{"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/online-identification-and-tracking-of","title":"Online Identification and Tracking of Subspaces from Highly Incomplete Information","arxiv_id":"1006.4046","date":"2010-06-21","proceeding":null,"authors":["Laura Balzano","Robert Nowak","Benjamin Recht"],"abstract":"This work presents GROUSE (Grassmanian Rank-One Update Subspace Estimation),\nan efficient online algorithm for tracking subspaces from highly incomplete\nobservations. GROUSE requires only basic linear algebraic manipulations at each\niteration, and each subspace update can be performed in linear time in the\ndimension of the subspace. The algorithm is derived by analyzing incremental\ngradient descent on the Grassmannian manifold of subspaces. With a slight\nmodification, GROUSE can also be used as an online incremental algorithm for\nthe matrix completion problem of imputing missing entries of a low-rank matrix.\nGROUSE performs exceptionally well in practice both in tracking subspaces and\nas an online algorithm for matrix completion.","url_abs":"http://arxiv.org/abs/1006.4046v2","url_pdf":"http://arxiv.org/pdf/1006.4046v2.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":"online-identification-and-tracking-of","repo_url":"https://github.com/hiroyuki-kasai/OLSTEC","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"matrix-completion","task_name":"Matrix Completion"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1006.4046","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}