Comparison of the mixture and the classification maximum likelihood in cluster analysis

Abstract

Generally, the mixture and the classification approaches via maximum likelihood had been contrasted under different underlying assumptions.In the classification approach, the mixing proportions are assumed to be equal whereas, in the mixture approach, there are supposed to be unknown.In this paper, Monte-Carlo numerical experiments comparing both approaches, mixture and classification, in both assumptions, equal and unknown mixing proprotions are reported.These numerical experiments exhibited that assumptions on the mixing proportions is a more sensitive factor than the choice of the clustering approach, especially in the small setting.Morever, the differences between the finited sample and the asymptotic behaviour of both approaches are analyzed through additional simulations.