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
An improved Gaussian mixture model （GMM）- based clustering method is proposed for the difficult case where the true distribution of data is against the assumed GMM. First, an improved model selection criterion, the ...An improved Gaussian mixture model （GMM）- based clustering method is proposed for the difficult case where the true distribution of data is against the assumed GMM. First, an improved model selection criterion, the completed likelihood minimum message length criterion, is derived. It can measure both the goodness-of-fit of the candidate GMM to the data and the goodness-of-partition of the data. Secondly, by utilizing the proposed criterion as the clustering objective function, an improved expectation- maximization （EM） algorithm is developed, which can avoid poor local optimal solutions compared to the standard EM algorithm for estimating the model parameters. The experimental results demonstrate that the proposed method can rectify the over-fitting tendency of representative GMM-based clustering approaches and can robustly provide more accurate clustering results.展开更多
Since the joint probabilistic data association(JPDA)algorithm results in calculation explosion with the increasing number of targets,a multi-target tracking algorithm based on Gaussian mixture model(GMM)clustering is ...Since the joint probabilistic data association(JPDA)algorithm results in calculation explosion with the increasing number of targets,a multi-target tracking algorithm based on Gaussian mixture model(GMM)clustering is proposed.The algorithm is used to cluster the measurements,and the association matrix between measurements and tracks is constructed by the posterior probability.Compared with the traditional data association algorithm,this algorithm has better tracking performance and less computational complexity.Simulation results demonstrate the effectiveness of the proposed algorithm.展开更多
An efficient approach was proposed for discriminating shadows from moving objects. In the background subtraction stage, moving objects were extracted. Then, the initial classification for moving shadow pixels and fore...An efficient approach was proposed for discriminating shadows from moving objects. In the background subtraction stage, moving objects were extracted. Then, the initial classification for moving shadow pixels and foreground object pixels was performed by using color invariant features. In the shadow model learning stage, instead of a single Gaussian distribution, it was assumed that the density function computed on the values of chromaticity difference or bright difference, can be modeled as a mixture of Gaussian consisting of two density functions. Meanwhile, the Gaussian parameter estimation was performed by using EM algorithm. The estimates were used to obtain shadow mask according to two constraints. Finally, experiments were carried out. The visual experiment results confirm the effectiveness of proposed method. Quantitative results in terms of the shadow detection rate and the shadow discrimination rate(the maximum values are 85.79% and 97.56%, respectively) show that the proposed approach achieves a satisfying result with post-processing step.展开更多
To solve the problem of color distortion after dehazing in the sky region by using the classical dark channel prior method to process the hazy images with large regions of sky,an improved dark channel image dehazing m...To solve the problem of color distortion after dehazing in the sky region by using the classical dark channel prior method to process the hazy images with large regions of sky,an improved dark channel image dehazing method based on Gaussian mixture model is proposed.Firstly,we use the Gaussian mixture model to model the hazy image,and then use the expectation maximization(EM)algorithm to optimize the parameters,so that the hazy image can be divided into the sky region and the non-sky region.Secondly,the sky region is divided into a light haze region,a medium haze region and a heavy haze region according to the different dark channel values to estimate the transmission respectively.Thirdly,the restored image is obtained by combining the atmospheric scattering model.Finally,adaptive local tone mapping for high dynamic range images is used to adjust the brightness of the restored image.The experimental results show that the proposed method can effectively eliminate the color distortion in the sky region,and the restored image is clearer and has better visual effect.展开更多
This paper discusses the estimation of parameters in the zero-inflated Poisson (ZIP) model by the method of moments. The method of moments estimators (MMEs) are analytically compared with the maximum likelihood estima...This paper discusses the estimation of parameters in the zero-inflated Poisson (ZIP) model by the method of moments. The method of moments estimators (MMEs) are analytically compared with the maximum likelihood estimators (MLEs). The results of a modest simulation study are presented.展开更多
In this paper, a Gaussian mixture model (GMM) based classifier is described to tell whether precipitation events will happen on a certain day at a certain time from historical meteorological data. The classifier deals...In this paper, a Gaussian mixture model (GMM) based classifier is described to tell whether precipitation events will happen on a certain day at a certain time from historical meteorological data. The classifier deals with a two-class classification problem where one class represents precipitation events and the other represents non-precipitation events. The concept of ambiguity is introduced to represent cases where weather conditions between the two classes like drizzles, intermittent or overcast are more likely to happen. Six groups of experiments are carried out to evaluate the performance of the classifier using different configurations based on the observation data released by Shanghai Baoshan weather station. Specifically, a typical classification performance of about 75% accuracy, 30% precision and 80% recall is achieved for prediction tasks with a time span of 12 hours.展开更多
Semi-Supervised Classification (SSC),which makes use of both labeled and unlabeled data to determine classification borders in feature space,has great advantages in extracting classification information from mass data...Semi-Supervised Classification (SSC),which makes use of both labeled and unlabeled data to determine classification borders in feature space,has great advantages in extracting classification information from mass data.In this paper,a novel SSC method based on Gaussian Mixture Model (GMM) is proposed,in which each class’s feature space is described by one GMM.Experiments show the proposed method can achieve high classification accuracy with small amount of labeled data.However,for the same accuracy,supervised classification methods such as Support Vector Machine,Object Oriented Classification,etc.should be provided with much more labeled data.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 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
Normal mixture regression models are one of the most important statistical data analysis tools in a heterogeneous population. When the data set under consideration involves asymmetric outcomes, in the last two decades...Normal mixture regression models are one of the most important statistical data analysis tools in a heterogeneous population. When the data set under consideration involves asymmetric outcomes, in the last two decades, the skew normal distribution has been shown beneficial in dealing with asymmetric data in various theoretic and applied problems. In this paper, we propose and study a novel class of models： a skew-normal mixture of joint location, scale and skewness models to analyze the heteroscedastic skew-normal data coming from a heterogeneous population. The issues of maximum likelihood estimation are addressed. In particular, an Expectation-Maximization （EM） algorithm for estimating the model parameters is developed. Properties of the estimators of the regression coefficients are evaluated through Monte Carlo experiments. Results from the analysis of a real data set from the Body Mass Index （BMI） data are presented.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.
基金The National Natural Science Foundation of China(No.61105048,60972165)the Doctoral Fund of Ministry of Education of China(No.20110092120034)+2 种基金the Natural Science Foundation of Jiangsu Province(No.BK2010240)the Technology Foundation for Selected Overseas Chinese Scholar,Ministry of Human Resources and Social Security of China(No.6722000008)the Open Fund of Jiangsu Province Key Laboratory for Remote Measuring and Control(No.YCCK201005)
文摘An improved Gaussian mixture model （GMM）- based clustering method is proposed for the difficult case where the true distribution of data is against the assumed GMM. First, an improved model selection criterion, the completed likelihood minimum message length criterion, is derived. It can measure both the goodness-of-fit of the candidate GMM to the data and the goodness-of-partition of the data. Secondly, by utilizing the proposed criterion as the clustering objective function, an improved expectation- maximization （EM） algorithm is developed, which can avoid poor local optimal solutions compared to the standard EM algorithm for estimating the model parameters. The experimental results demonstrate that the proposed method can rectify the over-fitting tendency of representative GMM-based clustering approaches and can robustly provide more accurate clustering results.
基金the National Natural Science Foundation of China(61771367)the Science and Technology on Communication Networks Laboratory(HHS19641X003).
文摘Since the joint probabilistic data association(JPDA)algorithm results in calculation explosion with the increasing number of targets,a multi-target tracking algorithm based on Gaussian mixture model(GMM)clustering is proposed.The algorithm is used to cluster the measurements,and the association matrix between measurements and tracks is constructed by the posterior probability.Compared with the traditional data association algorithm,this algorithm has better tracking performance and less computational complexity.Simulation results demonstrate the effectiveness of the proposed algorithm.
基金Project(50805023)supported by the National Natural Science Foundation of ChinaProject(BA2010093)supported by the Special Fund of Jiangsu Province for the Transformation of Scientific and Technological Achievements,ChinaProject(2008144)supported by the Hexa-type Elites Peak Program of Jiangsu Province,China
文摘An efficient approach was proposed for discriminating shadows from moving objects. In the background subtraction stage, moving objects were extracted. Then, the initial classification for moving shadow pixels and foreground object pixels was performed by using color invariant features. In the shadow model learning stage, instead of a single Gaussian distribution, it was assumed that the density function computed on the values of chromaticity difference or bright difference, can be modeled as a mixture of Gaussian consisting of two density functions. Meanwhile, the Gaussian parameter estimation was performed by using EM algorithm. The estimates were used to obtain shadow mask according to two constraints. Finally, experiments were carried out. The visual experiment results confirm the effectiveness of proposed method. Quantitative results in terms of the shadow detection rate and the shadow discrimination rate(the maximum values are 85.79% and 97.56%, respectively) show that the proposed approach achieves a satisfying result with post-processing step.
基金National Natural Science Foundation of China(Nos.61841303,61963023)Project of Humanities and Social Sciences of Ministry of Education in China(No.19YJC760012)。
文摘To solve the problem of color distortion after dehazing in the sky region by using the classical dark channel prior method to process the hazy images with large regions of sky,an improved dark channel image dehazing method based on Gaussian mixture model is proposed.Firstly,we use the Gaussian mixture model to model the hazy image,and then use the expectation maximization(EM)algorithm to optimize the parameters,so that the hazy image can be divided into the sky region and the non-sky region.Secondly,the sky region is divided into a light haze region,a medium haze region and a heavy haze region according to the different dark channel values to estimate the transmission respectively.Thirdly,the restored image is obtained by combining the atmospheric scattering model.Finally,adaptive local tone mapping for high dynamic range images is used to adjust the brightness of the restored image.The experimental results show that the proposed method can effectively eliminate the color distortion in the sky region,and the restored image is clearer and has better visual effect.
文摘This paper discusses the estimation of parameters in the zero-inflated Poisson (ZIP) model by the method of moments. The method of moments estimators (MMEs) are analytically compared with the maximum likelihood estimators (MLEs). The results of a modest simulation study are presented.
文摘In this paper, a Gaussian mixture model (GMM) based classifier is described to tell whether precipitation events will happen on a certain day at a certain time from historical meteorological data. The classifier deals with a two-class classification problem where one class represents precipitation events and the other represents non-precipitation events. The concept of ambiguity is introduced to represent cases where weather conditions between the two classes like drizzles, intermittent or overcast are more likely to happen. Six groups of experiments are carried out to evaluate the performance of the classifier using different configurations based on the observation data released by Shanghai Baoshan weather station. Specifically, a typical classification performance of about 75% accuracy, 30% precision and 80% recall is achieved for prediction tasks with a time span of 12 hours.
基金supported by the State Key Laboratory of Remote Sensing Science and Chinese Academy of Surveying & Mapping (Grant No.20903)
文摘Semi-Supervised Classification (SSC),which makes use of both labeled and unlabeled data to determine classification borders in feature space,has great advantages in extracting classification information from mass data.In this paper,a novel SSC method based on Gaussian Mixture Model (GMM) is proposed,in which each class’s feature space is described by one GMM.Experiments show the proposed method can achieve high classification accuracy with small amount of labeled data.However,for the same accuracy,supervised classification methods such as Support Vector Machine,Object Oriented Classification,etc.should be provided with much more labeled data.
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(11261025,11561075)the Natural Science Foundation of Yunnan Province(2016FB005)the Program for Middle-aged Backbone Teacher,Yunnan University
文摘Normal mixture regression models are one of the most important statistical data analysis tools in a heterogeneous population. When the data set under consideration involves asymmetric outcomes, in the last two decades, the skew normal distribution has been shown beneficial in dealing with asymmetric data in various theoretic and applied problems. In this paper, we propose and study a novel class of models： a skew-normal mixture of joint location, scale and skewness models to analyze the heteroscedastic skew-normal data coming from a heterogeneous population. The issues of maximum likelihood estimation are addressed. In particular, an Expectation-Maximization （EM） algorithm for estimating the model parameters is developed. Properties of the estimators of the regression coefficients are evaluated through Monte Carlo experiments. Results from the analysis of a real data set from the Body Mass Index （BMI） data are presented.
