multiscale analysis of adjacency graphs, which allows for the\nruntime of LLPD spectral clustering to be quasilinear in the number of data\npoints.","url_abs":"http://arxiv.org/abs/1712.06206v2","url_pdf":"http://arxiv.org/pdf/1712.06206v2.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":"path-based-spectral-clustering-guarantees","repo_url":"https://bitbucket.org/annavlittle/llpd_code","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":{"atlas_url":"https://app.syntology.ai/?focus=1712.06206","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}