{"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/recursive-sampling-for-the-nystrom-method","title":"Recursive Sampling for the Nyström Method","arxiv_id":"1605.07583","date":"2016-05-24","proceeding":null,"authors":["Cameron Musco","Christopher Musco"],"abstract":"We give the first algorithm for kernel Nystr\\\"om approximation that runs in\n*linear time in the number of training points* and is provably accurate for all\nkernel matrices, without dependence on regularity or incoherence conditions.\nThe algorithm projects the kernel onto a set of $s$ landmark points sampled by\ntheir *ridge leverage scores*, requiring just $O(ns)$ kernel evaluations and\n$O(ns^2)$ additional runtime. While leverage score sampling has long been known\nto give strong theoretical guarantees for Nystr\\\"om approximation, by employing\na fast recursive sampling scheme, our algorithm is the first to make the\napproach scalable. Empirically we show that it finds more accurate, lower rank\nkernel approximations in less time than popular techniques such as uniformly\nsampled Nystr\\\"om approximation and the random Fourier features method.","url_abs":"http://arxiv.org/abs/1605.07583v5","url_pdf":"http://arxiv.org/pdf/1605.07583v5.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":"recursive-sampling-for-the-nystrom-method","repo_url":"https://github.com/axelv/recursive-nystrom","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"recursive-sampling-for-the-nystrom-method","repo_url":"https://github.com/cnmusco/recursive-nystrom","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1605.07583","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}