{"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/the-power-mean-laplacian-for-multilayer-graph","title":"The Power Mean Laplacian for Multilayer Graph Clustering","arxiv_id":"1803.00491","date":"2018-03-01","proceeding":null,"authors":["Pedro Mercado","Antoine Gautier","Francesco Tudisco","Matthias Hein"],"abstract":"Multilayer graphs encode different kind of interactions between the same set\nof entities. When one wants to cluster such a multilayer graph, the natural\nquestion arises how one should merge the information different layers. We\nintroduce in this paper a one-parameter family of matrix power means for\nmerging the Laplacians from different layers and analyze it in expectation in\nthe stochastic block model. We show that this family allows to recover ground\ntruth clusters under different settings and verify this in real world data.\nWhile computing the matrix power mean can be very expensive for large graphs,\nwe introduce a numerical scheme to efficiently compute its eigenvectors for the\ncase of large sparse graphs.","url_abs":"http://arxiv.org/abs/1803.00491v1","url_pdf":"http://arxiv.org/pdf/1803.00491v1.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":"the-power-mean-laplacian-for-multilayer-graph","repo_url":"https://github.com/melopeo/PM","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"},{"task_slug":"graph-clustering","task_name":"Graph Clustering"},{"task_slug":"stochastic-block-model","task_name":"Stochastic Block Model"}],"methods":[],"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}