{"paper":{"title":"Nearly Optimal Dynamic $k$-Means Clustering for High-Dimensional Data","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"cs.DS","authors_text":"Lin F. Yang, Peilin Zhong, Wei Hu, Zhao Song","submitted_at":"2018-02-01T19:07:51Z","abstract_excerpt":"We consider the $k$-means clustering problem in the dynamic streaming setting, where points from a discrete Euclidean space $\\{1, 2, \\ldots, \\Delta\\}^d$ can be dynamically inserted to or deleted from the dataset. For this problem, we provide a one-pass coreset construction algorithm using space $\\tilde{O}(k\\cdot \\mathrm{poly}(d, \\log\\Delta))$, where $k$ is the target number of centers. To our knowledge, this is the first dynamic geometric data stream algorithm for $k$-means using space polynomial in dimension and nearly optimal (linear) in $k$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.00459","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}