  Determining the number of clusters present in a dataset is an important
problem in cluster analysis. Conventional clustering techniques generally
assume this parameter to be provided up front. %user supplied. %Recently,
robustness of any given clustering algorithm is analyzed to measure cluster
stability/instability which in turn determines the cluster number. In this
paper, we propose a method which analyzes cluster stability for predicting the
cluster number. Under the same computational framework, the technique also
finds representatives of the clusters. The method is apt for handling big data,
as we design the algorithm using \emph{Monte-Carlo} simulation. Also, we
explore a few pertinent issues found to be of also clustering. Experiments
reveal that the proposed method is capable of identifying a single cluster. It
is robust in handling high dimensional dataset and performs reasonably well
over datasets having cluster imbalance. Moreover, it can indicate cluster
hierarchy, if present. Overall we have observed significant improvement in
speed and quality for predicting cluster numbers as well as the composition of
clusters in a large dataset.
