On classifying mixture components as clusters
N. T. Longford and J. Bartosova

Abstract

An index is defined for characterising the separation of two distributions is introduced. It is applied to assessing whether mixture components are clusters. A related property of being a satellite and a partial ordering of the components are defined. A sequence of clustering structures is defined for a finite mixture with a continuum of thresholds that qualify a cluster. The approach is suitable for outcomes with arbitrary univariate or multivariate distributions and their mixtures. The properties of the index are explored by simulations and on examples.
 
  Statistical Modelling 14, 229-255, 2014.
June 2014