{"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-nonconvex-rank-approximation","title":"Robust PCA via Nonconvex Rank Approximation","arxiv_id":"1511.05261","date":"2015-11-17","proceeding":null,"authors":["Zhao Kang","Chong Peng","Qiang Cheng"],"abstract":"Numerous applications in data mining and machine learning require recovering\na matrix of minimal rank. Robust principal component analysis (RPCA) is a\ngeneral framework for handling this kind of problems. Nuclear norm based convex\nsurrogate of the rank function in RPCA is widely investigated. Under certain\nassumptions, it can recover the underlying true low rank matrix with high\nprobability. However, those assumptions may not hold in real-world\napplications. Since the nuclear norm approximates the rank by adding all\nsingular values together, which is essentially a $\\ell_1$-norm of the singular\nvalues, the resulting approximation error is not trivial and thus the resulting\nmatrix estimator can be significantly biased. To seek a closer approximation\nand to alleviate the above-mentioned limitations of the nuclear norm, we\npropose a nonconvex rank approximation. This approximation to the matrix rank\nis tighter than the nuclear norm. To solve the associated nonconvex\nminimization problem, we develop an efficient augmented Lagrange multiplier\nbased optimization algorithm. Experimental results demonstrate that our method\noutperforms current state-of-the-art algorithms in both accuracy and\nefficiency.","url_abs":"http://arxiv.org/abs/1511.05261v1","url_pdf":"http://arxiv.org/pdf/1511.05261v1.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-nonconvex-rank-approximation","repo_url":"https://github.com/sckangz/noncvx-PRCA","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1511.05261","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}