基于EM算法的ACPH分布数据拟合方法

ACPH分布继承了PH分布具有良好特性的特点,对其进行数据拟合的难度比PH大大降低。针对ACPH分布缺乏数值稳定拟合算法的问题,提出采用EM算法解决该问题,给出了ACPH分布数据拟合EM算法的理论推导,并通过3个拟合实例验证了算法的有效性。     

连续PH 分布数据拟合的确定性退火BP算法

针对目前连续PH 分布数据拟合EM(Expectation-Maximization)算法存在的初值敏感问题,提出运用确定性退火EM 算法进行连续PH 分布数据拟合,给出了详细的理论推导,并通过两个拟合实例与标准EM 算法进行了对比.对比结果表明所提出的方法可以有效地避免初值选择的不同对EM 算法结果的影响,减小陷入局部最优的可能性,能得到比标准EM算法更好的结果.     

连续PH分布数据拟合的确定性退火EM算法

针对目前连续PH分布数据拟合EM(Expectation-Maximization)算法存在的初值敏感问题,提出运用确定性退火EM算法进行连续PH分布数据拟合,给出了详细的理论推导,并通过两个拟合实例与标准EM算法进行了对比.对比结果表明所提出的方法可以有效地避免初值选择的不同对EM算法结果的影响,减小陷入局部最优的可能性,能得到比标准EM算法更好的结果.     

基于EM算法的高斯混合模型参数估计

讨论在一般的混合分布条件下,用EM算法,在最小熵原理的优化准则下的数据拟合问题。简单推导有限混合高斯分布的EM算法,并针对其收敛速度慢的缺点设计一种有效的选取参数初始值的方法。实验结果表明,该方法有助于EM算法以较快的速度在参数真值附近收敛。     

基于EM算法的高斯混合模型参数估计

讨论在一般的混合分布条件下,用EM算法,在最小熵原理的优化准则下的数据拟合问题。简单推导有限混合高斯分布的EM算法．并针对其收敛速度慢的缺点设计一种有效的选取参数初始值的方法。实验结果表明,该方法有助于EM算法以较快的速度在参数真值附近收敛。     

改进的EM算法——A-ECM算法

EM算法应用广泛于缺失数据的模型参数估计,但该算法收敛速度缓慢。本文提出了A-ECM算法,即结合Aitken加速和ECM算法的思想,并通过仿真实验分析,结果表明A-ECM算法既实现了对EM算法的分阶段加速,也达到了稳定收敛的目的。     

基于[t]分布混合模型的半监督网络流分类方法

针对传统高斯分布容易受到数据样本边缘值和离群点噪声的影响,改用t分布替代原有的高斯混合模型,并使用期望最大化（Expectation Maximization,EM）算法对网络流数据样本进行t分布混合模型的建模。为降低EM算法的迭代次数,对t分布混合模型进行了改进,用理论和实验验证了算法的有效性,并对网络多媒体业务流进行了分类研究。实验表明,提出的算法有较高的分类准确率,拟合的模型要优于传统的K-Means算法和传统的高斯混合模型的EM算法。     

数据缺失下学习贝叶斯网的一种混合启发方法

建立了具有数据缺失训练集下学习贝叶斯网的一种混合启发方法:SGS-EM-PACOB算法.它基于打分-搜索方法,利用GS和EM数据补全策略分别得到学习所需要的统计因子,并将两者联合起来作为PACOB算法的启发因子.实验证明,SGS-EM-PACOB算法充分保留GS和EM两者的优点,促使算法能够平稳地收敛到理想结果.相对于只具有单一数据补全策略的算法,该算法不仅在度量数据拟合程度的Logloss值上保持稳定,而且在学习到的贝叶斯网络结构上也有改进.     

面向大规模数据集的贝叶斯网络参数学习算法

贝叶斯网络的学习可以分为结构学习和参数学习。期望最大化（EM）算法通常用于不完整数据的参数学习，但是由于EM算法计算相对复杂，存在收敛速度慢和容易局部最大化等问题，传统的EM算法难于处理大规模数据集。研究了EM算法的主要问题，采用划分数据块的方法将大规模数据集划分为小的样本集来处理，降低了EM算法的计算量，同时也提高了计算精度。实验证明，该改进的EM算法具有较高的性能。     

一种适合于大数据集处理的混合EM算法

EM算法的计算强度较大，且当数据集较大时，计算效率较低。为此，提出了基于部分E步的混合EM算法，降低了算法的计算强度，提高了算法对数据集大小的适应能力，并且保持了EM算法的收敛特性。最后通过将算法应用于大的数据集，验证了该算法能减少计算强度。     

Unsupervised learning of finite mixture models

This paper proposes an unsupervised algorithm for learning a finite mixture model from multivariate data. The adjective "unsupervised" is justified by two properties of the algorithm: 1) it is capable of selecting the number of components and 2) unlike the standard expectation-maximization (EM) algorithm, it does not require careful initialization. The proposed method also avoids another drawback of EM for mixture fitting: the possibility of convergence toward a singular estimate at the boundary of the parameter space. The novelty of our approach is that we do not use a model selection criterion to choose one among a set of preestimated candidate models; instead, we seamlessly integrate estimation and model selection in a single algorithm. Our technique can be applied to any type of parametric mixture model for which it is possible to write an EM algorithm; in this paper, we illustrate it with experiments involving Gaussian mixtures. These experiments testify for the good performance of our approach     

A refined EM algorithm for PH distributions

This paper proposes an improved computation method of maximum likelihood (ML) estimation for phase-type (PH) distributions with a number of phases. We focus on the EM (expectation-maximization) algorithm proposed by Asmussen et al. [27] and refine it in terms of time complexity. Two ideas behind our method are a uniformization-based procedure for computing a convolution integral of the matrix exponential and an improvement of the forward-backward algorithm using time intervals. Compared with the differential-equation-based EM algorithm discussed in Asmussen et al. [27], our approach succeeds in the reduction of computation time for the PH fitting with a moderate to large number of phases. In addition to the improvement of time complexity, this paper discusses how to estimate the canonical form by applying the EM algorithm. In numerical experiments, we examine computation times of the proposed and differential-equation-based EM algorithms. Furthermore, the proposed EM algorithm is also compared with the existing PH fitting methods in terms of computation time and fitting accuracy.     

Comparative Analysis on Convergence Rates of The EM Algorithm and Its Two Modifications for Gaussian Mixtures

For Gaussian mixture, a comparative analysis has been made on the convergence rate by the Expectation-Maximization (EM) algorithm and its two types of modifications. One is a variant of the EM algorithm (denoted by VEM) which uses the old value of mean vectors instead of the latest updated one in the current updating of the covariance matrices. The other is obtained by adding a momentum term in the EM updating equation, called the Momentum EM algorithm (MEM). Their up-bound convergence rates have been obtained, including an extension and a modification of those given in Xu & Jordan (1996). It has been shown that the EM algorithm and VEM are equivalent in their local convergence and rates, and that the MEM can speed up the convergence of the EM algorithm if a suitable amount of momentum is added. Moreover, a theoretical guide on how to add momentum is proposed, and a possible approach for further speeding up the convergence is suggested.     

A fitting method with generalized Erlang distributions

We present a fitting technique that fits trace data into a generalized Erlang distribution class using an EM method. A generalized Erlang (GEr) distribution can be made by convolution of the third order ME distributions similar to the formulation of an Erlang distribution with exponential distributions. We give a sufficient condition for the representation to make a probability density function and we implement a fitting algorithm into a GEr distribution set by solving a nonlinear optimization problem with the EM algorithm. The effectiveness of the proposed fitting algorithm is presented by applying fitting methods to sets of synthetic data and measurement data. We present comparative numerical simulation results of our approach and other methods.     

步长加速法优化B样条参数的离散数据点拟合

采用迭代法拟合离散数据点时,数据点的参数化会同时影响逼近的效果和逼近的速度,为此,提出一种通过迭代调整优化控制顶点和数据点参数的方法,其收敛速度较快且拟合得到曲线更贴合控制点.首先,选取初始控制顶点,通过自适应的BFGS方法优化控制顶点得到拟合曲线;其次,保持控制顶点不变,利用步长加速法优化数据点对应的参数;最后,利用新参数值重新优化控制顶点并得到新的拟合曲线.数值实例表明,所提方法在迭代前期步骤中,收敛速度快于现有的基于控制顶点迭代法,且优化后的曲线更加逼近离散的数据点,拟合误差更小.     

嵌入单纯形法的混合类电磁机制算法

针对类电磁机制算法存在局部搜索能力差的问题,提出一种基于单纯形法的混合类电磁机制算法。该混合算法首先利用反向学习策略构造初始种群以保证粒子均匀分布在搜索空间中。利用单纯形法对最优粒子进行局部搜索,增强了算法在最优点附近的局部搜索能力,以加快算法的收敛速度。四个基准测试函数的仿真实验结果表明,该算法具有更好的寻优性能。     

一种新算法在ECT图像重建中的应用研究

为了解决大残量、小残量或零残量问题和普通迭代方法收敛速度慢的问题,引入NL2SOL优化算法,并与GaussNewton法相结合,提出了一种多项式加速的正则化迭代电容层析成像算法.在介绍12电极电容层析成像系统基本原理的基础上,给出了该算法的数学模型,并利用谱分析对该算法的收敛性进行了证明.仿真实验验证了该算法满足收敛条件且重建图像误差小,在电容层析成像应用中具有可行性.     

Serial and parallel implementations of model-based clustering via parsimonious Gaussian mixture models

Model-based clustering using a family of Gaussian mixture models, with parsimonious factor analysis like covariance structure, is described and an efficient algorithm for its implementation is presented. This algorithm uses the alternating expectation-conditional maximization (AECM) variant of the expectation-maximization (EM) algorithm. Two central issues around the implementation of this family of models, namely model selection and convergence criteria, are discussed. These central issues also have implications for other model-based clustering techniques and for the implementation of techniques like the EM algorithm, in general. The Bayesian information criterion (BIC) is used for model selection and Aitken’s acceleration, which is shown to outperform the lack of progress criterion, is used to determine convergence. A brief introduction to parallel computing is then given before the implementation of this algorithm in parallel is facilitated within the master-slave paradigm. A simulation study is then carried out to confirm the effectiveness of this parallelization. The resulting software is applied to two datasets to demonstrate its effectiveness when compared to existing software.