混响的混合高斯概率密度建模

混合高斯模型能够有效地拟合混响背景的一维概率密度分布。常用的混合高斯概率密度模型参数估计方法是EM迭代算法,但这种算法的主要缺点是估计精度过分依赖于初始值。而GreedyEM算法通过往混合模型中不断地加入高斯分量,能很好地解决这一问题。文章将多维图象处理中的GreedyEM算法加以合理简化,并给出模型自动定阶方法,从而成功应用于水声混响的一维混合高斯模型建模中。实验结果表明:应用新算法能从混响接收数据中准确拟合其概率密度曲线,并且能适应不同的数据长度,具有很好的通用性。     

混合高斯概率密度模型动态簇算法参数估计

混合高斯概率密度模型可以很好地拟合样本的概率密度。在各高斯分量概率密度互不重叠的条件下，使用动态簇算法可以快速而精确地估计出混合高斯概率密度模型参数。这是一种基于最小均方差原则的递推算法，在正向推导出各种可能簇边界后，再根据确定的最末边界值逆向推定各前导簇边界，从而得到混合高斯概率密度模型参数估计值。算法介绍之后，给出了两个拥有不同概率密度分布的仿真建模实例．最后总结分析了该算法的优劣，并简介了算法的推广．     

混合高斯概率密度模型参数的期望最大化估计

混合高斯模型是对非高斯数据进行概率密度拟合典型模型,其参数估计可以通过期望最大化(EM)迭代算法获得。多维混合高斯模型参数的EM估计因结构庞杂而难以求解,而对主动检测背景的统计特性拟合来说,一维的混合高斯模型一般即已足够。描述了该情形下的混合高斯模型及其参数估计问题之后,导出了一种工程实用的、简化的EM迭代算法,并给出了可计算机编程实现的算法流程图。然后详细探讨了对EM估计精度与速度有着重要影响的参数初始化问题,给出了三种可选择的初值设置方案:高速度方案、高精度方案和二者的折衷方案,并分析了它们各自的适用场合。最后,结合一组数值仿真实例,演示了EM迭代算法的良好的混合高斯模型参数估计性能。     

基于改进高斯混合模型的运动物体的图像检测

传统的高斯混合模型在RGB色彩空间只对孤立像素建模,检测结果不够准确,存在拖影现象,检测到的运动物体内部容易出现空洞.针对这些问题,本文提出了一种改进的高斯混合模型.该方法从更符合人眼视觉特性的HSV色彩空间对中心像素和周边像素构成的向量进行建模,改善了原算法的性能;利用彩色分割算法提取连通区域,充分地利用了运动物体的彩色信息,并基于Phong物体光照模型进行了阴影抑制,提高了传统高斯混合模型检测的准确性.实验结果表明,与传统高斯混合模型相比,本算法能更精确地检测出运动物体,对光照变化和阴影具有鲁棒性.     

基于时间规整网络的GMM说话人识别模型的初始化方法

1前言 对于与文本无关的说话人识别,一般采用混合高斯模型(Gaussian Mixture Model:GMM)[1,2]来进行识别,在训练GMM模型之前,模型的初始参数必须首先确定.初始化模型参数的有效方法是对训练数据进行分段,训练数据语音帧根据其特征分到M个不同的类中(M为混合数的个数),与初始的M个高斯分量相对应.每个类的均值和方差作为模型的初始化参数.     

基于高斯混合模型的非高斯随机振动幅值概率密度函数

针对非高斯振动信号的幅值概率密度函数难以用数学模型表述的问题,提出了基于高斯混合模型的非高斯概率密度函数表示方法。首先,基于时域样本信号得到非高斯振动信号的高阶矩估计值。其次,基于高斯随机过程偶次高阶矩之间的定量关系,结合二阶高斯混合模型建立方程组,求解得到混合模型中每个高斯分量的方差和权值。然后,将各高斯分量的权值和方差代入高斯混合模型,得到适用于对称非高斯振动信号的幅值概率密度函数。最后,通过仿真信号和实测振动信号,验证了该方法的有效性和适用性。     

基于混合偏正态数据下众数回归模型的变量选择

有限混合回归(Finite Mixture of Regression, FMR)模型的变量选择常常在统计建模中使用。目前关于FMR模型的研究主要集中在回归误差服从正态分布的情形，而这种假设不适用于研究非对称的数据。对于偏斜数据，众数的代表性优于均值。本文基于混合偏正态数据介绍了众数回归模型的变量选择方法，并证明了变量选择方法的相合性和参数估计的Oracle性质。为了估计模型的参数，提出了一种改进的EM (Expectation-Maximum)算法，通过模拟研究和实例分析进一步说明了所提出模型和变量选择方法的有效性。     

混合高斯参数估计的动态簇算法

混合高斯概率密度模型可以很好地拟合非高斯样本的概率密度。在各高斯分量概率密度互不重叠的条件下,使用动态簇算法可以快速而精确地估计出混合高斯概率密度模型参数。这是一种基于最小均方差原则的递推算法,在正向推导出各种可能的簇边界后,再根据确定的最末边界值逆向推定各前导簇边界,从而得到混合高斯概率密度模型参数估计值。描述模型及参数估计问题之后,动态簇算法被推导出来。然后深入探讨了该算法的实质及适用条件。最后结合数值仿真实例,分析了动态簇算法的估计性能。     

基于阴影消除和混合高斯模型的视频分割算法

针对固定场景监控中复杂背景、光照变化、阴影等影响视频分割的问题,提出了一种有效的混合高斯模型的自适应背景更新算法,各像素点根据其像素值出现的混乱程度采取不同个数的高斯分布描述,通过对背景模型的学习与更新、高斯分布生成准则等方面的改进和优化,采用基于形态学重构的阴影消除方法使得前景目标分割的性能得到了有效地提高。文中同时给出了光照突变检测及其背景更新方法。通过对各种实际场景的实验仿真表明,该算法能够快速准确地建立背景模型,准确分割前景目标,与其它算法比较具有更强的鲁棒性。     

基于阴影消除和混合高斯模型的视频分割算法

针对固定场景监控中复杂背景、光照变化、阴影等影响视频分割的问题,提出了一种有效的混合高斯模型的自适应背景更新算法,各像素点根据其像素值出现的混乱程度采取不同个数的高斯分布描述,通过对背景模型的学习与更新、高斯分布生成准则等方面的改进和优化,采用基于形态学重构的阴影消除方法使得前景目标分割的性能得到了有效地提高.文中同时给出了光照突变检测及其背景更新方法.通过对各种实际场景的实验仿真表明,该算法能够快速准确地建立背景模型,准确分割前景目标,与其它算法比较具有更强的鲁棒性.     

Online variational learning of finite inverted Beta-Liouville mixture model for biomedical analysis

Image segmentation is widely applied for biomedical image analysis. However, segmentation of medical images is challenging due to many image modalities, such as, CT, X-ray, MRI, microscopy among others. An additional challenge to this is the high variability, inconsistent regions with missing edges, absence of texture contrast, and high noise in the background of biomedical images. Thus, many segmentation approaches have been investigated to address these issues and to transform medical images into meaningful information. During the past decade, finite mixture models have been revealed to be one of the most flexible and popular approaches in data clustering. In this article, we propose a statistical framework for online variational learning of finite inverted Beta-Liouville mixture model for clustering medical images. The online variational learning framework is used to estimate the parameters and the number of mixture components simultaneously, thus decreasing the computational complexity of the model. To this end, we evaluated our proposed algorithm on five different biomedical image data sets including optic disc detection and localization in diabetic retinopathy, digital imaging in melanoma lesion detection and segmentation, brain tumor detection, colon cancer detection and computer aid detection (CAD) of Malaria. Furthermore, we compared the proposed algorithm with three other popular algorithms. In our results, we analyze that the proposed online variational learning of finite IBL mixture model algorithm performs accurately on multiple modalities of medical images. It detects the disease patterns with high confidence. Computational and statistical approaches like the one presented in this article hold a significant impact on medical image analysis and interpretation in both clinical applications and scientific research. We believe that the proposed algorithm has the capacity to address multi modal biomedical image data sets and can be further applied by researchers to analyze correct disease patterns.     

A copula-based Gaussian mixture closure method for stochastic response of nonlinear dynamic systems

Gaussian closure method is commonly used in the analysis of nonlinear stochastic systems. However, Gaussian closure may lead to unacceptable errors when system response is very much different from being Gaussian, and accuracy of the method decreases as the nonlinearity of the system increases. The need for better accuracy in strongly non-linear problems has caused the development of non-Gaussian closure schemes. In this paper, we develop a new copula-based Gaussian mixture closure method for randomly excited nonlinear systems. Our method relies on the assumption of marginal PDF of response in terms of finite Gaussian mixture model, and the derivation of joint PDF with aid of dependence modeling of Gaussian copula. By substituting the non-Gaussian PDF representation into moment equations of nonlinear system, we further develop an optimization-based closure scheme for the solution of the unknown parameters in joint PDF. In this way, PDF and thus, moments of response of highly nonlinear system can be described in a more flexible and robust way. Effectiveness of the new closure method is demonstrated by a nonlinear and a Duffing oscillator that are subjected to Gaussian white noise. The results are compared with the Gaussian closure and exact solution. It has been shown that Gaussian closure is a special case of the new closure method, and accuracy of Gaussian closure is the lower bound of that of the new closure method.     

混合高斯参数估计的两种EM算法比较

混合高斯模型是一种典型的非高斯概率密度模型,获得广泛应用。其参数的优效估计可以通过最大似然方法获得,但最大似然估计往往因其非线性而难以实现,故期望最大化(Expectation-Maximization,EM)迭代算法成为一种常用的替代方法。常规EM算法性能受迭代初值设置影响大,且不能对模型阶数做出估计。一种名为贪婪EM的改进算法可以克服这两个缺点,获得更为准确的模型参数估计,但其运算量一般会远大于前者。本文对这两种EM算法进行综合研究,深入挖掘两者之间的关系,并基于相同的数值仿真实例,直观地演示比较两者的性能差异。     

Finite mixture modeling for vehicle crash data with application to hotspot identification

The application of finite mixture regression models has recently gained an interest from highway safety researchers because of its considerable potential for addressing unobserved heterogeneity. Finite mixture models assume that the observations of a sample arise from two or more unobserved components with unknown proportions. Both fixed and varying weight parameter models have been shown to be useful for explaining the heterogeneity and the nature of the dispersion in crash data. Given the superior performance of the finite mixture model, this study, using observed and simulated data, investigated the relative performance of the finite mixture model and the traditional negative binomial (NB) model in terms of hotspot identification. For the observed data, rural multilane segment crash data for divided highways in California and Texas were used. The results showed that the difference measured by the percentage deviation in ranking orders was relatively small for this dataset. Nevertheless, the ranking results from the finite mixture model were considered more reliable than the NB model because of the better model specification. This finding was also supported by the simulation study which produced a high number of false positives and negatives when a mis-specified model was used for hotspot identification. Regarding an optimal threshold value for identifying hotspots, another simulation analysis indicated that there is a discrepancy between false discovery (increasing) and false negative rates (decreasing). Since the costs associated with false positives and false negatives are different, it is suggested that the selected optimal threshold value should be decided by considering the trade-offs between these two costs so that unnecessary expenses are minimized.     

A variable‐selection control chart via penalized likelihood and Gaussian mixture model for multimodal and high‐dimensional processes

With the development of the sensor network and manufacturing technology, multivariate processes face a new challenge of high‐dimensional data. However, traditional statistical methods based on small‐ or medium‐sized samples such as T² monitoring statistics may not be suitable because of the “curse of dimensionality” problem. To overcome this shortcoming, some control charts based on the variable‐selection (VS) algorithms using penalized likelihood have been suggested for process monitoring and fault diagnosis. Although there has been much effort to improve VS‐based control charts, there is usually a common distributional assumption that in‐control observations should follow a single multivariate Gaussian distribution. However, in current manufacturing processes, processes can have multimodal properties. To handle the high‐dimensionality and multimodality, in this study, a VS‐based control chart with a Gaussian mixture model (GMM) is proposed. We extend the VS‐based control chart framework to the process with multimodal distributions, so that the high‐dimensionality and multimodal information in the process can be better considered.     

基于遗传算法和有限混合分布的应力谱多模态建模

该文提出了一种基于遗传算法(genetic algorithm, GA)的有限混合分布参数估计方法, 应用该方法对青马大桥典型焊接节点的应力谱进行多模态建模。首先, 采用小波变换消除原始应变监测数据中的温度影响, 利用雨流计数法将应变时程曲线转化为日应力谱, 考虑到交通荷载(包括汽车荷载和火车荷载)和台风的影响, 建立标准日应力谱。然后, 采用三种不同的有限混合分布函数(有限混合正态分布函数、有限混合对数正态分布函数和有限混合威布尔分布函数)以及基于遗传算法的混合参数估计方法对应力幅进行多模态建模, 根据赤池信息准则(Akaike’s information criterion, AIC)确定最佳的有限混合模型。最后, 采用双变量有限混合分布和基于遗传算法的混合参数估计方法建立了应力幅和平均应力二维随机变量联合概率密度函数。结果表明, 该文提出的基于遗传算法的有限混合分布参数估计方法可以有效应用于二维随机变量的概率建模。     

基于多模型结合优化的非结构化道路检测算法

非结构化道路检测一直是道路检测算法中的难点．提出一种基于彩色混合高斯模型与抛物线模型相结合的优化的非结构化道路检测算法．首先采用中值滤波和二次采样法将待处理彩色图像由高分辨率变为低分辨率图像, 并对图像进行光照补偿;然后建立基于优化聚类中心的K means算法的混合高斯模型,通过最小二乘法求解左右道路抛物线模型参数;最后完成对道路边界线的拟合,实现其提取．实验结果表明,该算法对光照不均、阴影等影响的图像处理具有较强的抗干扰性,提高了运算速度,具有一定的鲁棒性和实时性．