{"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/an-objective-for-hierarchical-clustering-in","title":"An Objective for Hierarchical Clustering in Euclidean Space and its Connection to Bisecting K-means","arxiv_id":"2008.13235","date":"2020-08-30","proceeding":null,"authors":["Benjamin Moseley","Yuyan Wang"],"abstract":"This paper explores hierarchical clustering in the case where pairs of points have dissimilarity scores (e.g. distances) as a part of the input. The recently introduced objective for points with dissimilarity scores results in every tree being a 1/2 approximation if the distances form a metric. This shows the objective does not make a significant distinction between a good and poor hierarchical clustering in metric spaces. Motivated by this, the paper develops a new global objective for hierarchical clustering in Euclidean space. The objective captures the criterion that has motivated the use of divisive clustering algorithms: that when a split happens, points in the same cluster should be more similar than points in different clusters. Moreover, this objective gives reasonable results on ground-truth inputs for hierarchical clustering. The paper builds a theoretical connection between this objective and the bisecting k-means algorithm. This paper proves that the optimal 2-means solution results in a constant approximation for the objective. This is the first paper to show the bisecting k-means algorithm optimizes a natural global objective over the entire tree.","url_abs":"https://arxiv.org/abs/2008.13235v1","url_pdf":"https://arxiv.org/pdf/2008.13235v1.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":"an-objective-for-hierarchical-clustering-in","repo_url":"https://github.com/wangyuyan2333/hier_clustering_split_rev_obj_test","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2008.13235","atlas_url":"https://app.syntology.ai/?focus=2008.13235","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}