Multivariate Data Clustering for the Gaussian Mixture Model

Article type: Research Article

Authors: Kavaliauskas, Mindaugas | Rudzkis, Rimantas

Affiliations: Faculty of Fundamental Science, Kaunas University of Technology, Donelaičio 72, LT‐3000 Kaunas, Lithuania, e‐mail: snaiperiui@takas.lt | Department of Applied Statistics, Institute of Mathematics and Informatics, Akademijos 4, 08663 Vilnius, Lithuania, e‐mail: rudzkis@ktl.mii.lt

Abstract: 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.

Keywords: clustering, multivariate data, Gaussian mixture model, projection‐based clustering, EM algorithm

Journal: Informatica, vol. 16, no. 1, pp. 61-74, 2005