{"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/fast-and-simple-spectral-clustering-in-theory","title":"Fast and Simple Spectral Clustering in Theory and Practice","arxiv_id":null,"date":"2023-09-21","proceeding":"NeurIPS 2023 11","authors":[],"abstract":"Spectral clustering is a popular and effective algorithm designed to find $k$ clusters in a graph $G$.\nIn the classical spectral clustering algorithm, the vertices of $G$ are embedded into $\\mathbb{R}^k$ using $k$ eigenvectors of the graph Laplacian matrix.\nHowever, computing this embedding is computationally expensive and dominates the running time of the algorithm.\nIn this paper, we present a simple spectral clustering algorithm based on a vertex embedding with $O(\\log(k))$ vectors computed by the power method.\nThe vertex embedding is computed in nearly-linear time with respect to the size of the graph, and\nthe algorithm provably recovers the ground truth clusters under natural assumptions on the input graph.\nWe evaluate the new algorithm on several synthetic and real-world datasets, finding that it is significantly faster than alternative clustering algorithms,\nwhile producing results with approximately the same clustering accuracy.","url_abs":"https://openreview.net/forum?id=Q3FXnCPZ1X","url_pdf":"https://openreview.net/pdf?id=Q3FXnCPZ1X","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":"fast-and-simple-spectral-clustering-in-theory","repo_url":"https://github.com/pmacg/fast-spectral-clustering","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"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}