This paper focuses on hierarchical clustering of categorical data and compares two approaches which can be used for this task. The first one, an extremely common approach, is to perform a binary transformation of the categorical variables into sets of dummy variables and then use the similarity measures suited for binary data. These similarity measures are well examined, and they occur in both commercial and non-commercial software. However, a binary transformation can possibly cause a loss of information in the data or decrease the speed of the computations. The second approach uses similarity measures developed for the categorical data. But these measures are not so well examined as the binary ones and they are not implemented in commercial software. The comparison of these two approaches is performed on generated data sets with categorical variables and the evaluation is done using both the internal and the external evaluation criteria. The purpose of this paper is to show that the binary transformation is not necessary in the process of clustering categorical data since the second approach leads to at least comparably good clustering results as the first approach.

The paper compares 11 internal evaluation criteria for hierarchical clustering of categorical data regarding a correct number of clusters determination. The criteria are divided into three groups based on a way of treating the cluster quality. The variability-based criteria use the within-cluster variability, the likelihood-based criteria maximize the likelihood function, and the distance-based criteria use distances within and between clusters. The aim is to determine which evaluation criteria perform well and under what conditions. Different analysis settings, such as the used method of hierarchical clustering, and various dataset properties, such as the number of variables or the minimal between-cluster distances, are examined. The experiment is conducted on 810 generated datasets, where the evaluation criteria are assessed regarding the optimal number of clusters determination and mean absolute errors. The results indicate that the likelihood-based BIC1 and variability-based BK criteria perform relatively well in determining the optimal number of clusters and that some criteria, usually the distance-based ones, should be avoided.

The paper focuses on similarity and distance measures for binary data and their application in cluster analysis. There are 66 measures for binary data analyzed in the paper in order to provide a comprehensive insight into the problematics and to create their well-arranged overview. For this purpose, formulas by which they were defined are studied. In the next part of the research, the results of object clustering on generated datasets are compared, and the ability of measures to create similar or identical clustering solutions is evaluated. This is done by using chosen internal and external evaluation criteria, and comparing the assignments of objects into clusters in the process of hierarchical clustering. The paper shows which similarity measures and distance measures for binary data lead to similar or even identical results in hierarchical cluster analysis.

No abstract

The economic datasets have their specifics; they usually describe human behavior or activity, which are difficult to measure. Thus, in comparison to non-economic datasets, they are less consistent. The paper analyzes differences between categorical economic and non-economic datasets in hierarchical clustering (HCA). To achieve this goal, two analyses based on 25 realworld datasets are carried out. In the first one, groups of economic and non-economic datasets are compared from the point of view of their internal characteristics based on HCA results; in the second one, homogenous groups of datasets are recognized and they are further examined by internal characteristics and graphical outputs. For each group of datasets, the most appropriate similarity measures are identified. The results show substantial differences between economic and non-economic datasets, primarily in terms of the within-cluster variability decrease. We were also successful in classification of the examined datasets into easily interpretable groups, for which suitable similarity measures were identified.