  The evaluation of clustering results is difficult, highly dependent on the
evaluated data set and the perspective of the beholder. There are many
different clustering quality measures, which try to provide a general measure
to validate clustering results. A very popular measure is the Silhouette. We
discuss the efficient medoid-based variant of the Silhouette, perform a
theoretical analysis of its properties, and provide two fast versions for the
direct optimization. We combine ideas from the original Silhouette with the
well-known PAM algorithm and its latest improvements FasterPAM. One of the
versions guarantees equal results to the original variant and provides a run
speedup of $O(k^2)$. In experiments on real data with 30000 samples and
$k$=100, we observed a 10464$\times$ speedup compared to the original PAMMEDSIL
algorithm.
