  The increasing needs of clustering massive datasets and the high cost of
running clustering algorithms poses difficult problems for users. In this
context it is important to determine if a data set is clusterable, that is, it
may be partitioned efficiently into well-differentiated groups containing
similar objects. We approach data clusterability from an ultrametric-based
perspective. A novel approach to determine the ultrametricity of a dataset is
proposed via a special type of matrix product, which allows us to evaluate the
clusterability of the dataset. Furthermore, we show that by applying our
technique to a dissimilarity space will generate the sub-dominant ultrametric
of the dissimilarity.
