  The clusters of a distribution are often defined by the connected components
of a density level set. However, this definition depends on the user-specified
level. We address this issue by proposing a simple, generic algorithm, which
uses an almost arbitrary level set estimator to estimate the smallest level at
which there are more than one connected components. In the case where this
algorithm is fed with histogram-based level set estimates, we provide a finite
sample analysis, which is then used to show that the algorithm consistently
estimates both the smallest level and the corresponding connected components.
We further establish rates of convergence for the two estimation problems, and
last but not least, we present a simple, yet adaptive strategy for determining
the width-parameter of the involved density estimator in a data-depending way.
