Optimal Estimation Of Parameters For A Class Of Mixed Gaussian Models

Finite mixture distribution model is an effective and powerful modeling tool in the analysis of complex problems. In many of the mixture models, the use of gaussian mixture model is more widely, especially the application and promotion in the fields of image processing, facial recognition, signal and communication processing and so on. With the theory and numerical experiment of it,we knowgaussian mixture model can approximate any smooth distribution. And the effective estimation to parameters of gauss mixture model is the necessary premise of accurate analysis and simulate complex problem.For the estimation of model parameters, torque estimation and maximum likelihood estimate become the main point estimation.In the study of parameter estimate about the gaussian mixture model, the original method is to use torque estimate way to solve the parameter estimate about two branches. For the parameter estimate problem of gaussian mixture model with two or more branches, it is still difficult to get a satisfactory solution while the torque estimate method have been improved, and the maximum likelihood estimate can do better. EM algorithm is a useful method of maximum likelihood estimate.Since the propose of EM algorithm, it has become a very popular method of dealing with incomplete data. At the same time the sample,data set which is used to simulate problem can usually be regarded as incomplete data,.Then EM algorithm for parameter estimation of the gaussian mixture model provides a standard framework. But the EM algorithm is a kind of iterative algorithm with slow convergence speed and strong dependence on initial values,and it is easy to trap in some local optimal values, which make the ultima estimation result of parameters is not accurate.In order to get the optimized parameters estimate result of the gaussian mixture model, in this paper, we will apply the Genetic Algorithm and Particle Swarm Optimization to the frame of the EM algorithm to overcome its own shortcomings.GA is a optimized algorithm with the ability of strong global search, but it’s search results will be influenced badly by the randomness in the initial value setting and mutation operation.So in this paper, PSO algorithm was applied to initial solution selection and mutation operators of GA to improve it.Then we combined the improved GA with EM algorithm framework.One side, it reduces the reliance on initial value, the other,it also improves the convergence speed effectively. So perfect the precision of parameter estimation for the gaussian mixture model.Usually,we can estimate its parameters when we has known the branch number of the mixed model, but for most complicated problem of simulation, branch number is unknown to the gaussian mixture model. We will combine the minimum message length criteron framework with the improved EM algorithm to get reasonable branch number of the mixed model.Which not only optimizes the parameter estimaten of each branch, at the same time, estimates the branch number of the gaussian mixture model more accurate.In the end, proving the stability and feasibility of the proposed method in this paper by two sets of numerical experiments.