Numerical analysis of EM estimation of mixture model parameters

Abstract

Optimisation of distribution parameters is a very common problem. There are many sorts of distributions which can be used to model environment processes, biological functions or graphical data. However, it is common that parameters of those distribution may be, partially or completely unknown. Mixture models composed of a few distributions are easier to solve. In such a case simple estimation methods may be used to obtain results. Usually models are composed of several distributions. Those distributions may be of the same or different type. Such models are called mixture models. Finding their parameters may be complicated. Usually in such cases iterative methods need to be used. The paper gives a brief survey of algorithms designed for solving mixtures of distributions and problems connected with their usage.One of the most common method used to obtain mixture model parameters is Expectation-Maximization (EM) algorithm. EM is the iterative algorithm performing maximum likelihood estimation. The authors present the results of adjusting the Gaussian mixture models to the data. It is done with the usage of EM algorithm. The article gives advantages and disadvantages of EM algorithm. Improvements of EM applied in the case of large data are also presented. They help increase efficiency and decrease operation time of the algorithm. Another considered issue is the problem of optimal input parameters selection and its influence on the adjustment results. The authors also present algorithm performance observations.