基于独立混合模型的EM算法参数初始化实现方法

隐马尔科夫树( Hidden Markov Tree, HMT )的状态不能被观测到，只能观测到另一个与状态有联系的量，通过观测量估计HMT模型参数是一个不完全数据参数估计问题。期望最大化( Expectation Maximization, EM )算法是一种求参数极大似然估计的迭代算法，可以用于解决不完全数据参数估计问题，因此被广泛应用于HMT模型的参数估计中。当初始参数偏离真实参数较大时，EM算法迭代次数多，收敛速度慢，通过一个计算量不大的参数初始化处理，能够有效减少EM算法的迭代次数，加快收敛速度。本文提出了一种基于独立混合模型的参数初始化方法，详细介绍了该方法的实现过程，通过采用独立混合模型进行参数初始化，使得EM算法的迭代次数明显减少，收敛速度大大提高。最后，计算机仿真验证了该方法的可行性和有效性。 

A Novel Method of Initializing the Expectation Maximization Algorithm Based on the Independent Mixture Model

The state of the Hidden Markov Tree (HMT) model can not be observed, only the variable associated with the state is observed. So parameter estimation of the HMT model through observed variable is an incomplete data estimation problem. The Expectation Maximization (EM) algorithm, which can solve the maximum likelihood parameter estimation, plays an important role in dealing with the parameter estimation of incomplete data. It also has been widely applied to estimate the parameters of the HMT model. Especially, when initial parameters deviate from the true value greatly, iteration number of the EM algorithm is large and convergence rate becomes slow. Such problems can be solved after using a lower computation initialization method. In this paper, an initialization method based on the Independent Mixture (IM) model is proposed and the implementation of this method is analyzed in detail. After using the IM model to initialize the parameters of the EM algorithm, the iteration number is significantly reduced and the convergence rate is greatly improved when using the EM algorithm to estimate the parameters of the HMT model. Finally, computer simulation is employed to validate the feasibility and availability of this method.