{"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/low-rank-matrix-recovery-from-row-and-column","title":"Low-Rank Matrix Recovery from Row-and-Column Affine Measurements","arxiv_id":"1505.06292","date":"2015-05-23","proceeding":null,"authors":["Avishai Wagner","Or Zuk"],"abstract":"We propose and study a row-and-column affine measurement scheme for low-rank\nmatrix recovery. Each measurement is a linear combination of elements in one\nrow or one column of a matrix $X$. This setting arises naturally in\napplications from different domains. However, current algorithms developed for\nstandard matrix recovery problems do not perform well in our case, hence the\nneed for developing new algorithms and theory for our problem. We propose a\nsimple algorithm for the problem based on Singular Value Decomposition ($SVD$)\nand least-squares ($LS$), which we term \\alg. We prove that (a simplified\nversion of) our algorithm can recover $X$ exactly with the minimum possible\nnumber of measurements in the noiseless case. In the general noisy case, we\nprove performance guarantees on the reconstruction accuracy under the Frobenius\nnorm. In simulations, our row-and-column design and \\alg algorithm show\nimproved speed, and comparable and in some cases better accuracy compared to\nstandard measurements designs and algorithms. Our theoretical and experimental\nresults suggest that the proposed row-and-column affine measurements scheme,\ntogether with our recovery algorithm, may provide a powerful framework for\naffine matrix reconstruction.","url_abs":"http://arxiv.org/abs/1505.06292v1","url_pdf":"http://arxiv.org/pdf/1505.06292v1.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":"low-rank-matrix-recovery-from-row-and-column","repo_url":"https://github.com/avishaiwa/SVLS","is_official":1,"mentioned_in_paper":1,"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}