An empirical comparison and characterisation of nine popular clustering methods

Nine popular clustering methods are applied to 42 real data sets. The aim is to give a detailed characterisation of the methods by means of several cluster validation indexes that measure various individual aspects of the resulting clusters such as small within-cluster distances, separation of clusters, closeness to a Gaussian distribution etc. as introduced in Hennig (2019). 30 of the data sets come with a "true" clustering. On these data sets the similarity of the clusterings from the nine methods to the "true" clusterings is explored. Furthermore, a mixed effects regression relates the observable individual aspects of the clusters to the similarity with the "true" clusterings, which in real clustering problems is unobservable. The study gives new insight not only into the ability of the methods to discover "true" clusterings, but also into properties of clusterings that can be expected from the methods, which is crucial for the choice of a method in a real situation without a given "true" clustering.