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Gaussian-input Gaussian mixture model for representing density maps and atomic models

JOURNAL OF STRUCTURAL BIOLOGY 2018年第1期203卷 1-16页

作者： Kawabata, Takeshi Osaka Univ Inst Prot Res 3-2 Yamadaoka Suita Osaka 5650871 Japan

A new Gaussian mixture model (GMM) has been developed for better representations of both atomic models and electron microscopy 3D density maps. The standard GMM algorithm employs an EM algorithm to determine the parameters. It accepted a set of 3D points with weights, corresponding to voxel or atomic centers. Although the standard algorithm worked reasonably well;however, it had three problems. First, it ignored the size (voxel width or atomic radius) of the input, and thus it could lead to a GMM with a smaller spread than the input. Second, the algorithm had a singularity problem, as it sometimes stopped the iterative procedure due to a Gaussian function with almost zero variance. Third, a map with a large number of voxels required a long computation time for conversion to a GMM. To solve these problems, we have introduced a Gaussian-input GMM algorithm, which considers the input atoms or voxels as a set of Gaussian functions. The standard EM algorithm of GMM was extended to optimize the new GMM. The new GMM has identical radius of gyration to the input, and does not suddenly stop due to the singularity problem. For fast computation, we have introduced a downsampled Gaussian functions (DSG) by merging neighboring voxels into an anisotropic Gaussian function. It provides a GMM with thousands of Gaussian functions in a short computation time. We also have introduced a DSG-input GMM: the Gaussian-input GMM with the DSG as the input. This new algorithm is much faster than the standard algorithm.

关键词： Electron microscopy Fitting Superposition Atomic model Gaussian mixture model expectation maximization algorithm

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Prediction of Slope Stability using Naive Bayes Classifier

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KSCE JOURNAL OF CIVIL ENGINEERING 2018年第3期22卷 941-950页

作者： Feng, Xianda Li, Shuchen Yuan, Chao Zeng, Peng Sun, Yang Univ Jinan Sch Civil Engn & Architecture Jinan Shandong Peoples R China Shandong Univ Geotech Struct Engn Res Ctr Jinan Shandong Peoples R China Univ Grenoble Alpes Lab 3SR Grenoble France Chengdu Univ Technol State Key Lab Geohazard Prevent & Geoenvironm Pro Chengdu Sichuan Peoples R China

Slope stability prediction is of primary concern in identifying terrain that is susceptible to landslides and mitigating the damages caused by landslides. In this study, a Naive Bayes Classifier (NBC) was employed to predict slope stability for a slope subjected to circular failures, based on six input factors: slope height (H), slope angle (alpha), cohesion (c), friction angle (phi), unit weight (gamma), and pore pressure ratio (r (u) ). An expectation maximization algorithm was used to perform parameter learning for the NBC with an incomplete data set of 69 slope cases. The model validation with 13 new cases shows that, when compared to the existing empirical approach, the proposed NBC model yields better performance in terms of both accuracy and applicability (i.e., the NBC allows us to determine the probability of slope stability based on any subset of the six input factors).

关键词： slope stability naive bayes classifier incomplete data expectation maximization algorithm circular failures

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Mixed Gaussian Models for Modeling Fluctuation Process Characteristics of Photovoltaic Outputs

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FRONTIERS IN ENERGY RESEARCH 2019年 7卷

作者： Wang, Zhenhao Kang, Jia Cheng, Long Pei, Zheyi Dong, Cun Liang, Zhifeng Northeast Elect Power Univ Sch Elect Engn Jilin Jilin Peoples R China Natl Elect Power Dispatching & Commun Ctr Beijing Peoples R China

In order to model fluctuation process characteristics of photovoltaic (PV) outputs, this paper proposes a novel mixed Gaussian model with the expectation maximization (EM) algorithm. Firstly, random components of PV outputs are obtained through computing the difference between the measured data of PV output and its theoretical outputs. Secondly, the EM algorithm is used to determine the weight of different Gaussian distribution functions. Finally, the mixed Gaussian model is obtained by linearly superimposing these Gaussian functions with the weight. Based on the simulation results on the measured data in Xichang City, China, the effectiveness of the proposed model is verified. Furthermore, this model has proven to be significantly better than other traditional models including t location-scale (TLS) distribution model.

关键词： PV output modeling fluctuation characteristics probability density distribution expectation maximization algorithm mixed Gaussian models

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A Note on Parameters Estimation for Nonlinear Wiener Processes With Measurement Errors

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IEEE ACCESS 2019年 7卷 176756-176766页

作者： Tang, Shengjin Yu, Chuanqiang Sun, Xiaoyan Fan, Hongdong Si, Xiaosheng High Tech Inst Xian Xian 710025 Peoples R China

The nonlinear Wiener process has been widely used as a model for the degradation process. This note concerns parameters estimation of nonlinear Wiener processes with measurement errors (WPME) by the maximum likelihood estimation method. Firstly, we prove a rule that the estimated results based on the sample likelihood function developed through observations at each point are equal to the results from the first differences of the observations. This rule indicates that for reducing computation complexity the first differences of the observations may develop the sample likelihood function. Then we present a simple method to calculate the determinant and the inverse matrix of the covariance matrix of the WPME. This simple method could avoid the overflow error when calculating the determinant of the covariance matrix and the case that the inverse matrix is close to be singular, which could result in wrong estimation results. Secondly, we highlight the unit-specific assumption, which has a significant impact on parameters estimation but has been neglected in many papers. Then, we propose a modified expectation maximization algorithm for parameters estimation with random effects. Finally, to demonstrate the application and superiority of the proposed method, we provide a numerical example and a case study with comparison to several representative methods in the literature.

关键词： Degradation model maximum likelihood estimation Wiener process measurement error nonlinear expectation maximization algorithm

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expectation maximization estimates of the offspring probabilities in a class of multitype branching processes with binary family trees

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MATHEMATICAL POPULATION STUDIES 2017年第4期24卷 246-256页

作者： Daskalova, Nina Sofia Univ St Kliment Ohridski Fac Math & Informat 5 James Bourchier Blvd Sofia 1164 Bulgaria

When proliferating cells are counted in several independent colonies at some time points, the maximum likelihood estimates of the parameters of the multitype branching process are obtained trough an expectation maximization algorithm. In the case of an offspring distribution governed by a Markov branching process with binary family trees, this method, relying then on a partial knowledge of the tree, yields the same estimates as those computed with the complete knowledge of the tree.

关键词： cell proliferation expectation maximization algorithm maximum likelihood estimation multitype branching processes offspring distribution

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Lifetime Estimation for Multi-Phase Deteriorating Process with Random Abrupt Jumps

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SENSORS 2019年第6期19卷 1472.-1472.页

作者： Zhang, Jianxun Si, Xiaosheng Du, Dangbo Hu, Chen Hu, Changhua Xian Res Inst High Tech Dept Automat Xian 710025 Shaanxi Peoples R China Xi An Jiao Tong Univ Key Lab Educ Minist Modern Design & Rotor Bearing Syst Xian 710049 Shaanxi Peoples R China

Owing to operating condition changing, physical mutation, and sudden shocks, degradation trajectories usually exhibit multi-phase features, and the abrupt jump often appears at the changing time, which makes the traditional methods of lifetime estimation unavailable. In this paper, we mainly focus on how to estimate the lifetime of the multi-phase degradation process with abrupt jumps at the change points under the concept of the first passage time (FPT). Firstly, a multi-phase degradation model with jumps based on the Wiener process is formulated to describe the multi-phase degradation pattern. Then, we attain the lifetime's closed-form expression for the two-phase model with fixed jump relying on the distribution of the degradation state at the change point. Furthermore, we continue to investigate the lifetime estimation of the degradation process with random effect caused by unit-to-unit variability and the multi-phase degradation process. We extend the results of the two-phase case with fixed parameters to these two cases. For better implementation, a model identification method with off-line and on-line parts based on expectation maximization (EM) algorithm and Bayesian rule is proposed. Finally, a numerical case study and a practical example of gyro are provided for illustration.

关键词： life prognostics reliability multi-phase degradation expectation maximization algorithm random jump

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Label Fusion Based Brain MR Image Segmentation via a Latent Selective Model 9

Label Fusion Based Brain MR Image Segmentation via a Latent ...

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9th International Conference on Graphic and Image Processing (ICGIP)

作者： Liu, Gang Guo, Xiantang Zhu, Kai Liao, Hengxu Shanghai Univ Elect Power Sch Automat Engn Shanghai 200090 Peoples R China State Grid Corp China Jinhua Power Supply Co Hangzhou 321000 Zhejiang Peoples R China

ISBN: (数字)9781510617421

ISBN: (纸本)9781510617421

Multi-atlas segmentation is an effective approach and increasingly popular for automatically labeling objects of interest in medical images. Recently, segmentation methods based on generative models and patch-based techniques have become the two principal branches of label fusion. However, these generative models and patch-based techniques are only loosely related, and the requirement for higher accuracy, faster segmentation, and robustness is always a great challenge. In this paper, we propose novel algorithm that combines the two branches using global weighted fusion strategy based on a patch latent selective model to perform segmentation of specific anatomical structures for human brain magnetic resonance (MR) images. In establishing this probabilistic model of label fusion between the target patch and patch dictionary, we explored the Kronecker delta function in the label prior, which is more suitable than other models, and designed a latent selective model as a membership prior to determine from which training patch the intensity and label of the target patch are generated at each spatial location. Because the image background is an equally important factor for segmentation, it is analyzed in label fusion procedure and we regard it as an isolated label to keep the same privilege between the background and the regions of interest. During label fusion with the global weighted fusion scheme, we use Bayesian inference and expectation maximization algorithm to estimate the labels of the target scan to produce the segmentation map. Experimental results indicate that the proposed algorithm is more accurate and robust than the other segmentation methods.

关键词： Multi-atlas segmentation latent selective model patch-based segmentation global weighted fusion image background analysis bayesian inference expectation maximization algorithm

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Outlier Detection algorithm Based on Gaussian Mixture Model

Outlier Detection Algorithm Based on Gaussian Mixture Model

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IEEE International Conference on Power, Intelligent Computing and Systems

作者： Wenbo Liu Delong Cui Zhiping Peng Jihai Zhong Faulty of Computer Science Guangdong University of Technology Department of Computer and Electronic Information Guangdong University of Petrochemical Technology

ISBN: (纸本)9781728137216

Outlier detection is an important aspect in the field of data mining. In order to solve the problem of outlier detection in high-dimensional datasets, an outlier detection algorithm based on Gaussian mixture model is proposed. First of all, for the data set to be tested, the global optimization expectation maximization algorithm is used to fit a Gaussian mixture model, and then the three-time standard deviation principle is introduced on each Gaussian component, the outlier is the data point outside the range of the mean deviation of the mean value of three times the standard deviation. Through the experiments on the simulation dataset and the real data set, the effectiveness of the algorithm on the outlier detection of high-dimensional data sets is verified.

关键词： Data mining Outlier detection Gaussian mixture model expectation maximization algorithm The principle of three times standard deviation expectation-maximisation algorithm data mining Mixture models outliers Detection algorithms Dataset Mean deviation mean value

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Identification of ARX System Based on Shifted Asymmetric Laplace Distribution

Identification of ARX System Based on Shifted Asymmetric Lap...

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第三十八届中国控制会议

作者： Miao Yu Tianyi Zhang Xianqiang Yang Research Institute of Intelligent Control and System Harbin Institute of Technology

The identification of AutoRegressive eXogenous(ARX) model by outliers is addressed in this paper. Shifted(noncentralized) asymmetric Laplace(SAL) distribution and expectation maximization(EM) algorithm are employed to estimate the unknown model parameters. Outliers are common in the signal acquisition process and have a serious impact on data-driven modeling method. In this paper, the probability method is used to solve the problem of outliers. When the noise parameter is regarded as a prior exponential distribution, the model output obeys the SAL distribution which is robust to outliers. The known statistical properties of SAL distribution are applied to calculate the M-step in the EM algorithm and get the iterative parametric formula. The accuracy of the proposed algorithm is verified by a numerical simulation example.

关键词： shifted asymmetric Laplace distribution expectation maximization algorithm autoRegressive eXogenous model

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Quasi Maximum Likelihood Estimation and Inference of Large Approximate Dynamic Factor Models via the EM algorithm

arXiv

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arXiv 2019年

作者： Barigozzi, Matteo Luciani, Matteo Università di Bologna Italy Federal Reserve Board United States

We study estimation of large Dynamic Factor models implemented through the expectation maximization (EM) algorithm, jointly with the Kalman smoother. We prove that as both the cross-sectional dimension, n, and the sample size, T, diverge to infinity: (i) the estimated loadings are √T-consistent, asymptotically normal and equivalent to their Quasi Maximum Likelihood estimates;(ii) the estimated factors are √nconsistent, asymptotically normal and equivalent to their Weighted Least Squares estimates. Moreover, the estimated loadings are asymptotically as efficient as those obtained by Principal Components analysis, while the estimated factors are more efficient if the idiosyncratic covariance is sparse enough. © 2019, CC BY.

关键词： expectation maximization algorithm

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