  A popular method for selecting the number of clusters is based on stability
arguments: one chooses the number of clusters such that the corresponding
clustering results are "most stable". In recent years, a series of papers has
analyzed the behavior of this method from a theoretical point of view. However,
the results are very technical and difficult to interpret for non-experts. In
this paper we give a high-level overview about the existing literature on
clustering stability. In addition to presenting the results in a slightly
informal but accessible way, we relate them to each other and discuss their
different implications.
