A clustering method combining multiple range tests and K-means. Issue 21 (2nd November 2022)

• Record Type: Journal Article
• Authors: Devika, T. J.; Ravichandran, J.
• Is Part Of: Communications in statistics. Volume 51:Issue 21(2022)
• Page Start: 7322
• Page End: 7339
• Publication Date: 2022-11-02
• Subjects: Clustering -- Duncan's MCT procedure -- K-means procedure -- non overlapping clusters; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2021.1872639
• Languages: English
• ISSNs: 0361-0926

Abstract

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.