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Constrained expectation maximisation algorithm for estimating ARMA models in state space representation

EURASIP JOURNAL ON ADVANCES IN SIGNAL PROCESSING 2020年第1期2020卷 23-23页

作者： Galka, Andreas Moontaha, Sidratul Siniatchkin, Michael Bundeswehr Tech Ctr Ships & Naval Weap Naval Technol & Res WTD 71 Berliner Str 115 Eckernforde Germany Univ Kiel Inst Med Psychol & Med Sociol Preusserstr 1-9 Kiel Germany Potsdam Univ Digital Hlth Ctr Hasso Plattner Inst Rudolf Breitscheid Str 187 Potsdam Germany Clin Pediat & Adolescent Psychiat & Psychotherapy Remterweg 13a Bielefeld Germany

This paper discusses the fitting of linear state space models to given multivariate time series in the presence of constraints imposed on the four main parameter matrices of these models. Constraints arise partly from the assumption that the models have a block-diagonal structure, with each block corresponding to an ARMA process, that allows the reconstruction of independent source components from linear mixtures, and partly from the need to keep models identifiable. The first stage of parameter fitting is performed by the expectation maximisation (EM) algorithm. Due to the identifiability constraint, a subset of the diagonal elements of the dynamical noise covariance matrix needs to be constrained to fixed values (usually unity). For this kind of constraints, so far, no closed-form update rules were available. We present new update rules for this situation, both for updating the dynamical noise covariance matrix directly and for updating a matrix square-root of this matrix. The practical applicability of the proposed algorithm is demonstrated by a low-dimensional simulation example. The behaviour of the EM algorithm, as observed in this example, illustrates the well-known fact that in practical applications, the EM algorithm should be combined with a different algorithm for numerical optimisation, such as a quasi-Newton algorithm.

关键词： Kalman filtering State space modelling expectation maximisation algorithm

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Robust multi-response surface optimisation based on Bayesian quantile model

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2023年第10期61卷 3260-3278页

作者： Yang, Shijuan Wang, Jianjun Tu, Yiliu Han, Yunxia Ren, Xiaolei Ding, Chunfeng Chen, Xiaoying Nanjing Univ Sci & Technol Dept Management Sci & Engn 200 Xiaolingwei Nanjing 210094 Jiangsu Peoples R China Univ Calgary Dept Mech & Mfg Engn Nw Calgary AB Canada Yangzhou Univ Business Sch Yangzhou Jiangsu Peoples R China

In robust parameter design, model parameter uncertainty and quality of experimental data often affect the establishment of response surface models, which in turn affect the acquisition of the optimal operating conditions. This paper proposes a robust multi-response surface modelling and optimisation method based on Bayesian quantile regression, which is a robust regression technique insensitive to outliers, to address the above problems. We first incorporate quantile regression into the Bayesian framework and use Bayes's theorem to obtain posterior inference of model parameters. Then, the Monte Carlo-based expectation maximisation algorithm is used to estimate the model parameters, and the entropy-based overall desirability function is taken as an optimisation objective to obtain the optimal settings. The effectiveness of the proposed method is demonstrated by an additive manufacturing process and a simulation study. Compared with other existing methods, the proposed method can resist the disturbance of outliers, and thus obtain more accurate optimisation results.

关键词： Parameter design Bayesian inference quantile regression expectation maximisation algorithm entropy-based desirability function

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On theoretical justification of the forward-backward algorithm for the variational learning of Bayesian hidden Markov models

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IET SIGNAL PROCESSING 2022年第6期16卷 674-679页

作者： Li, Tao Ma, Jinwen Peking Univ Dept Informat & Computat Sci Sch Math Sci & LMAM Beijing 100871 Peoples R China

In the variational learning process of a Bayesian Hidden Markov model, the forward-backward algorithm is heuristically applied without theoretical justification. This is potentially problematic, because the original derivation of the forward-backward algorithm implicitly requires the parameters to be normalized, which does not hold in the variational learning process of Bayesian HMM. In this paper, we prove that such a requirement is not necessary for the forward-backward algorithm to obtain the correct result. We prove the result from two perspectives. The first proof straightforwardly verifies that implementing the forward-backward algorithm with the unnormalised parameters is equivalent to implementing it with the normalized parameters. The second proof provides a new derivation of the forward-backward algorithm without hidden Markov assumptions and probabilistic meanings of the parameters. As a result, we justify that applying the forward-backward algorithm is theoretically correct and reasonable in the variational learning of Bayesian hidden Markov models.

关键词： expectation maximisation algorithm hidden Markov model variational technique

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Maximum likelihood inference for a class of discrete-time Markov switching time series models with multiple delays

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EURASIP JOURNAL ON ADVANCES IN SIGNAL PROCESSING 2024年第1期2024卷 74页

作者： Martinez-Ordonez, Jose. A. Lopez-Santiago, Javier Miguez, Joaquin Univ Carlos III Madrid Dept Signal Theory & Commun Madrid Spain

Autoregressive Markov switching (ARMS) time series models are used to represent real-world signals whose dynamics may change over time. They have found application in many areas of the natural and social sciences, as well as in engineering. In general, inference in this kind of systems involves two problems: (a) detecting the number of distinct dynamical models that the signal may adopt and (b) estimating any unknown parameters in these models. In this paper, we introduce a new class of nonlinear ARMS time series models with delays that includes, among others, many systems resulting from the discretisation of stochastic delay differential equations (DDEs). Remarkably, this class includes cases in which the discretisation time grid is not necessarily aligned with the delays of the DDE, resulting in discrete-time ARMS models with real (non-integer) delays. The incorporation of real, possibly long, delays is a key departure compared to typical ARMS models in the literature. We describe methods for the maximum likelihood detection of the number of dynamical modes and the estimation of unknown parameters (including the possibly non-integer delays) and illustrate their application with a nonlinear ARMS model of El Ni & ntilde;o-southern oscillation (ENSO) phenomenon.

关键词： Markov switch Time series models Delay difference equations Maximum likelihood estimation expectation maximisation algorithm ENSO

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Image patch prior learning based on random neighbourhood resampling for image denoising

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IET IMAGE PROCESSING 2020年第5期14卷 838-844页

作者： Ji, Jian Wei, Jiajie Fan, Guoliang Bai, Mengqi Huang, Jingjing Miao, Qiguang Xidian Univ Sch Comp Sci & Technol Xian 710071 Peoples R China Oklahoma State Univ Sch Elect & Comp Engn Stillwater OK 74078 USA

Image patch priors become a popular tool for image denoising. The Gaussian mixture model (GMM) is remarkably effective in modelling natural image patches. However, GMM prior learning using the expectation maximisation (EM) algorithm is sensitive to the initialisation, often leading to low convergence rate of parameter estimation. In this study, a novel sampling method called random neighbourhood resampling (RNR) is proposed to improve the accuracy and efficiency of parameter estimation. An enhanced GMM (EGMM) learning algorithm is further developed by incorporating RNR into the EM algorithm to initialise and update the GMM prior. The learned EGMM prior is applied in the expected patch log-likelihood (EPLL) framework for image denoising. The effectiveness and performance of the proposed RNR and EGMM algorithm are demonstrated via extensive experimental results comparing with the state-of-the-art image denoising methods, the experimental results show the higher PSNR result of the denoised images using the proposed method. Meanwhile, the authors verified that the proposed method can efficiently reduce the time of image denoising compared with the basic EPLL method.

关键词： image denoising mixture models learning (artificial intelligence) Gaussian processes expectation-maximisation algorithm random neighbourhood resampling Gaussian mixture model natural image patches expectation maximisation algorithm parameter estimation RNR enhanced GMM learning algorithm expected patch log-likelihood framework EGMM algorithm image denoising methods image patch prior learning EM algorithm EPLL framework

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Automated acute lymphoblastic leukaemia detection system using microscopic images

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IET IMAGE PROCESSING 2019年第13期13卷 2548-2553页

作者： Sukhia, Komal Nain Ghafoor, Abdul Riaz, Muhammad Mohsin Iltaf, Naima NUST Islamabad Pakistan COMSATS Islamabad CAST Islamabad Pakistan

An automatic and novel approach for acute lymphoblastic leukaemia classification is proposed. The proposed scheme is based on pre-processing and segmentation of white blood cell nuclei using expectation maximisation algorithm, feature extraction, feature selection using principal component analysis and classification using sparse representation. The accuracy of the proposed scheme significantly outperforms the existing schemes in terms of acute lymphoblastic leukaemia classification.

关键词： cellular biophysics principal component analysis expectation-maximisation algorithm feature extraction medical image processing image segmentation image classification blood cancer microscopic images automatic approach acute lymphoblastic leukaemia classification white blood cell nuclei expectation maximisation algorithm feature extraction principal component analysis automated acute lymphoblastic leukaemia detection system sparse representation

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HANKEL-EM-SVD: a hybrid data dropout estimation technique for high voltage partial discharge signals

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IET SCIENCE MEASUREMENT & TECHNOLOGY 2019年第6期13卷 824-835页

作者： Govindarajan, Suganya Subbaiah, Jayalalitha Krithivasan, Kannan Natarajan, Muthukumar SASTRA Deemed Be Univ Sch EEE Thanjavur Tamil Nadu India SASTRA Deemed Be Univ Tata Realty Srinivasa Ramanujam Res Cell Data Sci Lab Thanjavur India

Partial discharge (PD) measurement and characterisation is the most effective method to assess the insulation conditions of equipment for its diagnosis. A significant challenge in this area is PD denoising. Despite recent advancements in denoising algorithms, data drops out because of inappropriate threshold selection during denoising. Processing PD signals with missing data leads to an inaccurate assessment of the insulation conditions, indicating recovering such missed data is a potential research scope under the moonlight. This study addresses the issues of recovering such data dropouts by considering the PD data vector matrix as a low-rank matrix that needs completion by Hankel-matrix decomposition methods. After finding the probabilistic estimate of the missing values using an expectation maximisation algorithm, singular-value decomposition is used to find the actual missing values by soft-thresholding the singular values of the matrix. After testing this technique on simulated PD data, it is implemented to test SASTRA-High-Voltage Laboratory data, showing root mean square error (RMSE) 0.77% and mean absolute error 0.84%. The efficiency of this technique is confirmed when tested with large-sized noise free PD data of 36 samples from the Laboratory of BOLOGNA University (with RMSE varying from 0.15 to 0.31% and mean absolute error varying from 0.29 to 0.6%).

关键词： mean square error methods expectation-maximisation algorithm signal denoising partial discharge measurement partial discharges singular value decomposition HANKEL-EM-SVD high voltage partial discharge signals insulation conditions PD denoising inappropriate threshold selection inaccurate assessment missed data potential research scope PD-data vector-matrix low-rank matrix Hankel-matrix decomposition methods probabilistic estimate expectation maximisation algorithm singular-value decomposition actual missing values singular values simulated PD data SASTRA-High-Voltage Laboratory data root mean square mean absolute error hybrid data dropout estimation technique partial discharge measurement partial discharge characterisation PD signal processing BOLOGNA University

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Robust external calibration of terrestrial laser scanner and digital camera for structural monitoring

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JOURNAL OF APPLIED GEODESY 2019年第2期13卷 105-134页

作者： Omidalizarandi, Mohammad Kargoll, Boris Paffenholz, Jens-Andre Neumann, Ingo Leibniz Univ Hannover Geodet Inst Nienburger Str 1 D-30167 Hannover Germany

In the last two decades, the integration of a terrestrial laser scanner (TLS) and digital photogrammetry, besides other sensors integration, has received considerable attention for deformation monitoring of natural or man-made structures. Typically, a TLS is used for an area-based deformation analysis. A high-resolution digital camera may be attached on top of the TLS to increase the accuracy and completeness of deformation analysis by optimally combining points or line features extracted both from three-dimensional (3D) point clouds and captured images at different epochs of time. For this purpose, the external calibration parameters between the TLS and digital camera needs to be determined precisely. The camera calibration and internal TLS calibration are commonly carried out in advance in the laboratory environments. The focus of this research is to highly accurately and robustly estimate the external calibration parameters between the fused sensors using signalised target points. The observables are the image measurements, the 3D point clouds, and the horizontal angle reading of a TLS. In addition, laser tracker observations are used for the purpose of validation. The functional models are determined based on the space resection in photogrammetry using the collinearity condition equations, the 3D Helmert transformation and the constraint equation, which are solved in a rigorous bundle adjustment procedure. Three different adjustment procedures are developed and implemented: (1) an expectation maximization (EM) algorithm to solve a Gauss-Helmert model (GHM) with grouped t-distributed random deviations, (2) a novel EM algorithm to solve a corresponding quasi-Gauss-Markov model (qGMM) with t-distributed pseudo-misclosures, and (3) a classical least-squares procedure to solve the GHM with variance components and outlier removal. The comparison of the results demonstrates the precise, reliable, accurate and robust estimation of the parameters in particular by the sec

关键词： Terrestrial laser scanner digital camera external calibration Gauss-Helmert model quasi-Gauss-Markov model adaptive robust estimation expectation maximisation algorithm structural monitoring

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Conditional anomaly detection based on a latent class model

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TOTAL QUALITY MANAGEMENT & BUSINESS EXCELLENCE 2019年第Sup1期30卷 S227-S239页

作者： Ohkubo, Masato Nagata, Yasushi Toyo Univ Dept Business Adm Fac Business Adm Bunkyo City Japan Waseda Univ Sch Creat Sci & Engn Dept Ind & Management Syst Engn Shinjuku City Japan

In recent years, the progress of the Internet of Things has promoted data utilisation in manufacturing industries and has created new possibilities for monitoring the condition of production equipment. By applying anomaly detection procedures to the data acquired from sensors, it is possible to capture early signs of occurring anomalies, which leads to improvement of operating rates and prevention of accidents. However, in conventional anomaly detection procedures, it is not always possible to properly detect anomalies when usage situations change. This is because the definition of anomalies changes depending on the usage situation. In other words, when 'environment variables' indicating usage conditions and 'monitoring variables' indicating monitoring targets exist, it is necessary to regard them as a conditional anomaly detection problem, which is a problem of detecting anomalies occurring in a monitoring variable on the condition that an environmental variable has occurred. In this paper, we propose a novel analysis procedure to solve such conditional anomaly detection problems. In particular, we propose a conditional anomaly detection procedure when categorical environmental variables and continuous monitoring variables are observed. Through Monte Carlo simulation, we show that the proposed procedure can accurately detect 'conditional anomalies' that cannot be detected by conventional procedures.

关键词： auxiliary variables expectation maximisation algorithm Gaussian mixture model latent class model statistical anomaly detection

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Switching LDS detection for GNSS-based train integrity monitoring system

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IET INTELLIGENT TRANSPORT SYSTEMS 2017年第5期11卷 299-307页

作者： Li, Sihui Cai, Baigen Wei Shangguan Schnieder, Eckehard Toro, Federico Grasso Beijing Jiaotong Univ Sch Elect & Informat Engn Beijing Peoples R China Tech Univ Carolo Wilhelmina Braunschweig Inst Traff Safety & Automat Engn Braunschweig Germany

Train integrity whilst in service establishes the foundation for railway safety. This study investigates train integrity detection which reliably deduces whether the train consists remain intact. A switching linear dynamic system (SLDS) based train integrity detection method is proposed for Global Navigation Satellite System (GNSS) based train integrity Monitoring System (TIMS) using the relative distance, velocity and acceleration of the locomotive and the last van. There, expectation maximisation (EM) algorithm estimates the parameters of SLDS model while the Gaussian Sum Filter infers train integrity state. After that, to cope with false detection and misdetection, a verification procedure and train parting time estimation are designed. The approach is evaluated with both field trials and simulated data. Results show that the false alarm rate and misdetection rate of SLDS-based integrity detection approach are 0 and 0.09% respectively, which proves better than the estimated train length based detection model and Hidden Markov Model (HMM).

关键词： satellite navigation railway safety expectation-maximisation algorithm hidden Markov models GNSS-based train integrity monitoring system railway safety switching linear dynamic system train integrity detection method global navigation satellite system TIMS relative distance expectation maximisation algorithm EM algorithm SLDS model Gaussian sum filter verification procedure train parting time estimation false alarm rate misdetection rate train length based detection model hidden Markov model HMM

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