Classification and Mixture Approaches to Clustering Via Maximum Likelihood

Mixtures of distributions, in particular the normal distribution, have been used extensively as models in a wide variety of important practical situations where the population of interest may be considered to consist of two or more subpopulations mixed in varying proportions. The problem of decomposing such a mixture of distributions is of considerable interest and utility. Two commonly used clustering methods based on maximum likelihood are considered in the context of the classification problem where observations of unknown origin belong to one of the two possible populations. The basic assumptions and associated properties of the two methods are contrasted and illustrated by a series of simulations under two different sampling schemes, namely the mixture sampling scheme and the separate sampling scheme. A case study is presented to demonstrate the basic differences between these two methods.