  A key issue in cluster analysis is the choice of an appropriate clustering
method and the determination of the best number of clusters. Different
clusterings are optimal on the same data set according to different criteria,
and the choice of such criteria depends on the context and aim of clustering.
Therefore, researchers need to consider what data analytic characteristics the
clusters they are aiming at are supposed to have, among others within-cluster
homogeneity, between-clusters separation, and stability. Here, a set of
internal clustering validity indexes measuring different aspects of clustering
quality is proposed, including some indexes from the literature. Users can
choose the indexes that are relevant in the application at hand. In order to
measure the overall quality of a clustering (for comparing clusterings from
different methods and/or different numbers of clusters), the index values are
calibrated for aggregation. Calibration is relative to a set of random
clusterings on the same data. Two specific aggregated indexes are proposed and
compared with existing indexes on simulated and real data.
