Parameter Estimation Of Constrained Parameter Space In Gaussian Mixture Models

The Gaussian mixture model has been studied by many scholars because of its wide application.Among them,parameter estimation in the Gaussian mixture model is the focus of research.Many scholars have developed some effective methods to estimate parameters in the GMM model,such as the expected maximum algorithm,and methods based on fuzzy clustering,vector coding learning,Monte Carlo sampling,and so on.Domestic and foreign scholars have studied the parameter estimation method of Gaussian mixture model more,and there are fewer problems in parameter estimation under the condition that the parameter space is limited in the model.This article is mainly based on the research basis of previous scholars,according to the actual problems in the disease grouping detection,to study the parameters of the parameter space under the condition of the parameter estimation problem.In group testing,the sample sample tested is subjected to a Gaussian mixture model.The group size is K.The hidden variable is the number of positive individuals in the group.The distribution of continuous variables depends on the number of positive individuals in the group.The number of positive individuals is 0 to K,so the Gaussian mixture model has K+1 classes.In the traditional Gaussian mixture model,three types of parameters(mean,variance,and weight coefficients)need to be estimated.There are 3K+2 free-transformed parameters.In the model studied in this paper,the observations in our group are the average of individual observations,and individual observations depend on the state of the individual.Suppose that an individual obeys Gaussian distributions with different types of parameters.Each type of Gaussian distribution contains two parameters.Therefore,in the group detection Gaussian mixture model with group size K,five parameters need to be estimated,which is lower than 3K+2 of the traditional Gaussian mixture model.The traditional EM algorithm and other methods are no longer applicable to this model.For this situation,this paper proposes parameter-constrained EM algorithm,corresponding moment estimation method and ECM method to estimate parameter space-constrained parameter estimation problem.In addition,the simulation results show that our statistics have very good statistical properties.