{"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/finite-sample-guarantees-for-pca-in-non","title":"Finite Sample Guarantees for PCA in Non-Isotropic and Data-Dependent Noise","arxiv_id":"1709.06255","date":"2017-09-19","proceeding":null,"authors":["Namrata Vaswani","Praneeth Narayanamurthy"],"abstract":"This work obtains novel finite sample guarantees for Principal Component\nAnalysis (PCA). These hold even when the corrupting noise is non-isotropic, and\na part (or all of it) is data-dependent. Because of the latter, in general, the\nnoise and the true data are correlated. The results in this work are a\nsignificant improvement over those given in our earlier work where this\n\"correlated-PCA\" problem was first studied. In fact, in certain regimes, our\nresults imply that the sample complexity required to achieve subspace recovery\nerror that is a constant fraction of the noise level is near-optimal. Useful\ncorollaries of our result include guarantees for PCA in sparse data-dependent\nnoise and for PCA with missing data. An important application of the former is\nin proving correctness of the subspace update step of a popular online\nalgorithm for dynamic robust PCA.","url_abs":"http://arxiv.org/abs/1709.06255v1","url_pdf":"http://arxiv.org/pdf/1709.06255v1.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":"finite-sample-guarantees-for-pca-in-non","repo_url":"https://github.com/praneethmurthy/correlated-pca","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[],"methods":[{"method_slug":"pca","method_name":"PCA"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1709.06255","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}