{"paper":{"title":"A New Rejection Sampling Approach to $k$-$\\mathtt{means}$++ With Improved Trade-Offs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.DS","authors_text":"Poojan Shah, Ragesh Jaiswal, Shashwat Agrawal","submitted_at":"2025-02-04T08:05:34Z","abstract_excerpt":"The $k$-$\\mathtt{means}$++ seeding algorithm (Arthur & Vassilvitskii, 2007) is widely used in practice for the $k$-means clustering problem where the goal is to cluster a dataset $\\mathcal{X} \\subset \\mathbb{R} ^d$ into $k$ clusters.\n  The popularity of this algorithm is due to its simplicity and provable guarantee of being $O(\\log k)$ competitive with the optimal solution in expectation. However, its running time is $O(|\\mathcal{X}|kd)$, making it expensive for large datasets.\n  In this work, we present a simple and effective rejection sampling based approach for speeding up $k$-$\\mathtt{mean"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.02085","kind":"arxiv","version":1},"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/2502.02085/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"}