{"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/robust-subspace-clustering-via-tighter-rank","title":"Robust Subspace Clustering via Tighter Rank Approximation","arxiv_id":"1510.08971","date":"2015-10-30","proceeding":null,"authors":["Zhao Kang","Chong Peng","Qiang Cheng"],"abstract":"Matrix rank minimization problem is in general NP-hard. The nuclear norm is\nused to substitute the rank function in many recent studies. Nevertheless, the\nnuclear norm approximation adds all singular values together and the\napproximation error may depend heavily on the magnitudes of singular values.\nThis might restrict its capability in dealing with many practical problems. In\nthis paper, an arctangent function is used as a tighter approximation to the\nrank function. We use it on the challenging subspace clustering problem. For\nthis nonconvex minimization problem, we develop an effective optimization\nprocedure based on a type of augmented Lagrange multipliers (ALM) method.\nExtensive experiments on face clustering and motion segmentation show that the\nproposed method is effective for rank approximation.","url_abs":"http://arxiv.org/abs/1510.08971v1","url_pdf":"http://arxiv.org/pdf/1510.08971v1.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":"robust-subspace-clustering-via-tighter-rank","repo_url":"https://github.com/sckangz/arctangent","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"},{"task_slug":"face-clustering","task_name":"Face Clustering"},{"task_slug":"motion-segmentation","task_name":"Motion Segmentation"}],"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}