The Em Algorithm And Its Applied Research, To Improve The Mixture Model Parameter Estimation

Finite mixture model is a flexible and powerful tool for analyzing complicated phenomena, which provide an efficient method of simulating complicated density with simple structures and present a natural frame and semi-parameter structure of modeling unobserved population homogeneity and heterogeneity.The expectation-maximization (EM) algorithm is a standard frame for maximum likelihood estimation in finite mixture models. The EM iterative formulas for Gaussian mixtures are derived in the present paper, and we propose an efficient initialization method for these iterative formulas to accelerate the EM algorithm' speed of convergence. Experiences of numerical simulation show that the proposed initial method contributes to accelerate the algorithm's speed of convergence, the more accurate results can be obtained.The EM algorithm is realized easily because of it's simplify. Unfortunately, optimal results are not always achieved because the EM algorithm, iterative in nature, is only guaranteed to produce a local maximum. As we known, the Genetic algorithm (GA) has much stronger global searching ability, we import the GA algorithm for improving the EM algorithm, and propose a genetic-based expectation-maximization (GA-EM) algorithm. The EM algorithm is restricted to a predefined number of components. However, in many practical applications, the optimal number of components is unknown, therefore, finding the optimum number of components in the mixture is an important but very difficult problem. We'll learn Gaussian mixture models from multivariate data the GA-EM algorithm . This algorithm is caballing of selecting the number of components of the model using the minimum description length (MDL) criterion. Our algorithm benefits from the properties of Genetic algorithm (GA) and EM algorithm by combination of both into a single procedure. The population-based stochastic search of the GA explores the search space more thoroughly than the EM algorithm, therefore, our algorithm enables escaping from local optimal solutions since the algorithm becomes less sensitive to its initialization. The experiments on simulated data show that the GA-EM algorithm maintains the monotonic convergence property of the EM algorithm, taking on a good robustness to initial values of parameters: 1) we have obtained a better MDL score while using exactly the same termination condition for both algorithm. 2) our approach identifies the number of components which were used to generate the underlying data more often than the EM algorithm.