{"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/accelerated-alternating-projections-for","title":"Accelerated Alternating Projections for Robust Principal Component Analysis","arxiv_id":"1711.05519","date":"2017-11-15","proceeding":null,"authors":["HanQin Cai","Jian-Feng Cai","Ke Wei"],"abstract":"We study robust PCA for the fully observed setting, which is about separating\na low rank matrix $\\boldsymbol{L}$ and a sparse matrix $\\boldsymbol{S}$ from\ntheir sum $\\boldsymbol{D}=\\boldsymbol{L}+\\boldsymbol{S}$. In this paper, a new\nalgorithm, dubbed accelerated alternating projections, is introduced for robust\nPCA which significantly improves the computational efficiency of the existing\nalternating projections proposed in [Netrapalli, Praneeth, et al., 2014] when\nupdating the low rank factor. The acceleration is achieved by first projecting\na matrix onto some low dimensional subspace before obtaining a new estimate of\nthe low rank matrix via truncated SVD. Exact recovery guarantee has been\nestablished which shows linear convergence of the proposed algorithm. Empirical\nperformance evaluations establish the advantage of our algorithm over other\nstate-of-the-art algorithms for robust PCA.","url_abs":"http://arxiv.org/abs/1711.05519v4","url_pdf":"http://arxiv.org/pdf/1711.05519v4.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":"accelerated-alternating-projections-for","repo_url":"https://github.com/caesarcai/AccAltProj_for_RPCA","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"computational-efficiency","task_name":"Computational Efficiency"}],"methods":[{"method_slug":"pca","method_name":"PCA"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1711.05519","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}