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Dynamic mode decomposition based on expectation-maximization algorithm for simultaneous system identification and denoising

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MECHANICAL SYSTEMS AND SIGNAL PROCESSING 2025年 223卷

作者： Iwasaki, Yuto Sasaki, Yasuo Nagata, Takayuki Kaneko, Sayumi Nonomura, Taku Tohoku Univ Grad Sch Engn Dept Aerosp Engn 6-6-01 Aramaki Aza AobaAoba Ku Sendai Miyagi 9808579 Japan

The present study proposes a novel dynamic mode decomposition (DMD) that can simultaneously estimate the reduced-order model, the original signal, and the system/observation noise model only from the noisy data. An expectation-maximization (EM)-algorithm DMD (EMDMD) combines DMD and the parameter adjustment of the linear dynamical system (LDS) based on the EM algorithm. The initial parameters based on the linearity of the reduced-order data are set by using DMD. Subsequently, the log-likelihood of the complete data is maximized by adjusting the LDS parameters while separating the noise. The proposed algorithm is applied to the benchmark data of the short-fat and tall-skinny data matrices with different noise and the time-series velocity fields of the flow around a circular cylinder and the separated flow around an airfoil. The performance of EMDMD in terms of system identification and noise separation from the noisy data is evaluated, and the EMDMD shows the highest system identification and noise separation performance in all data.

关键词： Dynamic mode decomposition expectation-maximization algorithm Linear dynamical system System identification Denoising

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expectation-maximization algorithm for bilinear state-space models with time-varying delays under non-Gaussian noise

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INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING 2023年第10期37卷 2706-2724页

作者： Wang, Xinyue Ma, Junxia Xiong, Weili Jiangnan Univ Sch Internet Things Engn Minist Educ Key Lab Adv Proc Control Light Ind Wuxi 214122 Peoples R China

In this paper, the parameter identification of bilinear state-space model (SSM) in the presence of random outliers and time-varying delays is investigated. Under the basis of the observable canonical form of the bilinear model, the system output can be written as a regressive form, and a bilinear state observer is applied to estimate the unknown states. To eliminate the influence of outliers and time-varying delays on parameter estimation, we employ the Student's t$$ t $$ distribution to deal with the measurement noise and use a first-order Markov chain to model the delays. In the framework of expectation-maximization (EM) algorithm, the unknown parameters, delays, noise variance, states and transition probability matrix can be estimated iteratively. A numerical simulation and a continuous stirred tank reactor (CSTR) process demonstrate that the proposed algorithm has good immunity against outliers and time-varying delays and offers good estimation accuracy for the bilinear SSM.

关键词： bilinear state-space model expectation-maximization algorithm outliers parameter identification time-varying delays

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expectation-maximization algorithm for finite mixture of α-stable distributions

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NEUROCOMPUTING 2020年 413卷 210-216页

作者： Castillo-Barnes, D. Martinez-Murcia, F. J. Ramirez, J. Gorriz, J. M. Salas-Gonzalez, D. Univ Granada Dept Signal Theory Networking & Commun Granada Spain Univ Malaga Dept Commun Engn Malaga Spain

A Gaussian Mixture Model (GMM) is a parametric probability density function built as a weighted sum of Gaussian distributions. Gaussian mixtures are used for modelling the probability distribution in many fields of research nowadays. Nevertheless, in many real applications, the components are skewed or heavy tailed. For that reason, it is useful to model the mixtures as components with alpha-stable distribution. In this work, we present a mixture of skewed alpha-stable model where the parameters are estimated using the expectation-maximization algorithm. As the Gaussian distribution is a particular limiting case of alpha-stable distribution, the proposed model is a generalization of the widely used GMM. The proposed algorithm is much faster than the parameter estimation of the alpha-stable mixture model using a Bayesian approach and Markov chain Monte Carlo methods. Therefore, it is more suitable to be used for large vector observations. (C) 2020 Elsevier B.V. All rights reserved.

关键词： Alpha-stable mixture model Alpha-stable distribution expectation-maximization algorithm

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expectation-maximization algorithm with Local Adaptivity

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SIAM JOURNAL ON IMAGING SCIENCES 2009年第3期2卷 834-857页

作者： Leung, Shingyu Liang, Gang Solna, Knut Zhao, Hongkai Hong Kong Univ Sci & Technol Dept Math Hong Kong Hong Kong Peoples R China Univ Calif Irvine Dept Stat Irvine CA 92697 USA Univ Calif Irvine Dept Math Irvine CA 92697 USA

We develop an expectation-maximization algorithm with local adaptivity for image segmentation and classification. The key idea of our approach is to combine global statistics extracted from the Gaussian mixture model or other proper statistical models with local statistics and geometrical information, such as local probability distribution, orientation, and anisotropy. The combined information is used to design an adaptive local classification strategy that improves the robustness of the algorithm and also keeps fine features in the image. The proposed methodology is flexible and can be easily generalized to deal with other inferred information/quantities and statistical methods/models.

关键词： expectation-maximization algorithm Gaussian mixture model posterior probability local adaptivity image segmentation

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expectation-maximization algorithm for Evaluation of Wind Direction Characteristics 15

Expectation-Maximization Algorithm for Evaluation of Wind Di...

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15th IEEE International Conference on Environment and Electrical Engineering (EEEIC)

作者： Marek, Jaroslav Heckenbergerova, Jana Univ Pardubice Dept Math & Phys Elect Engn & Informat Pardubice Czech Republic

ISBN: (纸本)9781479979929

Directional statistical distributions can be used to model a wide range of industrial and phenomena. Finite mixtures of circular normal von Mises (MvM) distributions have been used to represent directional data from various domains including energy industry, medical science, and information retrieval. This paper presents the probabilistic modeling of the prevailing wind directions. expectation-maximization algorithm (EM algorithm) is employed to evaluate unknown parameters of MvM distribution. The evaluation is carried out using real-world data sets describing annual wind direction at St. John's airport in Newfoundland, Canada. Experimental results show that EM algorithm is able to find good model parameters corresponding to input data. However, because the termination criterion chi(2) - function converges to 335, the resulting distribution cannot pass Pearson's test of goodness of fit.

关键词： expectation-maximization algorithm wind direction modelling circular data Mixture of von Mises Distribution

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Economic design of multiple inspection plans via the expectation-maximization algorithm

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 2023年第3期74卷 762-776页

作者： Chun, Young H. Louisiana State Univ Baton Rouge LA 70803 USA

Because of inspection errors, expensive items such as computer chips are usually inspected more than once with the same testing device to further improve the quality of accepted items. Many researchers have considered various multiple inspection plans that minimize the expected total cost of inspection and misclassifications. We first propose a new Markovian inspection plan under which each item is tested repeatedly until we have a sufficient number of positive or negative test results. We then deal with the problem of estimating three model parameters: the type I and II errors of an automated test equipment and the fraction defective of incoming items. Because of computational difficulties in maximizing the likelihood of the three parameters, we propose the use of the expectation-maximization (EM) algorithm as an easy alternative. In a numerical analysis, we demonstrate the outstanding performance of our new inspection plan over previous ones.

关键词： Product quality Markov chain expectation-maximization algorithm inspection reliability

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Estimation of physical parameters under location uncertainty using an ensemble²- expectation-maximization algorithm

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QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY 2019年第719期145卷 418-433页

作者： Yang, Yin Memin, Etienne Irstea UR OPAALE F-35044 Rennes France Inria Fluminance Grp Campus Univ Beaulieu Rennes France

Estimating the parameters of geophysical dynamic models is an important task in the data assimilation (DA) techniques used to forecast initialization and reanalysis. In the past, most parameter estimation strategies were derived by state augmentation, yielding algorithms that are easy to implement but may exhibit convergence difficulties. The expectation-maximization (EM) algorithm is considered advantageous because it employs two iterative steps to estimate the model state and the model parameter separately. In this work, we propose a novel ensemble formulation of the maximization step in EM that allows a direct optimal estimation of the physical parameters using iterative methods for linear systems. This departs from current EM formulations that are only capable of dealing with additive model error structures. This contribution shows how the EM technique can be used for dynamics identification problems with the model error parameterized as an arbitrary complex form. The proposed technique is used here for the identification of stochastic subgrid terms that account for processes unresolved by a geophysical fluid model. This method, together with the augmented state technique, is evaluated to estimate such subgrid terms through high-resolution data. As compared to the augmented state technique, our method is shown to yield considerably more accurate parameters. In addition, in terms of prediction capacity, it leads to a smaller generalization error as a result of the overfitting of the trained model on the presented data and eventually better forecasts.

关键词： data assimilation expectation-maximization algorithm parameter estimation stochastic modelling

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Mixed model for interoccurrence times of earthquakes based on the expectation-maximization algorithm

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ACTA GEOPHYSICA 2011年第5期59卷 872-890页

作者： Tahernia, Nadia Khodabin, Morteza Mirzaei, Noorbakhsh Islamic Azad Univ Dept Geophys Sci & Res Branch Tehran Iran Islamic Azad Univ Dept Math Karaj Branch Karaj Iran Univ Tehran Inst Geophys Tehran Iran

In this paper, the goodness-of-fit test based on a convex combination of Akaike and Bayesian information criteria is used to explain the features of interoccurrence times of earthquakes. By analyzing the seismic catalog of Iran for different tectonic settings, we have found that the probability distributions of time intervals between successive earthquakes can be described by the generalized normal distribution. This indicates that the sequence of successive earthquakes is not a Poisson process. It is found that by decreasing the threshold magnitude, the interoccurrence time distribution changes from the generalized normal distribution to the gamma distribution in some seismotectonic regions. As a new insight, the probability distribution of time intervals between earthquakes is described as a mixture distribution via the expectation-maximization algorithm.

关键词： expectation-maximization algorithm mixture model information criteria generalized gamma family interoccurrence time

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Mixed-Supervised Scene Text Detection With expectation-maximization algorithm

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IEEE TRANSACTIONS ON IMAGE PROCESSING 2022年 31卷 5513-5528页

作者： Zhao, Mengbiao Feng, Wei Yin, Fei Zhang, Xu-Yao Liu, Cheng-Lin Chinese Acad Sci Inst Automat Natl Lab Pattern Recognit Beijing 100190 Peoples R China Univ Chinese Acad Sci Sch Artificial Intelligence Beijing 100049 Peoples R China

Scene text detection is an important and challenging task in computer vision. For detecting arbitrarily-shaped texts, most existing methods require heavy data labeling efforts to produce polygon-level text region labels for supervised training. In order to reduce the cost in data labeling, we study mixed-supervised arbitrarily-shaped text detection by combining various weak supervision forms (e.g., image-level tags, coarse, loose and tight bounding boxes), which are far easier to annotate. Whereas the existing weakly-supervised learning methods (such as multiple instance learning) do not promote full object coverage, to approximate the performance of fully-supervised detection, we propose an expectation-maximization (EM) based mixed-supervised learning framework to train scene text detector using only a small amount of polygon-level annotated data combined with a large amount of weakly annotated data. The polygon-level labels are treated as latent variables and recovered from the weak labels by the EM algorithm. A new contour-based scene text detector is also proposed to facilitate the use of weak labels in our mixed-supervised learning framework. Extensive experiments on six scene text benchmarks show that (1) using only 10% strongly annotated data and 90% weakly annotated data, our method yields comparable performance to that of fully supervised methods, (2) with 100% strongly annotated data, our method achieves state-of-the-art performance on five scene text benchmarks (CTW1500, Total-Text, ICDAR-ArT, MSRA-TD500, and C-SVT), and competitive results on the ICDAR2015 Dataset. We will make our weakly annotated datasets publicly available.

关键词： Costs Annotations Training Labeling Detectors Data models Benchmark testing Mixed-supervised learning scene text detection weak supervision forms expectation-maximization algorithm

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FORWARD-REVERSE expectation-maximization algorithm FOR MARKOV CHAINS: CONVERGENCE AND NUMERICAL ANALYSIS

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ADVANCES IN APPLIED PROBABILITY 2018年第2期50卷 621-644页

作者： Bayer, Christian Mai, Hilmar Schoenmakers, John Weierstrass Inst Appl Anal & Stochast Mohrenstr 39 D-10117 Berlin Germany Deutsch Bank AG Otto Suhr Allee 16 D-10585 Berlin Germany

We develop a forward-reverse expectation-maximization (FREM) algorithm for estimating parameters of a discrete-time Markov chain evolving through a certain measurable state-space. For the construction of the FREM method, we develop forward-reverse representations for Markov chains conditioned on a certain terminal state. We prove almost sure convergence of our algorithm for a Markov chain model with curved exponential family structure. On the numerical side, we carry out a complexity analysis of the forward-reverse algorithm by deriving its expected cost. Two application examples are discussed.

关键词： expectation-maximization algorithm Markov chain estimation forward-reverse representation maximum likelihood estimation Monte Carlo simulation

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