k -均值聚类问题的混合整数线性规划公式

IF 1.4 4区管理学 Q3 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Central European Journal of Operations Research Pub Date : 2023-10-27 DOI:10.1007/s10100-023-00881-1

Kolos Cs. Ágoston, Marianna E.-Nagy

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引用次数: 0

摘要

最小平方和聚类是应用最广泛的聚类方法。最小平方和聚类通常采用启发式KMEANS算法求解，该算法收敛于局部最优。为了解决这类问题已经做了大量的工作，但是仍然缺少一个混合整数线性规划公式(MILP)。在本文中，我们建立了MILP模型。MILP公式的优点是用户可以将原问题扩展为任意线性约束。我们也给出了数值结果，我们解决了这些模型，直到样本量为150。

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Mixed integer linear programming formulation for K-means clustering problem

Abstract The minimum sum-of-squares clusering is the most widely used clustering method. The minimum sum-of-squares clustering is usually solved by the heuristic KMEANS algorithm, which converges to a local optimum. A lot of effort has been made to solve such kind of problems, but a mixed integer linear programming formulation (MILP) is still missing. In this paper, we formulate MILP models. The advantage of MILP formulation is that users can extend the original problem with arbitrary linear constraints. We also present numerical results, we solve these models up to sample size of 150.

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来源期刊

Central European Journal of Operations Research 管理科学-运筹学与管理科学

CiteScore

4.70

自引率

11.80%

发文量

审稿时长

3 months

期刊介绍： The Central European Journal of Operations Research provides an international readership with high quality papers that cover the theory and practice of OR and the relationship of OR methods to modern quantitative economics and business administration. The focus is on topics such as: - finance and banking - measuring productivity and efficiency in the public sector - environmental and energy issues - computational tools for strategic decision support - production management and logistics - planning and scheduling The journal publishes theoretical papers as well as application-oriented contributions and practical case studies. Occasionally, special issues feature a particular area of OR or report on the results of scientific meetings.