{"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-and-efficient-subspace-segmentation","title":"Robust and Efficient Subspace Segmentation via Least Squares Regression","arxiv_id":"1404.6736","date":"2014-04-27","proceeding":null,"authors":["Can-Yi Lu","Hai Min","Zhong-Qiu Zhao","Lin Zhu","De-Shuang Huang","Shuicheng Yan"],"abstract":"This paper studies the subspace segmentation problem which aims to segment\ndata drawn from a union of multiple linear subspaces. Recent works by using\nsparse representation, low rank representation and their extensions attract\nmuch attention. If the subspaces from which the data drawn are independent or\northogonal, they are able to obtain a block diagonal affinity matrix, which\nusually leads to a correct segmentation. The main differences among them are\ntheir objective functions. We theoretically show that if the objective function\nsatisfies some conditions, and the data are sufficiently drawn from independent\nsubspaces, the obtained affinity matrix is always block diagonal. Furthermore,\nthe data sampling can be insufficient if the subspaces are orthogonal. Some\nexisting methods are all special cases. Then we present the Least Squares\nRegression (LSR) method for subspace segmentation. It takes advantage of data\ncorrelation, which is common in real data. LSR encourages a grouping effect\nwhich tends to group highly correlated data together. Experimental results on\nthe Hopkins 155 database and Extended Yale Database B show that our method\nsignificantly outperforms state-of-the-art methods. Beyond segmentation\naccuracy, all experiments demonstrate that LSR is much more efficient.","url_abs":"http://arxiv.org/abs/1404.6736v1","url_pdf":"http://arxiv.org/pdf/1404.6736v1.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-and-efficient-subspace-segmentation","repo_url":"https://github.com/sjtrny/SubKit","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"segmentation","task_name":"Segmentation"},{"task_slug":"regression-1","task_name":"regression"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1404.6736","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}