Comparison of new approaches for hierarchical clustering of mixed data with non-hierarchical methods

This thesis compares some of the hierarchical and non-hierarchical methods which can be used for clustering of the mixed data. There are described and compared 16 methods such as Gower’s distance, recently introduced distance measures for hierarchical clustering, k-medoids, k-prototypes and model-based clustering method. These methods are used for clustering of the generated data. In total, 972 datasets have been generated. These datasets are different in various characteristics such as number of clusters, overlap of clusters, number of variables, ratio of nominal and numeric variables, number of categories of nominal variables and proportion of clusters. There are several aims of the thesis. The main objective is to compare various methods for clustering of mixed data within different characteristics of the datasets. Regarding this aim is also found, how the quality of clustering is changing with the changes of these characteristics. One of the sub-objectives is a comparation of ARI (Adjusted Rand Index) and AMI (Adjusted Mutual Information) metrics which are used to measure the clustering quality. Given the focus of the thesis on mixed data, another sub-objective is to further examine whether the success of methods within changes in characteristics is different in the case of various ratios of the nominal and numeric variables. It was found that the most successful methods are k-prototypes and xSV distance which is one of the recently introduced modifications of Gower’s distance. These methods had better results compared to other examined methods almost under any conditions. Majority of modifications of Gower's distance performed better when the ratio of nominal variables was higher. ARI a AMI metrics evaluated the results rather similarly; their evaluation trend of methods was different in case of changes in number of clusters and proportion of clusters.