{"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/matrix-recovery-with-implicitly-low-rank-data","title":"Matrix Recovery with Implicitly Low-Rank Data","arxiv_id":"1811.03945","date":"2018-11-09","proceeding":null,"authors":["Xingyu Xie","Jianlong Wu","Guangcan Liu","Jun Wang"],"abstract":"In this paper, we study the problem of matrix recovery, which aims to restore\na target matrix of authentic samples from grossly corrupted observations. Most\nof the existing methods, such as the well-known Robust Principal Component\nAnalysis (RPCA), assume that the target matrix we wish to recover is low-rank.\nHowever, the underlying data structure is often non-linear in practice,\ntherefore the low-rankness assumption could be violated. To tackle this issue,\nwe propose a novel method for matrix recovery in this paper, which could well\nhandle the case where the target matrix is low-rank in an implicit feature\nspace but high-rank or even full-rank in its original form. Namely, our method\npursues the low-rank structure of the target matrix in an implicit feature\nspace. By making use of the specifics of an accelerated proximal gradient based\noptimization algorithm, the proposed method could recover the target matrix\nwith non-linear structures from its corrupted version. Comprehensive\nexperiments on both synthetic and real datasets demonstrate the superiority of\nour method.","url_abs":"http://arxiv.org/abs/1811.03945v1","url_pdf":"http://arxiv.org/pdf/1811.03945v1.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":"matrix-recovery-with-implicitly-low-rank-data","repo_url":"https://github.com/XingyuXie/Matrix-recovery-with-implicitly-low-rank-data","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}