{"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-smoothed-rank","title":"Robust Subspace Clustering via Smoothed Rank Approximation","arxiv_id":"1508.04467","date":"2015-08-18","proceeding":null,"authors":["Zhao Kang","Chong Peng","Qiang Cheng"],"abstract":"Matrix rank minimizing subject to affine constraints arises in many\napplication areas, ranging from signal processing to machine learning. Nuclear\nnorm is a convex relaxation for this problem which can recover the rank exactly\nunder some restricted and theoretically interesting conditions. However, for\nmany real-world applications, nuclear norm approximation to the rank function\ncan only produce a result far from the optimum. To seek a solution of higher\naccuracy than the nuclear norm, in this paper, we propose a rank approximation\nbased on Logarithm-Determinant. We consider using this rank approximation for\nsubspace clustering application. Our framework can model different kinds of\nerrors and noise. Effective optimization strategy is developed with theoretical\nguarantee to converge to a stationary point. The proposed method gives\npromising results on face clustering and motion segmentation tasks compared to\nthe state-of-the-art subspace clustering algorithms.","url_abs":"http://arxiv.org/abs/1508.04467v1","url_pdf":"http://arxiv.org/pdf/1508.04467v1.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-smoothed-rank","repo_url":"https://github.com/sckangz/logdet","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}