{"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/pecok-a-convex-optimization-approach-to","title":"PECOK: a convex optimization approach to variable clustering","arxiv_id":"1606.05100","date":"2016-06-16","proceeding":null,"authors":["Florentina Bunea","Christophe Giraud","Martin Royer","Nicolas Verzelen"],"abstract":"The problem of variable clustering is that of grouping similar components of a $p$-dimensional vector $X=(X_{1},\\ldots,X_{p})$, and estimating these groups from $n$ independent copies of $X$. When cluster similarity is defined via $G$-latent models, in which groups of $X$-variables have a common latent generator, and groups are relative to a partition $G$ of the index set $\\{1, \\ldots, p\\}$, the most natural clustering strategy is $K$-means. We explain why this strategy cannot lead to perfect cluster recovery and offer a correction, based on semi-definite programing, that can be viewed as a penalized convex relaxation of $K$-means (PECOK). We introduce a cluster separation measure tailored to $G$-latent models, and derive its minimax lower bound for perfect cluster recovery. The clusters estimated by PECOK are shown to recover $G$ at a near minimax optimal cluster separation rate, a result that holds true even if $K$, the number of clusters, is estimated adaptively from the data. We compare PECOK with appropriate corrections of spectral clustering-type procedures, and show that the former outperforms the latter for perfect cluster recovery of minimally separated clusters.","url_abs":"http://arxiv.org/abs/1606.05100v1","url_pdf":"http://arxiv.org/pdf/1606.05100v1.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":"pecok-a-convex-optimization-approach-to","repo_url":"https://github.com/martinroyer/pecok","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1606.05100","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1606.05100"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/martinroyer/pecok","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"unverified":2},"by_repo_kind":{"listed":{"samples":2,"ran":0,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"bd4f740d9f3a4dd7","entry":"gamma_hat","repo":"martinroyer/pecok","repo_kind":"listed","path":"pecok/gamma.py","file_url":"https://github.com/martinroyer/pecok/blob/HEAD/pecok/gamma.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"bd4f740d9f3a4dd7"}},{"code_sha256_prefix":"a2ed09914bf034ac","entry":"pecok_admm","repo":"martinroyer/pecok","repo_kind":"listed","path":"pecok/admm.py","file_url":"https://github.com/martinroyer/pecok/blob/HEAD/pecok/admm.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"a2ed09914bf034ac"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}