{"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/algorithms-for-lipschitz-learning-on-graphs","title":"Algorithms for Lipschitz Learning on Graphs","arxiv_id":"1505.00290","date":"2015-05-01","proceeding":null,"authors":["Rasmus Kyng","Anup Rao","Sushant Sachdeva","Daniel A. Spielman"],"abstract":"We develop fast algorithms for solving regression problems on graphs where\none is given the value of a function at some vertices, and must find its\nsmoothest possible extension to all vertices. The extension we compute is the\nabsolutely minimal Lipschitz extension, and is the limit for large $p$ of\n$p$-Laplacian regularization. We present an algorithm that computes a minimal\nLipschitz extension in expected linear time, and an algorithm that computes an\nabsolutely minimal Lipschitz extension in expected time $\\widetilde{O} (m n)$.\nThe latter algorithm has variants that seem to run much faster in practice.\nThese extensions are particularly amenable to regularization: we can perform\n$l_{0}$-regularization on the given values in polynomial time and\n$l_{1}$-regularization on the initial function values and on graph edge weights\nin time $\\widetilde{O} (m^{3/2})$.","url_abs":"http://arxiv.org/abs/1505.00290v2","url_pdf":"http://arxiv.org/pdf/1505.00290v2.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":"algorithms-for-lipschitz-learning-on-graphs","repo_url":"https://github.com/danspielman/YINSlex","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"GPL-3.0"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1505.00290","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}