{"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/clustering-signed-networks-with-the-geometric","title":"Clustering Signed Networks with the Geometric Mean of Laplacians","arxiv_id":"1701.00757","date":"2017-01-03","proceeding":"NeurIPS 2016 12","authors":["Pedro Mercado","Francesco Tudisco","Matthias Hein"],"abstract":"Signed networks allow to model positive and negative relationships. We\nanalyze existing extensions of spectral clustering to signed networks. It turns\nout that existing approaches do not recover the ground truth clustering in\nseveral situations where either the positive or the negative network structures\ncontain no noise. Our analysis shows that these problems arise as existing\napproaches take some form of arithmetic mean of the Laplacians of the positive\nand negative part. As a solution we propose to use the geometric mean of the\nLaplacians of positive and negative part and show that it outperforms the\nexisting approaches. While the geometric mean of matrices is computationally\nexpensive, we show that eigenvectors of the geometric mean can be computed\nefficiently, leading to a numerical scheme for sparse matrices which is of\nindependent interest.","url_abs":"http://arxiv.org/abs/1701.00757v1","url_pdf":"http://arxiv.org/pdf/1701.00757v1.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":"clustering-signed-networks-with-the-geometric","repo_url":"https://github.com/melopeo/GM","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"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=1701.00757","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}