{"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/optimal-non-convex-exact-recovery-in","title":"Optimal Non-Convex Exact Recovery in Stochastic Block Model via Projected Power Method","arxiv_id":"2106.05644","date":"2021-06-10","proceeding":null,"authors":["Peng Wang","Huikang Liu","Zirui Zhou","Anthony Man-Cho So"],"abstract":"In this paper, we study the problem of exact community recovery in the symmetric stochastic block model, where a graph of $n$ vertices is randomly generated by partitioning the vertices into $K \\ge 2$ equal-sized communities and then connecting each pair of vertices with probability that depends on their community memberships. Although the maximum-likelihood formulation of this problem is discrete and non-convex, we propose to tackle it directly using projected power iterations with an initialization that satisfies a partial recovery condition. Such an initialization can be obtained by a host of existing methods. We show that in the logarithmic degree regime of the considered problem, the proposed method can exactly recover the underlying communities at the information-theoretic limit. Moreover, with a qualified initialization, it runs in $\\mathcal{O}(n\\log^2n/\\log\\log n)$ time, which is competitive with existing state-of-the-art methods. We also present numerical results of the proposed method to support and complement our theoretical development.","url_abs":"https://arxiv.org/abs/2106.05644v1","url_pdf":"https://arxiv.org/pdf/2106.05644v1.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"optimal-non-convex-exact-recovery-in","repo_url":"https://github.com/peng8wang/ICML2021-PPM-SBM","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2106.05644","atlas_url":"https://app.syntology.ai/?focus=2106.05644","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}