Multivariate Data Clustering for the Gaussian Mixture Model

摘要

Straipsnyje nagrinejamas didelio matavimo nepriklausomu atsitiktiniu dydžiu, tenkinančiu Gauso skirstiniu mišinio modeli, imties negriežto klasterizavimo (klasifikavimo be apmokymo) uždavinys. Pagrindinis demesys skiriamas algoritmams, kune remiasi duomeni) projektavimu i mažesnio matavimo erdves. Pasiulyta nauja keliu etapu klasterizavimo procedura, apimanti stebejimu vie-namačiu projekciju pasiskirstymo statistine analize, daugiamates imties klasterizavima geometri-niais metodais ir EM algoritmo taikyma. Darbe pateikiami nagrinejamu metodu tikslumo analizes rezultatai, gauti Monte-Karlo budu.%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.