On the mixture maximum likelihood approach to estimation and clustering
Selvanayagam Ganesalingam · Bulletin of the Australian Mathematical Society · 1981
In this study attention is focussed on the performance of the mixture maximum likelihood approach as an estimation and a clustering procedure.There is available a sample of p-dimensional observations where each maybelong to one of several subpopulations.Estimation on the basis of this sample is considered in a cluster analysis context where it is not known from which subpopulation an observation comes.Under the mixture likelihood approach the sample is assumed to have been drawn from a mixture of a specified number of subpopulations in varying proportions.Adopting some parametric form for the density function in each underlying subpopulation, a likelihood can be formed in terms of the mixutre density, and the unknown parameters estimated by maximum likelihood.Parameters of particular interest are the discriminant function coefficients as we shall be primarily concerned with the ability of the mixutre maximum likelihood approach to provide a satisfactory discrimination rule for allocating the initial unclassified observations as well as any subsequent unclassified data.A comprehensive account of existing work on the estimation problem for finite mixtures of distributions is presented.There are many clustering procedures available, and a review is undertaken of the general classification problem in order to demonstrate where the mixture maximum likelihood approach fits into the existing framework of cluster analysis.The mixture maximum likelihood approach can be applied, at least in