{"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/robust-pca-via-outlier-pursuit","title":"Robust PCA via Outlier Pursuit","arxiv_id":"1010.4237","date":"2010-10-20","proceeding":"NeurIPS 2010 12","authors":["Huan Xu","Constantine Caramanis","Sujay Sanghavi"],"abstract":"Singular Value Decomposition (and Principal Component Analysis) is one of the\nmost widely used techniques for dimensionality reduction: successful and\nefficiently computable, it is nevertheless plagued by a well-known,\nwell-documented sensitivity to outliers. Recent work has considered the setting\nwhere each point has a few arbitrarily corrupted components. Yet, in\napplications of SVD or PCA such as robust collaborative filtering or\nbioinformatics, malicious agents, defective genes, or simply corrupted or\ncontaminated experiments may effectively yield entire points that are\ncompletely corrupted.\n  We present an efficient convex optimization-based algorithm we call Outlier\nPursuit, that under some mild assumptions on the uncorrupted points (satisfied,\ne.g., by the standard generative assumption in PCA problems) recovers the exact\noptimal low-dimensional subspace, and identifies the corrupted points. Such\nidentification of corrupted points that do not conform to the low-dimensional\napproximation, is of paramount interest in bioinformatics and financial\napplications, and beyond. Our techniques involve matrix decomposition using\nnuclear norm minimization, however, our results, setup, and approach,\nnecessarily differ considerably from the existing line of work in matrix\ncompletion and matrix decomposition, since we develop an approach to recover\nthe correct column space of the uncorrupted matrix, rather than the exact\nmatrix itself. In any problem where one seeks to recover a structure rather\nthan the exact initial matrices, techniques developed thus far relying on\ncertificates of optimality, will fail. We present an important extension of\nthese methods, that allows the treatment of such problems.","url_abs":"http://arxiv.org/abs/1010.4237v2","url_pdf":"http://arxiv.org/pdf/1010.4237v2.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":"robust-pca-via-outlier-pursuit","repo_url":"https://github.com/hoonose/robust-filter","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"collaborative-filtering","task_name":"Collaborative Filtering"},{"task_slug":"dimensionality-reduction","task_name":"Dimensionality Reduction"},{"task_slug":"matrix-completion","task_name":"Matrix Completion"}],"methods":[{"method_slug":"pca","method_name":"PCA"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1010.4237","atlas_url":"https://app.syntology.ai/?focus=1010.4237","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}