Research Of The Clustering Algorithm Based On Mixture Model And Its Robustness

Finite mixture-models as an extremely flexible and powerful probability and statistical-based modeling tool have received increasing attention in statistics, a wide range of pattern recognition and engineer fields as so on .Its most important use is to cluster multivariate data sets.In this thesis, we mostly research the initialization strategies and robustness of the algorithm of multivariate Gaussian mixture models. Because the mixtures of Gaussian lack robustness in the presence o f observations that are atypical of the components ,we choose multivariate mixtures of t distribute to fit such data. Especially, we use EM algorithm to fit the mixture models of multivariate t distributions on data sets with missing value. The main work as follow :1, When the optimal number of components in a mixture model is not deteminated improperly , using S/R/S initialization strategies^[4] may get spurious local higliest likelihood value . Aiming at the essential shortcoming of these initialization strategies, we provide four improved initialization strategies,, Their availabity are compared in the multivariate Gaussian mixtures on the basis of numerical experiments on both simulated and real data sets .2, Considering that mixtures of Gaussians lack robustness, we research and improve the EM algorithm of multivariate t distributions with missing information^[36].We apply this improved algorithm to cluster the real data sets with missing value.On the data sets with the varying proportions of missing values, improved algorithm is more effective and robust than the original algorithm136'.