Informatica

This paper discusses a soft sample clustering problem for multivariate independent random data satisfying the mixture model of the Gaussian distribution. The theory recommends to estimate the parameters of model by the maximum likelihood method and to use “plug-in” approach for data clustering. Unfortunately, the calculation problem of the maximum likelihood estimate is not completely solved in multivariate case. This work proposes a new constructive a few stage procedure to solve this task. This procedure includes statistical distribution analysis of a large number of the univariate projections of observations, geometric clustering of a multivariate sample and application of EM algorithm. The results of the accuracy analysis of the proposed methods is made by means of Monte-Carlo simulation.

Influence of projection pursuit on classification errors and estimates of a posteriori probabilities from the sample is considered. Observed random variable is supposed to satisfy a multidimensional Gaussian mixture model. Presented computer simulation results show that for comparatively small sample size classification using projection pursuit algorithm gives better accuracy of estimates of a posteriori probabilities and less classification error.