  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.
