{"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/k-bmom-a-robust-lloyd-type-clustering","title":"K-bMOM: a robust Lloyd-type clustering algorithm based on bootstrap Median-of-Means","arxiv_id":"2002.03899","date":"2020-02-10","proceeding":null,"authors":["Camille Brunet-Saumard","Edouard Genetay","Adrien Saumard"],"abstract":"We propose a new clustering algorithm that is robust to the presence of outliers in the dataset. We perform Lloyd-type iterations with robust estimates of the centroids. More precisely, we build on the idea of median-of-means statistics to estimate the centroids, but allow for replacement while constructing the blocks. We call this methodology the bootstrap median-of-means (bMOM) and prove that if enough blocks are generated through the bootstrap sampling, then it has a better breakdown point for mean estimation than the classical median-of-means (MOM), where the blocks form a partition of the dataset. From a clustering perspective, bMOM enables to take many blocks of a desired size, thus avoiding possible disappearance of clusters in some blocks, a pitfall that can occur for the partition-based generation of blocks of the classical median-of-means. Experiments on simulated datasets show that the proposed approach, called K-bMOM, performs better than existing robust K-means based methods. Guidelines are provided for tuning the hyper-parameters K-bMOM in practice. It is also recommended to the practitionner to use such a robust approach to initialize their clustering algorithm. Finally, considering a simplified and theoretical version of our estimator, we prove its robustness to adversarial contamination by deriving robust rates of convergence for the K-means distorsion. To our knowledge, it is the first result of this kind for the K-means distorsion.","url_abs":"https://arxiv.org/abs/2002.03899v2","url_pdf":"https://arxiv.org/pdf/2002.03899v2.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":"k-bmom-a-robust-lloyd-type-clustering","repo_url":"https://github.com/csaumard/kbMOM","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null},{"paper_slug":"k-bmom-a-robust-lloyd-type-clustering","repo_url":"https://github.com/GENETAY/GenetayEdouard","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2002.03899","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2002.03899"}},"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. 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