Parameter Estimation Of T-distribution Mixture Models Based On EM Algorithm

Model-based clustering,as one of many clustering analysis methods,has been widely used in various fields.It is clear that model-based clustering is better than other clustering methods if a particular distribution can better characterize a dataset.The Gaussian-mixture model is most convenient to use in computation,but it is very easy to be influenced by outliers.The T-distribution mixture model has better robustness than Gaussian-mixture model because of its heavy-tailed feature so that used especially in the fields of image processing,biology and medicine.The EM algorithm is the representative of its solution method.Therefore,it is a significant work to study the T-distribution model and the EM algorithm of the solving method.The main work of this paper is as follows:First,respectively,we have studied the two and three population of univariate T-distribution mixture model.Furthermore,using EM algorithm to solve the maximum likelihood estimation of model parameters.We have overcome the problem in the multivariate mixed T-distribution model of the covariance matrix to the univariate T-distribution mixture model of the scaling parameters in the transformation process of parameter derivation.In the iterative process,It is a key problem how to initialize the parameter.This paper applies the k-means algorithm firstly to the selection of initial parameters of the univariate T-distribution mixture model.The speed of convergence is fast and the efficiency of calculation is greatly improved.For Gaussian mixture model and t-distribution model,the ability of fitting data is compared and analyzed by Gaussian mixture data,T-distribution mixture data and noisy mixed Gaussian data.The experiment shows that the fitting effect of the T-distribution mixture model under three kinds of data is quite considerable.For the mixed Gaussian data,the model is not worse than the Gaussian mixture model.For the mixed T-distribution data,the model is better than the Gaussian mixture model.For the Gaussian mixture data with noise,all the effect of the model fitting is almost better than the Gaussian mixture model.This shows the advantages of the T-distribution mixture model in processing the data with longer than normal tails.