{"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-groups-a-generalization-of-k-means","title":"K-groups: A Generalization of K-means Clustering","arxiv_id":"1711.04359","date":"2017-11-12","proceeding":null,"authors":["Songzi Li","Maria L. Rizzo"],"abstract":"We propose a new class of distribution-based clustering algorithms, called k-groups, based on energy distance between samples. The energy distance clustering criterion assigns observations to clusters according to a multi-sample energy statistic that measures the distance between distributions. The energy distance determines a consistent test for equality of distributions, and it is based on a population distance that characterizes equality of distributions. The k-groups procedure therefore generalizes the k-means method, which separates clusters that have different means. We propose two k-groups algorithms: k-groups by first variation; and k-groups by second variation. The implementation of k-groups is partly based on Hartigan and Wong's algorithm for k-means. The algorithm is generalized from moving one point on each iteration (first variation) to moving $m$ $(m > 1)$ points. For univariate data, we prove that Hartigan and Wong's k-means algorithm is a special case of k-groups by first variation. The simulation results from univariate and multivariate cases show that our k-groups algorithms perform as well as Hartigan and Wong's k-means algorithm when clusters are well-separated and normally distributed. Moreover, both k-groups algorithms perform better than k-means when data does not have a finite first moment or data has strong skewness and heavy tails. For non--spherical clusters, both k-groups algorithms performed better than k-means in high dimension, and k-groups by first variation is consistent as dimension increases. In a case study on dermatology data with 34 features, both k-groups algorithms performed better than k-means.","url_abs":"http://arxiv.org/abs/1711.04359v1","url_pdf":"http://arxiv.org/pdf/1711.04359v1.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"k-groups-a-generalization-of-k-means","repo_url":"https://github.com/mariarizzo/kgroups","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}