{"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/shape-interaction-matrix-revisited-and","title":"Shape Interaction Matrix Revisited and Robustified: Efficient Subspace Clustering with Corrupted and Incomplete Data","arxiv_id":"1509.02649","date":"2015-09-09","proceeding":"ICCV 2015 12","authors":["Pan Ji","Mathieu Salzmann","Hongdong Li"],"abstract":"The Shape Interaction Matrix (SIM) is one of the earliest approaches to\nperforming subspace clustering (i.e., separating points drawn from a union of\nsubspaces). In this paper, we revisit the SIM and reveal its connections to\nseveral recent subspace clustering methods. Our analysis lets us derive a\nsimple, yet effective algorithm to robustify the SIM and make it applicable to\nrealistic scenarios where the data is corrupted by noise. We justify our method\nby intuitive examples and the matrix perturbation theory. We then show how this\napproach can be extended to handle missing data, thus yielding an efficient and\ngeneral subspace clustering algorithm. We demonstrate the benefits of our\napproach over state-of-the-art subspace clustering methods on several\nchallenging motion segmentation and face clustering problems, where the data\nincludes corrupted and missing measurements.","url_abs":"http://arxiv.org/abs/1509.02649v2","url_pdf":"http://arxiv.org/pdf/1509.02649v2.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":"shape-interaction-matrix-revisited-and","repo_url":"https://github.com/panji530/Robust-shape-interaction-matrix","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"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":[{"leaderboard":"/sota/motion-segmentation-on-hopkins155","task":"Motion Segmentation","dataset":"Hopkins155","model":"RSIM","rank_in_archive_order":2,"of":4,"metrics":{"Classification Error":"1.01"},"uses_additional_data":false}],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1509.02649","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}