{"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/provable-dynamic-robust-pca-or-robust","title":"Provable Dynamic Robust PCA or Robust Subspace Tracking","arxiv_id":"1705.08948","date":"2017-05-24","proceeding":null,"authors":["Praneeth Narayanamurthy","Namrata Vaswani"],"abstract":"Dynamic robust PCA refers to the dynamic (time-varying) extension of robust\nPCA (RPCA). It assumes that the true (uncorrupted) data lies in a\nlow-dimensional subspace that can change with time, albeit slowly. The goal is\nto track this changing subspace over time in the presence of sparse outliers.\nWe develop and study a novel algorithm, that we call simple-ReProCS, based on\nthe recently introduced Recursive Projected Compressive Sensing (ReProCS)\nframework. Our work provides the first guarantee for dynamic RPCA that holds\nunder weakened versions of standard RPCA assumptions, slow subspace change and\na lower bound assumption on most outlier magnitudes. Our result is significant\nbecause (i) it removes the strong assumptions needed by the two previous\ncomplete guarantees for ReProCS-based algorithms; (ii) it shows that it is\npossible to achieve significantly improved outlier tolerance, compared with all\nexisting RPCA or dynamic RPCA solutions by exploiting the above two simple\nextra assumptions; and (iii) it proves that simple-ReProCS is online (after\ninitialization), fast, and, has near-optimal memory complexity.","url_abs":"http://arxiv.org/abs/1705.08948v4","url_pdf":"http://arxiv.org/pdf/1705.08948v4.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":"provable-dynamic-robust-pca-or-robust","repo_url":"https://github.com/andrewssobral/lrslibrary","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"provable-dynamic-robust-pca-or-robust","repo_url":"https://github.com/praneethmurthy/ReProCS","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"compressive-sensing","task_name":"Compressive Sensing"}],"methods":[{"method_slug":"pca","method_name":"PCA"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}