  Model selection in clustering requires (i) to specify a suitable clustering
principle and (ii) to control the model order complexity by choosing an
appropriate number of clusters depending on the noise level in the data. We
advocate an information theoretic perspective where the uncertainty in the
measurements quantizes the set of data partitionings and, thereby, induces
uncertainty in the solution space of clusterings. A clustering model, which can
tolerate a higher level of fluctuations in the measurements than alternative
models, is considered to be superior provided that the clustering solution is
equally informative. This tradeoff between \emph{informativeness} and
\emph{robustness} is used as a model selection criterion. The requirement that
data partitionings should generalize from one data set to an equally probable
second data set gives rise to a new notion of structure induced information.
