  Inferring cluster structure in microarray datasets is a fundamental task for
the -omic sciences. A fundamental question in Statistics, Data Analysis and
Classification, is the prediction of the number of clusters in a dataset,
usually established via internal validation measures. Despite the wealth of
internal measures available in the literature, new ones have been recently
proposed, some of them specifically for microarray data. In this dissertation,
a study of internal validation measures is given, paying particular attention
to the stability based ones. Indeed, this class of measures is particularly
prominent and promising in order to have a reliable estimate the number of
clusters in a dataset. For those measures, a new general algorithmic paradigm
is proposed here that highlights the richness of measures in this class and
accounts for the ones already available in the literature. Moreover, some of
the most representative validation measures are also considered. Experiments on
12 benchmark datasets are performed in order to assess both the intrinsic
ability of a measure to predict the correct number of clusters in a dataset and
its merit relative to the other measures. The main result is a hierarchy of
internal validation measures in terms of precision and speed, highlighting some
of their merits and limitations not reported before in the literature. This
hierarchy shows that the faster the measure, the less accurate it is. In order
to reduce the time performance gap between the fastest and the most precise
measures, the technique of designing fast approximation algorithms is
systematically applied. The end result is a speed-up of many of the measures
studied here that brings the gap between the fastest and the most precise
within one order of magnitude in time, with no degradation in their prediction
power. Prior to this work, the time gap was at least two orders of magnitude.
