Two clustering methods based on the Ward's method and dendrograms with interval-valued dissimilarities for interval-valued data

Numerous studies have focused on clustering methods for interval-valued data, which is a type of symbolic data. However, limited attention has been awarded to a clustering method employing interval-valued dissimilarity measures. To address this issue, herein, we propose two clustering approaches based on the Ward method using interval-valued dissimilarity for the interval-valued data. Each clustering method has different interval-valued dissimilarities. An interval-valued dissimilarity is generally not used to elucidate the computational result of a hierarchical clustering method by a traditional dendrogram; this is because the nodes of a dendrogram only designate real numbers and not an interval of numbers. We also present a new dendrogram with an arrow symbol, which is named arrow-dendrogram, to demonstrate the results of the clustering methods proposed in this study. In addition, we present the differences between the two clustering methods using numerical examples and numerical experimentation. The results of this study prove that the proposed clustering methods can intuitively provide reasonable and consistent results for our example data, thereby enabling us to completely comprehend the results of the clustering methods using interval-valued dissimilarity, via the arrow-dendrogram. (C) 2020 Elsevier Inc. All rights reserved.