  The Average Silhouette Width (ASW; Rousseeuw (1987)) is a popular cluster
validation index to estimate the number of clusters. Here we address the
question whether it also is suitable as a general objective function to be
optimized for finding a clustering. We will propose two algorithms (the
standard version OSil and a fast version FOSil) and compare them with existing
clustering methods in an extensive simulation study covering the cases of a
known and unknown number of clusters. Real data sets are also analysed, partly
exploring the use of the new methods with non-Euclidean distances. We will also
show that the ASW satisfies some axioms that have been proposed for cluster
quality functions (Ackerman and Ben-David (2009)). The new methods prove useful
and sensible in many cases, but some weaknesses are also highlighted. These
also concern the use of the ASW for estimating the number of clusters together
with other methods, which is of general interest due to the popularity of the
ASW for this task.
