{"title":"The computational complexity of some explainable clustering problems","authors":"Eduardo Sany Laber","doi":"10.1016/j.ipl.2023.106437","DOIUrl":null,"url":null,"abstract":"<div><p>Let <span><math><mi>X</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> be a set of points and <span><math><mi>k</mi><mo>≥</mo><mn>2</mn></math></span> be an integer. Dasgupta et al. <span>[1]</span> considered the problem of building a partition of <span><math><mi>X</mi></math></span> into <em>k</em><span> groups, induced by an axis-aligned decision tree with </span><em>k</em><span> leaves. The motivation is obtaining partitions that are simple to explain. We study the computational complexity of this problem for </span><em>k</em>-means, <em>k</em>-medians and the <em>k</em><span>-center cost-functions. We prove that the optimization problems induced by these cost-functions are hard to approximate.</span></p></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"184 ","pages":"Article 106437"},"PeriodicalIF":0.7000,"publicationDate":"2023-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Information Processing Letters","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0020019023000807","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, INFORMATION SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
Let be a set of points and be an integer. Dasgupta et al. [1] considered the problem of building a partition of into k groups, induced by an axis-aligned decision tree with k leaves. The motivation is obtaining partitions that are simple to explain. We study the computational complexity of this problem for k-means, k-medians and the k-center cost-functions. We prove that the optimization problems induced by these cost-functions are hard to approximate.
期刊介绍:
Information Processing Letters invites submission of original research articles that focus on fundamental aspects of information processing and computing. This naturally includes work in the broadly understood field of theoretical computer science; although papers in all areas of scientific inquiry will be given consideration, provided that they describe research contributions credibly motivated by applications to computing and involve rigorous methodology. High quality experimental papers that address topics of sufficiently broad interest may also be considered.
Since its inception in 1971, Information Processing Letters has served as a forum for timely dissemination of short, concise and focused research contributions. Continuing with this tradition, and to expedite the reviewing process, manuscripts are generally limited in length to nine pages when they appear in print.