{"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/incremental-kernel-pca-and-the-nystrom-method","title":"Incremental kernel PCA and the Nyström method","arxiv_id":"1802.00043","date":"2018-01-31","proceeding":null,"authors":["Fredrik Hallgren","Paul Northrop"],"abstract":"Incremental versions of batch algorithms are often desired, for increased\ntime efficiency in the streaming data setting, or increased memory efficiency\nin general. In this paper we present a novel algorithm for incremental kernel\nPCA, based on rank one updates to the eigendecomposition of the kernel matrix,\nwhich is more computationally efficient than comparable existing algorithms. We\nextend our algorithm to incremental calculation of the Nystr\\\"om approximation\nto the kernel matrix, the first such algorithm proposed. Incremental\ncalculation of the Nystr\\\"om approximation leads to further gains in memory\nefficiency, and allows for empirical evaluation of when a subset of sufficient\nsize has been obtained.","url_abs":"http://arxiv.org/abs/1802.00043v1","url_pdf":"http://arxiv.org/pdf/1802.00043v1.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":"incremental-kernel-pca-and-the-nystrom-method","repo_url":"https://github.com/cfjhallgren/inkpca","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}