Hierarchical cluster analysis of categorical data - Šulc, Zdeněk (2024)
This habilitation thesis deals with two important areas of hierarchical clustering of categorical data, namely similarity measures for categorical data represented by nominal variables with more than two categories and evaluation criteria for the cluster quality assessment. The conducted literature review shows more research needs to be done in this area. Thus, the thesis explores these topics deeply using two experiments based on generated datasets with controlled properties, such as the number of variables or clusters. The first experiment performed on 2,700 datasets analyzes 16 similarity measures concerning their ability to produce good-quality clusters in different dataset properties and linkage methods. Some of the analyzed similarity measures are analyzed for the very first time in the domain of cluster analysis. The second experiment performed on 8,100 datasets compares 11 evaluation criteria for categorical data proposed in various papers. Two of them are newly proposed in this thesis. The criteria are examined from different perspectives, such as their mutual similarity or dependence on the clustered dataset's properties. In the conclusions of both experiments, the most appropriate similarity measures for a specific dataset's properties and evaluation criteria for several intended tasks are recommended. Since the thesis focuses on a practical application of the research outcomes, it presents and further improves a convenient software application that enables researchers to easily replicate the results in the thesis and, more importantly, to perform advanced approaches to categorical data clustering on their own.