{"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-thresholding","title":"Robust Subspace Clustering via Thresholding","arxiv_id":"1307.4891","date":"2013-07-18","proceeding":null,"authors":["Reinhard Heckel","Helmut Bölcskei"],"abstract":"The problem of clustering noisy and incompletely observed high-dimensional\ndata points into a union of low-dimensional subspaces and a set of outliers is\nconsidered. The number of subspaces, their dimensions, and their orientations\nare assumed unknown. We propose a simple low-complexity subspace clustering\nalgorithm, which applies spectral clustering to an adjacency matrix obtained by\nthresholding the correlations between data points. In other words, the\nadjacency matrix is constructed from the nearest neighbors of each data point\nin spherical distance. A statistical performance analysis shows that the\nalgorithm exhibits robustness to additive noise and succeeds even when the\nsubspaces intersect. Specifically, our results reveal an explicit tradeoff\nbetween the affinity of the subspaces and the tolerable noise level. We\nfurthermore prove that the algorithm succeeds even when the data points are\nincompletely observed with the number of missing entries allowed to be (up to a\nlog-factor) linear in the ambient dimension. We also propose a simple scheme\nthat provably detects outliers, and we present numerical results on real and\nsynthetic data.","url_abs":"http://arxiv.org/abs/1307.4891v4","url_pdf":"http://arxiv.org/pdf/1307.4891v4.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-thresholding","repo_url":"https://github.com/omarghanem1210/threshold_clustering","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"}],"methods":[{"method_slug":"spectral-clustering","method_name":"Spectral Clustering"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1307.4891","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}