{"paper":{"title":"Do you know what q-means?","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS","cs.LG"],"primary_cat":"quant-ph","authors_text":"Alessandro Luongo, Arjan Cornelissen, Ewin Tang, Joao F. Doriguello","submitted_at":"2023-08-18T17:52:12Z","abstract_excerpt":"Clustering is one of the most important tools for analysis of large datasets, and perhaps the most popular clustering algorithm is Lloyd's algorithm for $k$-means. This algorithm takes $n$ vectors $V=[v_1,\\dots,v_n]\\in\\mathbb{R}^{d\\times n}$ and outputs $k$ centroids $c_1,\\dots,c_k\\in\\mathbb{R}^d$; these partition the vectors into clusters based on which centroid is closest to a particular vector. We present a classical $\\varepsilon$-$k$-means algorithm that performs an approximate version of one iteration of Lloyd's algorithm with time complexity $\\tilde{O}\\big(\\frac{\\|V\\|_F^2}{n}\\frac{k^{2}d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.09701","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2308.09701/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}