{"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/clustering-by-the-probability-distributions","title":"Clustering by the Probability Distributions from Extreme Value Theory","arxiv_id":"2202.09784","date":"2022-02-20","proceeding":null,"authors":["Sixiao Zheng","Ke Fan","Yanxi Hou","Jianfeng Feng","Yanwei Fu"],"abstract":"Clustering is an essential task to unsupervised learning. It tries to automatically separate instances into coherent subsets. As one of the most well-known clustering algorithms, k-means assigns sample points at the boundary to a unique cluster, while it does not utilize the information of sample distribution or density. Comparably, it would potentially be more beneficial to consider the probability of each sample in a possible cluster. To this end, this paper generalizes k-means to model the distribution of clusters. Our novel clustering algorithm thus models the distributions of distances to centroids over a threshold by Generalized Pareto Distribution (GPD) in Extreme Value Theory (EVT). Notably, we propose the concept of centroid margin distance, use GPD to establish a probability model for each cluster, and perform a clustering algorithm based on the covering probability function derived from GPD. Such a GPD k-means thus enables the clustering algorithm from the probabilistic perspective. Correspondingly, we also introduce a naive baseline, dubbed as Generalized Extreme Value (GEV) k-means. GEV fits the distribution of the block maxima. In contrast, the GPD fits the distribution of distance to the centroid exceeding a sufficiently large threshold, leading to a more stable performance of GPD k-means. Notably, GEV k-means can also estimate cluster structure and thus perform reasonably well over classical k-means. Thus, extensive experiments on synthetic datasets and real datasets demonstrate that GPD k-means outperforms competitors. The github codes are released in https://github.com/sixiaozheng/EVT-K-means.","url_abs":"https://arxiv.org/abs/2202.09784v1","url_pdf":"https://arxiv.org/pdf/2202.09784v1.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":"clustering-by-the-probability-distributions","repo_url":"https://github.com/sixiaozheng/evt-k-means","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"}],"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}