Comparison of internal evaluation criteria in hierarchical clustering of categorical data

Abstract

The paper discusses eleven internal evaluation criteria that can be used in the area of hierarchical clustering of categorical data. The criteria are divided into two distinct groups based on how they treat the cluster quality: variability- and distance-based. The paper follows three main aims. The first one is to compare the examined criteria regarding their mutual similarity and dependence on the clustered datasets’ properties and the used similarity measures. The second one is to analyze the relationships between internal and external cluster evaluation to determine how well the internal criteria can recognize the original number of clusters in datasets and to what extent they provide comparable results to the external criteria. The third aim is to propose two new variability-based internal evaluation criteria. In the experiment, 81 types of generated datasets with controlled properties are used. The results show which internal criteria can be recommended for specific tasks, such as judging the cluster quality or the optimal number of clusters determination.