{"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/orthogonal-rank-one-matrix-pursuit-for-low","title":"Orthogonal Rank-One Matrix Pursuit for Low Rank Matrix Completion","arxiv_id":"1404.1377","date":"2014-04-04","proceeding":null,"authors":["Zheng Wang","Ming-Jun Lai","Zhaosong Lu","Wei Fan","Hasan Davulcu","Jieping Ye"],"abstract":"In this paper, we propose an efficient and scalable low rank matrix\ncompletion algorithm. The key idea is to extend orthogonal matching pursuit\nmethod from the vector case to the matrix case. We further propose an economic\nversion of our algorithm by introducing a novel weight updating rule to reduce\nthe time and storage complexity. Both versions are computationally inexpensive\nfor each matrix pursuit iteration, and find satisfactory results in a few\niterations. Another advantage of our proposed algorithm is that it has only one\ntunable parameter, which is the rank. It is easy to understand and to use by\nthe user. This becomes especially important in large-scale learning problems.\nIn addition, we rigorously show that both versions achieve a linear convergence\nrate, which is significantly better than the previous known results. We also\nempirically compare the proposed algorithms with several state-of-the-art\nmatrix completion algorithms on many real-world datasets, including the\nlarge-scale recommendation dataset Netflix as well as the MovieLens datasets.\nNumerical results show that our proposed algorithm is more efficient than\ncompeting algorithms while achieving similar or better prediction performance.","url_abs":"http://arxiv.org/abs/1404.1377v2","url_pdf":"http://arxiv.org/pdf/1404.1377v2.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":"orthogonal-rank-one-matrix-pursuit-for-low","repo_url":"https://github.com/jasonsun0310/MatrixCompletion.jl","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"low-rank-matrix-completion","task_name":"Low-Rank Matrix Completion"},{"task_slug":"matrix-completion","task_name":"Matrix Completion"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=1404.1377","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}