{"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/nonlinear-higher-order-label-spreading","title":"Nonlinear Higher-Order Label Spreading","arxiv_id":"2006.04762","date":"2020-06-08","proceeding":null,"authors":["Francesco Tudisco","Austin R. Benson","Konstantin Prokopchik"],"abstract":"Label spreading is a general technique for semi-supervised learning with point cloud or network data, which can be interpreted as a diffusion of labels on a graph. While there are many variants of label spreading, nearly all of them are linear models, where the incoming information to a node is a weighted sum of information from neighboring nodes. Here, we add nonlinearity to label spreading through nonlinear functions of higher-order structure in the graph, namely triangles in the graph. For a broad class of nonlinear functions, we prove convergence of our nonlinear higher-order label spreading algorithm to the global solution of a constrained semi-supervised loss function. We demonstrate the efficiency and efficacy of our approach on a variety of point cloud and network datasets, where the nonlinear higher-order model compares favorably to classical label spreading, as well as hypergraph models and graph neural networks.","url_abs":"https://arxiv.org/abs/2006.04762v1","url_pdf":"https://arxiv.org/pdf/2006.04762v1.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":"nonlinear-higher-order-label-spreading","repo_url":"https://github.com/doublelucker/nhols","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2006.04762","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}