  Clustering is a NP-hard problem. Thus, no optimal algorithm exists,
heuristics are applied to cluster the data. Heuristics can be very
resource-intensive, if not applied properly. For substantially large data sets
computational efficiencies can be achieved by reducing the input space if a
minimal loss of information can be achieved. Clustering algorithms, in general,
face two common problems: 1) these converge to different settings with
different initial conditions and; 2) the number of clusters has to be
arbitrarily decided beforehand. This problem has become critical in the realm
of big data. Recently, clustering algorithms have emerged which can speedup
computations using parallel processing over the grid but face the
aforementioned problems. Goals: Our goals are to find methods to cluster data
which: 1) guarantee convergence to the same settings irrespective of the
initial conditions; 2) eliminate the need to establish the number of clusters
beforehand, and 3) can be applied to cluster large datasets. Methods: We
introduce a method that combines probabilistic and combinatorial clustering
methods to produce repeatable and compact clusters that are not sensitive to
initial conditions. This method harnesses the power of k-means (a combinatorial
clustering method) to cluster/partition very large dimensional datasets and
uses the Gaussian Mixture Model (a probabilistic clustering method) to validate
the k-means partitions. Results: We show that this method produces very compact
clusters that are not sensitive to initial conditions. This method can be used
to identify the most 'separable' set in a dataset which increases the
'clusterability' of a dataset. This method also eliminates the need to specify
the number of clusters in advance.
