1996 Volume 8 Issue 2 Pages 117-133
Mixtures of distributions, in particular the multivariate normal distribution, have been used extensively as models in a wide variety of practical situations where the population 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. In this paper, we consuder the problem of estimating suitable initial values for the EM algorithm in the fitting of normal mixture models to multivariate data. It is given that the likelihood equation often has multiple roots for multivariate mixture models, the selection of initial values is serious problem. Discussion is focused here on the use of clustering methods (i. e. hierarchical type and divisive type) to provide suitable initial structure of data set in this context, and we propose the procedure to obtain a global solution. Examples show how proposed procedure works for actual data sets. Moreover, Monte Carlo numerical experiments are presented which involve to exhibit an effectiveness of proposed procedure, and compare a performance of the conventional clustering methods and the mixture approaches to clustering.
