{"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-completion-on-graphs","title":"Matrix Completion on Graphs","arxiv_id":"1408.1717","date":"2014-08-07","proceeding":null,"authors":["Vassilis Kalofolias","Xavier Bresson","Michael Bronstein","Pierre Vandergheynst"],"abstract":"The problem of finding the missing values of a matrix given a few of its\nentries, called matrix completion, has gathered a lot of attention in the\nrecent years. Although the problem under the standard low rank assumption is\nNP-hard, Cand\\`es and Recht showed that it can be exactly relaxed if the number\nof observed entries is sufficiently large. In this work, we introduce a novel\nmatrix completion model that makes use of proximity information about rows and\ncolumns by assuming they form communities. This assumption makes sense in\nseveral real-world problems like in recommender systems, where there are\ncommunities of people sharing preferences, while products form clusters that\nreceive similar ratings. Our main goal is thus to find a low-rank solution that\nis structured by the proximities of rows and columns encoded by graphs. We\nborrow ideas from manifold learning to constrain our solution to be smooth on\nthese graphs, in order to implicitly force row and column proximities. Our\nmatrix recovery model is formulated as a convex non-smooth optimization\nproblem, for which a well-posed iterative scheme is provided. We study and\nevaluate the proposed matrix completion on synthetic and real data, showing\nthat the proposed structured low-rank recovery model outperforms the standard\nmatrix completion model in many situations.","url_abs":"http://arxiv.org/abs/1408.1717v3","url_pdf":"http://arxiv.org/pdf/1408.1717v3.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-completion-on-graphs","repo_url":"https://github.com/HarishFulara07/MCGraphs-scRNAseq","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"matrix-completion-on-graphs","repo_url":"https://github.com/kushagramahajan/GraphRegMC-scRNAseq","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"collaborative-filtering","task_name":"Collaborative Filtering"},{"task_slug":"matrix-completion","task_name":"Matrix Completion"},{"task_slug":"missing-values","task_name":"Missing Values"},{"task_slug":"recommendation-systems","task_name":"Recommendation Systems"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/collaborative-filtering-on-movielens-100k","task":"Recommendation Systems","dataset":"MovieLens 100K","model":"GMC","rank_in_archive_order":16,"of":18,"metrics":{"RMSE (u1 Splits)":"0.996"},"uses_additional_data":true}],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1408.1717","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}