Abstract

This paper explores possibilities of applying multiple comparison tests (MCTs) that are commonly used in statistics to group the means once the analysis of variance (ANOVA) procedure rejects the hypothesis that all the means are equal. It is proposed here to apply MCT procedure to perform clustering when the data are repetitive and multidimensional. Since MCT procedure may result in overlapping clusters, we further develop an approach to first form initial clusters and then apply $K$-means procedure to construct non overlapping clusters. It may be noted that the choice of initial clusters for $K$-means procedure is still ambiguous. Accordingly, the paper is presented in a sequence covering (i) an algorithm for step-by-step implementation of $K$-means procedure for clustering, (ii) an algorithm for step-by-step implementation of MCT procedure for clustering and (iii) an algorithm for step-by-step implementation of a combined procedure to resolve the overlapping clusters. Numerical examples including an open data set are considered to demonstrate the algorithms and also to study their performance in terms of total mean square errors.

摘要

一旦方差分析（ANOVA）程序拒绝了所有均数均等的假设，本文将探讨应用统计中常用的多个比较检验（MCT）对均值进行分组的可能性。在此建议当数据是重复的和多维的时，应用MCT程序执行聚类。由于MCT程序可能会导致重叠的簇，因此我们进一步开发了一种方法来首先形成初始簇，然后应用$ķ$-表示构建非重叠群集的过程。可能会注意到，对于$ķ$-means过程仍然不明确。相应地，本文以一个顺序呈现，涵盖了（i）一种逐步实现的算法$ķ$-表示群集的过程，（ii）用于群集的MCT程序的逐步实现的算法，以及（iii）用于解决重叠群集的组合过程的逐步实现的算法。考虑包括开放数据集在内的数值示例来说明算法，并根据总均方误差研究其性能。