{"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/scalable-sparse-subspace-clustering-by","title":"Scalable Sparse Subspace Clustering by Orthogonal Matching Pursuit","arxiv_id":"1507.01238","date":"2015-07-05","proceeding":"CVPR 2016 6","authors":["Chong You","Daniel P. Robinson","Rene Vidal"],"abstract":"Subspace clustering methods based on $\\ell_1$, $\\ell_2$ or nuclear norm\nregularization have become very popular due to their simplicity, theoretical\nguarantees and empirical success. However, the choice of the regularizer can\ngreatly impact both theory and practice. For instance, $\\ell_1$ regularization\nis guaranteed to give a subspace-preserving affinity (i.e., there are no\nconnections between points from different subspaces) under broad conditions\n(e.g., arbitrary subspaces and corrupted data). However, it requires solving a\nlarge scale convex optimization problem. On the other hand, $\\ell_2$ and\nnuclear norm regularization provide efficient closed form solutions, but\nrequire very strong assumptions to guarantee a subspace-preserving affinity,\ne.g., independent subspaces and uncorrupted data. In this paper we study a\nsubspace clustering method based on orthogonal matching pursuit. We show that\nthe method is both computationally efficient and guaranteed to give a\nsubspace-preserving affinity under broad conditions. Experiments on synthetic\ndata verify our theoretical analysis, and applications in handwritten digit and\nface clustering show that our approach achieves the best trade off between\naccuracy and efficiency.","url_abs":"http://arxiv.org/abs/1507.01238v3","url_pdf":"http://arxiv.org/pdf/1507.01238v3.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":"scalable-sparse-subspace-clustering-by","repo_url":"https://github.com/VilockLi/SBSC","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"scalable-sparse-subspace-clustering-by","repo_url":"https://github.com/ChongYou/subspace-clustering","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"},{"task_slug":"face-clustering","task_name":"Face Clustering"},{"task_slug":"image-clustering","task_name":"Image Clustering"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/image-clustering-on-extended-yale-b","task":"Image Clustering","dataset":"Extended Yale-B","model":"SSC-OMP","rank_in_archive_order":6,"of":9,"metrics":{"Accuracy":"0.776"},"uses_additional_data":false}],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1507.01238","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}