Although distance measures are used in many machine learning algorithms, the literature on the context-independent selection and evaluation of distance measures is limited in the sense that prior knowledge is used. In cluster analysis, current studies evaluate the choice of distance measure after applying unsupervised methods based on error probabilities, implicitly setting the goal of reproducing predefined partitions in data. Such studies use clusters of data that are often based on the context of the data as well as the custom goal of the specific study. Depending on the data context, different properties for distance distributions are judged to be relevant for appropriate distance selection. However, if cluster analysis is based on the task of finding similar partitions of data, then the intrapartition distances should be smaller than the interpartition distances. By systematically investigating this specification using distribution analysis through the mirrored-density (MD plot), it is shown that multimodal distance distributions are preferable in cluster analysis. As a consequence, it is advantageous to model distance distributions with Gaussian mixtures prior to the evaluation phase of unsupervised methods. Experiments are performed on several artificial datasets and natural datasets for the task of clustering.

Clustering is an important task in knowledge discovery with the goal of finding groups of similar data points in a dataset. Today there are many different approaches to clustering, including methods to incorporate user decisions into the clustering process. Some of these interactive approaches fall into the category of visual analytics and emphasize the power of visualizations to help find clusters manually in various types of datasets or to verify the results of clustering algorithms. The interactive projection-based clustering (IPBC) is an open-source and parameter-free method using user input on interactive visualizations to cluster high-dimensional data. This work introduces the IPBC approach and compares it to the results of accessible visual analytics approaches for clustering, showing that IPBC can outperform them.

The Databionic swarm (DBS) is a flexible and robust clustering framework that consists of three independent modules: swarm based projection, high-dimensional data visualization and representation guided clustering. The first module is the parameter-free projection method Pswarm, which exploits concepts of self-organization and emergence, game theory, and swarm intelligence. The second module is a parameter-free high-dimensional data visualization technique called topographic map. It uses the generalized U-matrix, which enables to estimate first, if any cluster tendency exists and second, the estimation of the number of clusters. The third module offers a clustering method which can be verified by the visualization and vice versa. Benchmarking w.r.t. conventional algorithms demonstrated that DBS can outperform them. Several applications showed that cluster structures provided by DBS are meaningful. Exemplary, a clustering of worldwide country-related data w.r.t the COVID-19 pandemic is presented here. Code and data is made available via open source.