Research on Initialization on EM Algorithm Based on Gaussian Mixture Model

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.

A multi-target tracking algorithm based on Gaussian mixture model

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.

Gaussian mixture model clustering with completed likelihood minimum message length criterion

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.

Improved dark channel image dehazing method based on Gaussian mixture model

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.

An efficient approach for shadow detection based on Gaussian mixture model

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.

基于高斯混合模型及EM算法的建筑工程数据预警治理方法

结合初期雨水调蓄大直径顶管工程的实际设计及施工经验,对软弱地层条件下长距离大直径平行双管曲线顶管在设计及施工过程中存在的重点难点问题进行总结,并对顶管过程中的顶力及管周摩阻力做了深入分析研究,有针对性地提出了相应的解决方案,使该顶管工程顺利贯通。建筑工程行业在现代社会中发挥着重要的经济和社会作用,然而,它也伴随着诸多风险和不确定性。为了有效地管理和预测这些风险,本文提出了一种基于高斯混合模型(GMM)和期望最大化(EM)算法的数据预警治理方法。该方法旨在通过对建筑工程数据的建模和分析,提前识别潜在的问题和风险,从而改善工程项目的管理和决策。

Predicting Precipitation Events Using Gaussian Mixture Model

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.

基于MapReduce的分布式EM算法的研究与应用

EM(Expectation-Maximization)算法在机器学习和自然语言处理方面应用非常广泛。随着电子信息技术的高速发展,人们更加需要从大量的数据信息中提出更多有价值的知识,用于后续的研究工作。但是,传统的应用到机器学习等领域的EM算法不能有效地处理当今社会海量规模的数据。本文基于现有流行的MapReduce计算框架,提出了求解混合模型的分布式EM算法。该算法能够高效地完成极大似然估计。实验表明,本文提出的算法具有很好的加速比以及可扩展性。

Variable selection for skew-normal mixture of joint location and scale models

Although there are many papers on variable selection methods based on mean model in the nite mixture of regression models,little work has been done on how to select signi cant explanatory variables in the modeling of the variance parameter.In this paper,we propose and study a novel class of models:a skew-normal mixture of joint location and scale models to analyze the heteroscedastic skew-normal data coming from a heterogeneous population.The problem of variable selection for the proposed models is considered.In particular,a modi ed Expectation-Maximization(EM)algorithm for estimating the model parameters is developed.The consistency and the oracle property of the penalized estimators is established.Simulation studies are conducted to investigate the nite sample performance of the proposed methodolo-gies.An example is illustrated by the proposed methodologies.

Variable Selection for Robust Mixture Regression Model with Skew Scale Mixtures of Normal Distributions

In this paper, we propose a robust mixture regression model based on the skew scale mixtures of normal distributions (RMR-SSMN) which can accommodate asymmetric, heavy-tailed and contaminated data better. For the variable selection problem, the penalized likelihood approach with a new combined penalty function which balances the SCAD and l2 penalty is proposed. The adjusted EM algorithm is presented to get parameter estimates of RMR-SSMN models at a faster convergence rate. As simulations show, our mixture models are more robust than general FMR models and the new combined penalty function outperforms SCAD for variable selection. Finally, the proposed methodology and algorithm are applied to a real data set and achieve reasonable results.

A Special Weight for Inverse Gaussian Mixing Distribution in Normal Variance Mean Mixture with Application

Normal Variance-Mean Mixture (NVMM) provides a general framework for deriving models with desirable properties for modelling financial market variables such as exchange rates, equity prices, and interest rates measured over short time intervals, i.e. daily or weekly. Such data sets are characterized by non-normality and are usually skewed, fat-tailed and exhibit excess kurtosis. The Generalised Hyperbolic distribution (GHD) introduced by Barndorff-Nielsen (1977) which act as Normal variance-mean mixtures with Generalised Inverse Gaussian (GIG) mixing distribution nest a number of special and limiting case distributions. The Normal Inverse Gaussian (NIG) distribution is obtained when the Inverse Gaussian is the mixing distribution, i.e., the index parameter of the GIG is . The NIG is very popular because of its analytical tractability. In the mixing mechanism, the mixing distribution characterizes the prior information of the random variable of the conditional distribution. Therefore, considering finite mixture models is one way of extending the work. The GIG is a three parameter distribution denoted by and nest several special and limiting cases. When , we have which is called an Inverse Gaussian (IG) distribution. When , , , we have , and distributions respectively. These distributions are related to and are called weighted inverse Gaussian distributions. In this work, we consider a finite mixture of and and show that the mixture is also a weighted Inverse Gaussian distribution and use it to construct a NVMM. Due to the complexity of the likelihood, direct maximization is difficult. An EM type algorithm is provided for the Maximum Likelihood estimation of the parameters of the proposed model. We adopt an iterative scheme which is not based on explicit solution to the normal equations. This subtle approach reduces the computational difficulty of solving the complicated quantities involved directly to designing an iterative scheme based on a representation of the normal equation. The algorithm is easily programmable and we obtained a monotonic convergence for the data sets used.

A Finite Mixture of Generalised Inverse Gaussian with Indexes -1/2 and -3/2 as Mixing Distribution for Normal Variance Mean Mixture with Application

Mixture models have become more popular in modelling compared to standard distributions. The mixing distributions play a role in capturing the variability of the random variable in the conditional distribution. Studies have lately focused on finite mixture models as mixing distributions in the mixing mechanism. In the present work, we consider a Normal Variance Mean mixture model. The mixing distribution is a finite mixture of two special cases of Generalised Inverse Gaussian distribution with indexes -1/2 and -3/2. The parameters of the mixed model are obtained via the Expectation-Maximization (EM) algorithm. The iterative scheme is based on a presentation of the normal equations. An application to some financial data has been done.

多种残差补偿的贝叶斯网络下的短期交通预测

为了解决道路车流量的数据生成条件时变场景下的交通预测问题,本文建立道路交通控制与交通流预测数据之间的联系,提出一种基于多种残差补偿的贝叶斯网络的短期交通预测方法。提取城市中大规模多路口主干道车道及车辆信息构造多个平行的贝叶斯网络,使用贝叶斯关系及期望最大化算法进行短期交通预测。再通过数据自相关残差补偿、车辆换道和多路口连通性的线性残差补偿提高了预测的精度,解决了传统研究对相邻路口和换道导致的误差等因素处理能力不足的问题。仿真结果表明:使用贝叶斯网络预测交通流,并基于车辆行为的残差进行精度补偿,可以更准确地预测复杂的交通演化场景的短期交通流。

基于FPGA的两阶段配电网拓扑实时辨识算法

对配电网拓扑进行准确的实时辨识是电力系统安全稳定运行的基础,但随着新能源的接入以及配电网规模不断增大,配电网拓扑结构的动态变化愈加频繁且难以辨识。然而,现有配电网拓扑辨识算法所使用的历史数据需要人工对其进行拓扑标注,且拓扑辨识时间长,难以实现配电网拓扑实时辨识。因此,文中提出了一种基于现场可编程逻辑门阵列(FPAG)的两阶段配电网拓扑结构实时辨识算法。该算法不需要预先给出配电网拓扑类别的数量,即可对已有历史数据进行相应的拓扑标注及分类,并且基于FPGA实现了对配电网拓扑的实时辨别。该算法分为2个阶段:第1阶段采用变分贝叶斯高斯混合模型,对已有历史数据进行相应的拓扑标注及分类;第2阶段采用麻雀搜索算法,使得支持向量机快速收敛得到最优参数,以实现对配电网拓扑结构的精准辨识。基于该算法,利用FPGA并行架构以及高速高密度特性建立了实时拓扑结构辨识平台。最后,通过算例分析验证了所提辨识方法的有效性和优越性。

一种基于高斯混合模型的改进EM算法研究

针对传统EM算法存在估计参数不具有最优性,以及在参数估计中需要人工参与等问题,提出一种基于高斯混合模型的改进EM算法。采用无人工参与的无监督思想,获取高斯混合模型对直方图拟合的最优参数组合。实验表明,该算法不仅能够快速地估计模型参量,而且能够给出最优参数,并在图像增强中使细节更明显,对比度更适中。

基于对数-主成分变换的EM算法用于遥感影像分类

提出对多光谱数据进行对数变换来凸显类型特征,然后进行主成分变换并根据主成分贡献率确定EM算法分类所需主成分数,消除方差协方差矩阵的奇异性,同时削弱噪声;对数变换后的第一主成分直方图充分反映类型信息,由此确定的初始类别标签作为多个主成分EM分类算法所需初始值,避开随机选初值的敏感问题。实验证明,所提出的计算方案分类精度优于普通EM方法和传统的K-means方法。

基于鲁棒高斯混合模型的加速EM算法研究

针对传统鲁棒高斯混合模型EM算法存在模型成分参数难以精确获取最优解以及收敛速度随样本数量的增加而快速降低等问题,提出了一种基于鲁棒高斯混合模型的加速EM算法。该算法采用隐含参量信息熵原理对高斯模型分量个数进行挑选,以及使用Aitken加速方法减少算法的迭代次数,当接近最优解时,EM步长的变化极为缓慢,这时使用Broyden对称秩1校正公式进行校正,使算法快速收敛,从而能够在很少的迭代次数内精确获取高斯混合模型的模型成分数。该算法通过与传统鲁棒EM算法和无监督的EM算法的聚类结果进行比较,实验证明该算法对初始值的设定并不敏感(成分数c无须预先设定),并且能够降低算法运算时间,提高聚类模型成分数(类簇)的正确率。

基于EM和GMM相结合的自适应灰度图像分割算法

提出一种阈值自适应、EM方法估计GMM参量的图像分割算法,能够根据图像的内容结合区域和边界两方面的信息自适应地选择阈值,精确地进行图像边界分割.算法首先提取图像的边界,然后根据边界的直方图计算图像的可分割性,由可分割性确定EM方法的阈值进行GMM分割,最后合并图像的近似区域.实验数据表明,相比其它图像分割算法,以及固定阈值的传统EM算法,本算法的分割结果更为准确.

基于快速EM算法的马尔可夫随机场模型运动目标自动分割

文章提出一种基于高斯马尔可夫随机场(GMRF)模型的运动目标自动分割算法。该算法采用高斯混合分布描述视频序列的差分图像,对标准Expectation-Maximization(EM)算法进行了改进,提出了快速EM算法,从不完整数据中估计出概率模型的参数。在此基础上建立马尔可夫随机场模型,构造系统能量函数。然后通过条件迭代模型(ICM)优化算法求解能量函数的最优解,得出标记场,提取出运动目标。实验结果证明,该算法对运动目标分割具有很好的分割效果。

一种基于贪心EM算法学习GMM的聚类算法

传统的聚类算法如k-means算法需要一些先验知识来确定初始参数,初始参数的选择通常会对聚类结果生产很大的影响。提出一种新的基于模型的聚类算法,通过优化给定的数据和数学模型之间的适应性发现数据对模型的最好匹配。由于高斯混合模型可以看作是一种“软分配聚类”方法,该算法结合一种贪心的EM算法来学习高斯混合模型(GMM),由贪心EM算法实现高斯混合模型结构和参数的自动学习,而不需要先验知识。这种聚类算法可以克服k-means等算法的缺点,实验结果表明该算法具有更好的聚类效果。