{"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/convergence-and-recovery-guarantees-of-the-k","title":"Convergence and Recovery Guarantees of the K-Subspaces Method for Subspace Clustering","arxiv_id":"2206.05553","date":"2022-06-11","proceeding":null,"authors":["Peng Wang","Huikang Liu","Anthony Man-Cho So","Laura Balzano"],"abstract":"The K-subspaces (KSS) method is a generalization of the K-means method for subspace clustering. In this work, we present local convergence analysis and a recovery guarantee for KSS, assuming data are generated by the semi-random union of subspaces model, where $N$ points are randomly sampled from $K \\ge 2$ overlapping subspaces. We show that if the initial assignment of the KSS method lies within a neighborhood of a true clustering, it converges at a superlinear rate and finds the correct clustering within $\\Theta(\\log\\log N)$ iterations with high probability. Moreover, we propose a thresholding inner-product based spectral method for initialization and prove that it produces a point in this neighborhood. We also present numerical results of the studied method to support our theoretical developments.","url_abs":"https://arxiv.org/abs/2206.05553v2","url_pdf":"https://arxiv.org/pdf/2206.05553v2.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":"convergence-and-recovery-guarantees-of-the-k","repo_url":"https://github.com/peng8wang/icml2022-k-subspaces","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2206.05553","atlas_url":"https://app.syntology.ai/?focus=2206.05553","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}