Cluster-wise assessment of cluster stability

Stability in cluster analysis is strongly dependent on the data set, especially on how well separated and how homogeneous the clusters are. In the same clustering, some clusters may be very stable and others may be extremely unstable. The Jaccard coefficient, a similarity measure between sets, is used as a clusterwise measure of cluster stability, which is assessed by the bootstrap distribution of the Jaccard coefficient for every single cluster of a clustering compared to the most similar cluster in the bootstrapped data sets. This can be applied to very general cluster analysis methods. Some alternative resampling methods are investigated as well, namely subsetting, jittering the data points and replacing some data points by artificial noise points. The different methods are compared by means of a simulation study. A data example illustrates the use of the cluster-wise stability assessment to distinguish between meaningful stable and spurious clusters, but it is also shown that clusters are sometimes only stable because of the inflexibility of certain clustering methods.