The EM algorithm is a very popular maximum likelihood estimation method, the iterative algorithm for solving the maximum likelihood estimator when the observation data is the incomplete data, but also is very effectiv...The EM algorithm is a very popular maximum likelihood estimation method, the iterative algorithm for solving the maximum likelihood estimator when the observation data is the incomplete data, but also is very effective algorithm to estimate the finite mixture model parameters. However, EM algorithm can not guarantee to find the global optimal solution, and often easy to fall into local optimal solution, so it is sensitive to the determination of initial value to iteration. Traditional EM algorithm select the initial value at random, we propose an improved method of selection of initial value. First, we use the k-nearest-neighbor method to delete outliers. Second, use the k-means to initialize the EM algorithm. Compare this method with the original random initial value method, numerical experiments show that the parameter estimation effect of the initialization of the EM algorithm is significantly better than the effect of the original EM algorithm.展开更多
Wireless Sensor Networks (WSNs) are mainly deployed for data acquisition, thus, the network performance can be passively measured by exploiting whether application data from various sensor nodes reach the sink. In thi...Wireless Sensor Networks (WSNs) are mainly deployed for data acquisition, thus, the network performance can be passively measured by exploiting whether application data from various sensor nodes reach the sink. In this paper, therefore, we take into account the unique data aggregation communication paradigm of WSNs and model the problem of link loss rates inference as a Maximum-Likelihood Estimation problem. And we propose an inference algorithm based on the standard Expectation-Maximization (EM) techniques. Our algorithm is applicable not only to periodic data collection scenarios but to event detection scenarios. Finally, we validate the algorithm through simulations and it exhibits good performance and scalability.展开更多
Classical survival analysis assumes all subjects will experience the event of interest, but in some cases, a portion of the population may never encounter the event. These survival methods further assume independent s...Classical survival analysis assumes all subjects will experience the event of interest, but in some cases, a portion of the population may never encounter the event. These survival methods further assume independent survival times, which is not valid for honey bees, which live in nests. The study introduces a semi-parametric marginal proportional hazards mixture cure (PHMC) model with exchangeable correlation structure, using generalized estimating equations for survival data analysis. The model was tested on clustered right-censored bees survival data with a cured fraction, where two bee species were subjected to different entomopathogens to test the effect of the entomopathogens on the survival of the bee species. The Expectation-Solution algorithm is used to estimate the parameters. The study notes a weak positive association between cure statuses (ρ1=0.0007) and survival times for uncured bees (ρ2=0.0890), emphasizing their importance. The odds of being uncured for A. mellifera is higher than the odds for species M. ferruginea. The bee species, A. mellifera are more susceptible to entomopathogens icipe 7, icipe 20, and icipe 69. The Cox-Snell residuals show that the proposed semiparametric PH model generally fits the data well as compared to model that assume independent correlation structure. Thus, the semi parametric marginal proportional hazards mixture cure is parsimonious model for correlated bees survival data.展开更多
The use of a general EM(expectation-maximization) algorithm in multi-spectral image classification is known to cause two problems:singularity of the variance-covariance matrix and sensitivity of randomly selected init...The use of a general EM(expectation-maximization) algorithm in multi-spectral image classification is known to cause two problems:singularity of the variance-covariance matrix and sensitivity of randomly selected initial values.The former causes computation failure;the latter produces unstable classification results.This paper proposes a modified approach to resolve these defects.First,a modification is proposed to determine reliable parameters for the EM algorithm based on a k-means algorithm with initial centers obtained from the density function of the first principal component,which avoids the selection of initial centers at random.A second modification uses the principal component transformation of the image to obtain a set of uncorrelated data.The number of principal components as the input of the EM algorithm is determined by the principal contribution rate.In this way,the modification can not only remove singularity but also weaken noise.Experimental results obtained from two sets of remote sensing images acquired by two different sensors confirm the validity of the proposed approach.展开更多
Based on Vector Aitken(VA) method,we propose an acceleration Expectation-Maximization(EM)algorithm,VA-accelerated EM algorithm,whose convergence speed is faster than that of EM algorithm.The VA-accelerated EM algorith...Based on Vector Aitken(VA) method,we propose an acceleration Expectation-Maximization(EM)algorithm,VA-accelerated EM algorithm,whose convergence speed is faster than that of EM algorithm.The VA-accelerated EM algorithm does not use the information matrix but only uses the sequence of estimates obtained from iterations of the EM algorithm,thus it keeps the flexibility and simplicity of the EM algorithm.Considering Steffensen iterative process,we have also given the Steffensen form of the VA-accelerated EM algorithm.It can be proved that the reform process is quadratic convergence.Numerical analysis illustrate the proposed methods are efficient and faster than EM algorithm.展开更多
A novel method under the interactive multiple model (IMM) filtering framework is presented in this paper, in which the expectation-maximization (EM) algorithm is used to identify the process noise covariance Q online....A novel method under the interactive multiple model (IMM) filtering framework is presented in this paper, in which the expectation-maximization (EM) algorithm is used to identify the process noise covariance Q online. For the existing IMM filtering theory, the matrix Q is determined by means of design experience, but Q is actually changed with the state of the maneuvering target. Meanwhile it is severely influenced by the environment around the target, i.e., it is a variable of time. Therefore, the experiential covariance Q can not represent the influence of state noise in the maneuvering process exactly. Firstly, it is assumed that the evolved state and the initial conditions of the system can be modeled by using Gaussian distribution, although the dynamic system is of a nonlinear measurement equation, and furthermore the EM algorithm based on IMM filtering with the Q identification online is proposed. Secondly, the truncated error analysis is performed. Finally, the Monte Carlo simulation results are given to show that the proposed algorithm outperforms the existing algorithms and the tracking precision for the maneuvering targets is improved efficiently.展开更多
This paper discusses the maximum likelihood estimate of β under linear inequalities A0β≥ a in a linear model with missing data, proposes the restricted EM algo rithm and proves the convergence.
The conventional method for testing hypotheses is to find an exact or asymptotic distributionof a test statistic. But when the model is complex and the sample size is small, difficulty often arises. Thispaper aims to ...The conventional method for testing hypotheses is to find an exact or asymptotic distributionof a test statistic. But when the model is complex and the sample size is small, difficulty often arises. Thispaper aims to present a method for finding maximum probability with the help of EM algorithm. For any fixedsample size, this method can be used not only to obtain an accurate test but also to check the real level ofa test which is build by large sample theory. Especially, while doing this, one needs neither the accurate norasymptotic distribution of the test statistic. So the method is easily performed and is especially useful for small samples.展开更多
函数型聚类分析在统计学领域被广泛关注,其分析过程通常在降维目标实现后进行。为了有效解决函数型主成分聚类问题,文章结合局部线性嵌入算法(Locally Linear Embedding,LLE)在非线性空间下的适用性,提出了一种局部线性下的函数型主成...函数型聚类分析在统计学领域被广泛关注,其分析过程通常在降维目标实现后进行。为了有效解决函数型主成分聚类问题,文章结合局部线性嵌入算法(Locally Linear Embedding,LLE)在非线性空间下的适用性,提出了一种局部线性下的函数型主成分分析模型(LLE Function Principle Component Analysis,LFPCA)。首先,采用函数型主成分分析法作为降维目标方法,改进了FPCA的算法模型,通过将LLE算法的权重系数矩阵与函数型主成分定义相结合,构建出一个适用于非线性空间下的聚类算法;其次,在求解算法的过程中定义了函数型主成分得分,并结合EM算法构建出GMM模型来近似函数型算法的概率密度函数,使模型更高效且适用性更强;最后,通过随机模拟实验及应用分析验证了LFPCA算法模型在真实数据集上具有良好的聚类效能。展开更多
文摘The EM algorithm is a very popular maximum likelihood estimation method, the iterative algorithm for solving the maximum likelihood estimator when the observation data is the incomplete data, but also is very effective algorithm to estimate the finite mixture model parameters. However, EM algorithm can not guarantee to find the global optimal solution, and often easy to fall into local optimal solution, so it is sensitive to the determination of initial value to iteration. Traditional EM algorithm select the initial value at random, we propose an improved method of selection of initial value. First, we use the k-nearest-neighbor method to delete outliers. Second, use the k-means to initialize the EM algorithm. Compare this method with the original random initial value method, numerical experiments show that the parameter estimation effect of the initialization of the EM algorithm is significantly better than the effect of the original EM algorithm.
文摘Wireless Sensor Networks (WSNs) are mainly deployed for data acquisition, thus, the network performance can be passively measured by exploiting whether application data from various sensor nodes reach the sink. In this paper, therefore, we take into account the unique data aggregation communication paradigm of WSNs and model the problem of link loss rates inference as a Maximum-Likelihood Estimation problem. And we propose an inference algorithm based on the standard Expectation-Maximization (EM) techniques. Our algorithm is applicable not only to periodic data collection scenarios but to event detection scenarios. Finally, we validate the algorithm through simulations and it exhibits good performance and scalability.
文摘Classical survival analysis assumes all subjects will experience the event of interest, but in some cases, a portion of the population may never encounter the event. These survival methods further assume independent survival times, which is not valid for honey bees, which live in nests. The study introduces a semi-parametric marginal proportional hazards mixture cure (PHMC) model with exchangeable correlation structure, using generalized estimating equations for survival data analysis. The model was tested on clustered right-censored bees survival data with a cured fraction, where two bee species were subjected to different entomopathogens to test the effect of the entomopathogens on the survival of the bee species. The Expectation-Solution algorithm is used to estimate the parameters. The study notes a weak positive association between cure statuses (ρ1=0.0007) and survival times for uncured bees (ρ2=0.0890), emphasizing their importance. The odds of being uncured for A. mellifera is higher than the odds for species M. ferruginea. The bee species, A. mellifera are more susceptible to entomopathogens icipe 7, icipe 20, and icipe 69. The Cox-Snell residuals show that the proposed semiparametric PH model generally fits the data well as compared to model that assume independent correlation structure. Thus, the semi parametric marginal proportional hazards mixture cure is parsimonious model for correlated bees survival data.
基金supported by the National High-tech R&D Program of China(2007AA12Z226 and SS2012AA120804)the National Natural Science Foundation of China(40674015 and 41074009)+2 种基金the Doctoral Fund of Ministry of Education of China(20100022110008)the Fundamental Research Funds for the Central Universities(2-9-2011-227)the Open Research Fund of Key Laboratory of Digital Earth Science,Center for Earth Observation and Digital Earth,Chinese Academy of Sciences (2010LDE002)
文摘The use of a general EM(expectation-maximization) algorithm in multi-spectral image classification is known to cause two problems:singularity of the variance-covariance matrix and sensitivity of randomly selected initial values.The former causes computation failure;the latter produces unstable classification results.This paper proposes a modified approach to resolve these defects.First,a modification is proposed to determine reliable parameters for the EM algorithm based on a k-means algorithm with initial centers obtained from the density function of the first principal component,which avoids the selection of initial centers at random.A second modification uses the principal component transformation of the image to obtain a set of uncorrelated data.The number of principal components as the input of the EM algorithm is determined by the principal contribution rate.In this way,the modification can not only remove singularity but also weaken noise.Experimental results obtained from two sets of remote sensing images acquired by two different sensors confirm the validity of the proposed approach.
基金Supported by the National Natural Science Foundation of China(No.11071253,11471335,11626130)
文摘Based on Vector Aitken(VA) method,we propose an acceleration Expectation-Maximization(EM)algorithm,VA-accelerated EM algorithm,whose convergence speed is faster than that of EM algorithm.The VA-accelerated EM algorithm does not use the information matrix but only uses the sequence of estimates obtained from iterations of the EM algorithm,thus it keeps the flexibility and simplicity of the EM algorithm.Considering Steffensen iterative process,we have also given the Steffensen form of the VA-accelerated EM algorithm.It can be proved that the reform process is quadratic convergence.Numerical analysis illustrate the proposed methods are efficient and faster than EM algorithm.
基金Supported by the National Key Fundamental Research & Development Programs of P. R. China (2001CB309403)
文摘A novel method under the interactive multiple model (IMM) filtering framework is presented in this paper, in which the expectation-maximization (EM) algorithm is used to identify the process noise covariance Q online. For the existing IMM filtering theory, the matrix Q is determined by means of design experience, but Q is actually changed with the state of the maneuvering target. Meanwhile it is severely influenced by the environment around the target, i.e., it is a variable of time. Therefore, the experiential covariance Q can not represent the influence of state noise in the maneuvering process exactly. Firstly, it is assumed that the evolved state and the initial conditions of the system can be modeled by using Gaussian distribution, although the dynamic system is of a nonlinear measurement equation, and furthermore the EM algorithm based on IMM filtering with the Q identification online is proposed. Secondly, the truncated error analysis is performed. Finally, the Monte Carlo simulation results are given to show that the proposed algorithm outperforms the existing algorithms and the tracking precision for the maneuvering targets is improved efficiently.
基金We would like to thank the referees for many useful suggestions on the earlier draft of the manuscript.This work was supported by the National Natural Foundation of China(Grant Nos.10431010,10329102&10371015)the Science and Technology Keystone Fund of MOE,China(Grant Nos.104070&00041)+1 种基金EYTP,the Distinguished Young Scholars Science Research Program of Jilin Province(Grant No.20030113)Young Teacher's Foundation of Northeast Normal University,China.
文摘This paper discusses the maximum likelihood estimate of β under linear inequalities A0β≥ a in a linear model with missing data, proposes the restricted EM algo rithm and proves the convergence.
基金This work was supported by the National Natural Science Foundation of China （51507015, 61773402, 61540037, 71271215, 61233008, 51425701, 70921001, 51577014）, the Natural Science Foundation of Hunan Province （2015JJ3008）, the Key Laboratory of Renewable Energy Electric-Technology of Hunan Province （2014ZNDL002）, and Hunan Province Science and Technology Program（2015NK3035）.
基金This work was supported by the National Natural Science Foundation of China(Grant No.10071004).
文摘The conventional method for testing hypotheses is to find an exact or asymptotic distributionof a test statistic. But when the model is complex and the sample size is small, difficulty often arises. Thispaper aims to present a method for finding maximum probability with the help of EM algorithm. For any fixedsample size, this method can be used not only to obtain an accurate test but also to check the real level ofa test which is build by large sample theory. Especially, while doing this, one needs neither the accurate norasymptotic distribution of the test statistic. So the method is easily performed and is especially useful for small samples.
文摘函数型聚类分析在统计学领域被广泛关注,其分析过程通常在降维目标实现后进行。为了有效解决函数型主成分聚类问题,文章结合局部线性嵌入算法(Locally Linear Embedding,LLE)在非线性空间下的适用性,提出了一种局部线性下的函数型主成分分析模型(LLE Function Principle Component Analysis,LFPCA)。首先,采用函数型主成分分析法作为降维目标方法,改进了FPCA的算法模型,通过将LLE算法的权重系数矩阵与函数型主成分定义相结合,构建出一个适用于非线性空间下的聚类算法;其次,在求解算法的过程中定义了函数型主成分得分,并结合EM算法构建出GMM模型来近似函数型算法的概率密度函数,使模型更高效且适用性更强;最后,通过随机模拟实验及应用分析验证了LFPCA算法模型在真实数据集上具有良好的聚类效能。
