Parameter Estimation Of Finite Mixture Model Based On Modified DA-EM Algorithm

In the context of big data,many data often come from different groups.The finite mixture model is highly regarded by the statistics and computer industry because of describing this heterogeneity very well.There are lots of researches on mathematical problems in finite mixture models.The first task of application deployment.Gaussian mixture model is the most widely used among them.Naturally,this paper mainly studies the parameter estimation problem of Gaussian mixture model.Compared with the classical EM algorithm,the Deterministic annealing expectationmaximization algorithm(DA-EM algorithm)introduces annealing parameters.However,using the initial value of the annealing parameter too small can easily cause the DA-EM algorithm to converge to a stable point and cause the iteration to stop prematurely.To solve this problem,some scholars proposed a method based on Jacobian matrix analysis to select the theoretically lower bound of the annealing parameter,but this method still cannot completely avoid the coincidence of the model mean vector.Aiming at the above problems,this paper proposes an modified DA-EM algorithm.On the basis of the DA-EM algorithm given the theoretically lower bound of the annealing parameter,the method modifies the log likelihood function by introducing two penalty terms and penalizing the mixture ratio and the distance of the model parameters.At the same time,the method maintains the convergence of the original algorithm.The experimental results of the simulated data and the real data show that: Under certain conditions,the modified DA-EM algorithm estimates the parameters of the Gaussian mixture model.The effect is more accurate and stable,and its convergence speed is faster than DA-EM algorithm.