{"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/oracle-based-active-set-algorithm-for","title":"Oracle Based Active Set Algorithm for Scalable Elastic Net Subspace Clustering","arxiv_id":"1605.02633","date":"2016-05-09","proceeding":"CVPR 2016 6","authors":["Chong You","Chun-Guang Li","Daniel P. Robinson","Rene Vidal"],"abstract":"State-of-the-art subspace clustering methods are based on expressing each\ndata point as a linear combination of other data points while regularizing the\nmatrix of coefficients with $\\ell_1$, $\\ell_2$ or nuclear norms. $\\ell_1$\nregularization is guaranteed to give a subspace-preserving affinity (i.e.,\nthere are no connections between points from different subspaces) under broad\ntheoretical conditions, but the clusters may not be connected. $\\ell_2$ and\nnuclear norm regularization often improve connectivity, but give a\nsubspace-preserving affinity only for independent subspaces. Mixed $\\ell_1$,\n$\\ell_2$ and nuclear norm regularizations offer a balance between the\nsubspace-preserving and connectedness properties, but this comes at the cost of\nincreased computational complexity. This paper studies the geometry of the\nelastic net regularizer (a mixture of the $\\ell_1$ and $\\ell_2$ norms) and uses\nit to derive a provably correct and scalable active set method for finding the\noptimal coefficients. Our geometric analysis also provides a theoretical\njustification and a geometric interpretation for the balance between the\nconnectedness (due to $\\ell_2$ regularization) and subspace-preserving (due to\n$\\ell_1$ regularization) properties for elastic net subspace clustering. Our\nexperiments show that the proposed active set method not only achieves\nstate-of-the-art clustering performance, but also efficiently handles\nlarge-scale datasets.","url_abs":"http://arxiv.org/abs/1605.02633v1","url_pdf":"http://arxiv.org/pdf/1605.02633v1.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":"oracle-based-active-set-algorithm-for","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":"image-clustering","task_name":"Image Clustering"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/image-clustering-on-mnist-full","task":"Image Clustering","dataset":"MNIST-full","model":"EnSC","rank_in_archive_order":8,"of":16,"metrics":{"Accuracy":"0.969","NMI":"0.941"},"uses_additional_data":false},{"leaderboard":"/sota/image-clustering-on-coil-100","task":"Image Clustering","dataset":"coil-100","model":"EnSC","rank_in_archive_order":10,"of":10,"metrics":{"Accuracy":"0.6924"},"uses_additional_data":false}],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1605.02633","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}