{"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/distributed-k-clustering-for-data-with-heavy","title":"Distributed $k$-Clustering for Data with Heavy Noise","arxiv_id":"1810.07852","date":"2018-10-18","proceeding":"NeurIPS 2018","authors":["Xiangyu Guo","Shi Li"],"abstract":"In this paper, we consider the $k$-center/median/means clustering with\noutliers problems (or the $(k, z)$-center/median/means problems) in the\ndistributed setting. Most previous distributed algorithms have their\ncommunication costs linearly depending on $z$, the number of outliers. Recently\nGuha et al. overcame this dependence issue by considering bi-criteria\napproximation algorithms that output solutions with $2z$ outliers. For the case\nwhere $z$ is large, the extra $z$ outliers discarded by the algorithms might be\ntoo large, considering that the data gathering process might be costly. In this\npaper, we improve the number of outliers to the best possible $(1+\\epsilon)z$,\nwhile maintaining the $O(1)$-approximation ratio and independence of\ncommunication cost on $z$. The problems we consider include the $(k, z)$-center\nproblem, and $(k, z)$-median/means problems in Euclidean metrics.\nImplementation of the our algorithm for $(k, z)$-center shows that it\noutperforms many previous algorithms, both in terms of the communication cost\nand quality of the output solution.","url_abs":"http://arxiv.org/abs/1810.07852v2","url_pdf":"http://arxiv.org/pdf/1810.07852v2.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":"distributed-k-clustering-for-data-with-heavy","repo_url":"https://github.com/xyguo/clusterz","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}