K-Plus anticlustering: An improved k-means criterion for maximizing between-group similarity

IF 1.5 3区 心理学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Martin Papenberg
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Abstract

Anticlustering refers to the process of partitioning elements into disjoint groups with the goal of obtaining high between-group similarity and high within-group heterogeneity. Anticlustering thereby reverses the logic of its better known twin—cluster analysis—and is usually approached by maximizing instead of minimizing a clustering objective function. This paper presents k-plus, an extension of the classical k-means objective of maximizing between-group similarity in anticlustering applications. K-plus represents between-group similarity as discrepancy in distribution moments (means, variance, and higher-order moments), whereas the k-means criterion only reflects group differences with regard to means. While constituting a new criterion for anticlustering, it is shown that k-plus anticlustering can be implemented by optimizing the original k-means criterion after the input data have been augmented with additional variables. A computer simulation and practical examples show that k-plus anticlustering achieves high between-group similarity with regard to multiple objectives. In particular, optimizing between-group similarity with regard to variances usually does not compromise similarity with regard to means; the k-plus extension is therefore generally preferred over classical k-means anticlustering. Examples are given on how k-plus anticlustering can be applied to real norming data using the open source R package anticlust, which is freely available via CRAN.

Abstract Image

K-Plus 反聚类法:最大化组间相似性的改进型 k-means 准则。
反聚类指的是将元素划分为互不相交的组的过程,其目标是获得高的组间相似性和高的组内异质性。反聚类分析与众所周知的孪生聚类分析的逻辑相反,通常是通过最大化而不是最小化聚类目标函数来实现的。本文介绍的 k-plus 是经典 k-means 目标的扩展,即在反聚类应用中最大化组间相似度。K-plus 将组间相似性表示为分布矩(均值、方差和高阶矩)的差异,而 k-means 准则只反映组间均值的差异。研究表明,k-plus 反聚类法是一种新的反聚类准则,它可以在输入数据添加额外变量后,通过优化原始的 k-means 准则来实现。计算机模拟和实际案例表明,k-plus 反聚类法在多个目标方面都能达到较高的组间相似度。特别是,优化组间相似性的方差通常不会影响相似性的均值;因此,k-plus 扩展通常优于经典的 k-means 反聚类法。本文举例说明了如何使用开源 R 软件包 anticlust 将 k-plus 反聚类应用于真实的常模数据,该软件包可通过 CRAN 免费获取。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
5.00
自引率
3.80%
发文量
34
审稿时长
>12 weeks
期刊介绍: The British Journal of Mathematical and Statistical Psychology publishes articles relating to areas of psychology which have a greater mathematical or statistical aspect of their argument than is usually acceptable to other journals including: • mathematical psychology • statistics • psychometrics • decision making • psychophysics • classification • relevant areas of mathematics, computing and computer software These include articles that address substantitive psychological issues or that develop and extend techniques useful to psychologists. New models for psychological processes, new approaches to existing data, critiques of existing models and improved algorithms for estimating the parameters of a model are examples of articles which may be favoured.
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