{"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/spectral-modification-of-graphs-for-improved","title":"Spectral Modification of Graphs for Improved Spectral Clustering","arxiv_id":null,"date":"2019-12-01","proceeding":"NeurIPS 2019 12","authors":["Ioannis Koutis","Huong Le"],"abstract":"Spectral clustering algorithms provide approximate solutions to  hard optimization problems that formulate graph partitioning  in terms of the graph conductance. It is well understood that  the quality of these approximate solutions is negatively affected  by a possibly significant gap between the conductance and the second eigenvalue  of the graph.  In this paper we show that for \\textbf{any} graph $G$,  there exists a `spectral maximizer' graph $H$ which is cut-similar to $G$,    but has eigenvalues that are near the theoretical limit  implied by the cut structure of $G$. Applying then spectral clustering  on $H$ has the potential to produce improved  cuts that also exist in $G$ due to  the cut similarity.   This leads to the second contribution of this  work: we describe a practical spectral modification algorithm that   raises the eigenvalues of the input graph, while preserving its  cuts. Combined with spectral clustering on the modified  graph, this yields demonstrably improved cuts.","url_abs":"http://papers.nips.cc/paper/8732-spectral-modification-of-graphs-for-improved-spectral-clustering","url_pdf":"http://papers.nips.cc/paper/8732-spectral-modification-of-graphs-for-improved-spectral-clustering.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":"spectral-modification-of-graphs-for-improved","repo_url":"https://github.com/ikoutis/spectral-modification","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"},{"task_slug":"graph-partitioning","task_name":"graph partitioning"}],"methods":[{"method_slug":"spectral-clustering","method_name":"Spectral Clustering"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}