In model-based cluster analysis, the expectation-maximization (EM) algorithm has a number of desirable properties, but in some situations, this algorithm can be slow to converge. Some variants are proposed to speed-up...
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In model-based cluster analysis, the expectation-maximization (EM) algorithm has a number of desirable properties, but in some situations, this algorithm can be slow to converge. Some variants are proposed to speed-up EM in reducing the time spent in the E-step, in the case of Gaussian mixture. The main aims of such methods is first to speed-up convergence of EM, and second to yield same results (or not so far) than EM itself. In this paper, we compare these methods from categorical data, with the latent class model, and we propose a new variant that sustains better results on synthetic and real data sets, in terms of convergence speed-up and number of misclassified objects.
This article addresses adaptive radar detection of N pulses coherently backscattered by a prospective target in heterogeneous disturbance. As customary K >= N range cells adjacent to the one under test are used for...
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This article addresses adaptive radar detection of N pulses coherently backscattered by a prospective target in heterogeneous disturbance. As customary K >= N range cells adjacent to the one under test are used for estimation purposes. The disturbance in each range cell is described by a non-Gaussian model based on a mixture of L < K Gaussian distributions. Gaussian components are characterized by an unknown low-rank matrix plus thermal noise with unknown power level. We first derive a detector inspired by the generalized likelihood ratio test that adaptively estimates the statistical properties of the disturbance from the observed data. To overcome the intractability of the involved maximum-likelihood estimation problem, a suitable approximate strategy based on the expectation-maximization algorithm is developed. This also allows us to classify the cell under test by selecting the "maximum a posteriori Gaussian distribution" for the disturbance (under both hypotheses). Accordingly, a likelihood ratio test is also proposed. An extensive performance analysis, conducted on synthetic data as well as on two different experimental datasets (PhaseOne and IPIX for land and sea radar returns, respectively), shows that the proposed approaches outperform state-of-the-art competitors in terms of both detection capabilities and false alarms control.
A solution is given to the problem of estimating reliability indicators in a context of crude data arising in an industrial study devoted to the reliability assessment of electronic calculators used in modern airplane...
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A solution is given to the problem of estimating reliability indicators in a context of crude data arising in an industrial study devoted to the reliability assessment of electronic calculators used in modern airplanes. We introduce the concept of amalgamated data and develop an expectation-maximization algorithm to obtain a maximum likelihood estimator of the reliability function and the cumulative failure intensity associated with the lifetime of calculators.
GNSS (Global Navigation Satellite Systems) tropospheric delay, specifically zenith wet delay (ZWD), shows clear spatial-temporal variations and is usually modeled as RWPN (random walk process noise). However, because ...
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GNSS (Global Navigation Satellite Systems) tropospheric delay, specifically zenith wet delay (ZWD), shows clear spatial-temporal variations and is usually modeled as RWPN (random walk process noise). However, because RWPN does not take the geographical position of GNSS stations and local weather conditions into account for precise point positioning (PPP), it may lead to biased ZWD estimates. To address the scientific problem and improve ZWD estimates, we adopt the expectation-maximization algorithm (EM algorithm) to validate the feasibility of estimating RWPN using only GNSS measurements. Numerical experiments reveal that using only GNSS observations is capable of determining the RWPN parameter, although it could take several days to reach a stable solution if the initial guess deviates far away from the truth. It is also shown that estimating RWPN can almost always effectively improve ZWD estimates by several millimeters in contrast with traditional PPP results. If the ambiguities are fixed to their integer values correctly, the accuracy of RWPN estimates for ZWD can be greatly reduced by 2mm/hour\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2\text{ mm}/\sqrt{\text{hour}}$$\end{document}.
The expectation-maximization (EM) algorithm is a popular tool in a wide variety of statistical settings, in particular in the maximum likelihood estimation of parameters when clustering using mixture models. A serious...
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The expectation-maximization (EM) algorithm is a popular tool in a wide variety of statistical settings, in particular in the maximum likelihood estimation of parameters when clustering using mixture models. A serious pitfall is that in the case of a multimodal likelihood function the algorithm may become trapped at a local maximum, resulting in an inferior clustering solution. In addition, convergence to an optimal solution can be very slow. Methods are proposed to address these issues: optimizing starting values for the algorithm and targeting maximization steps efficiently. It is demonstrated that these approaches can produce superior outcomes to initialization via random starts or hierarchical clustering and that the rate of convergence to an optimal solution can be greatly improved. (C) 2012 Elsevier B.V. All rights reserved.
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 bilin...
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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.
In this article, I provide an illustrative, step-by-step implementation of the expectation-maximization algorithm for the nonparametric estimation of mixed logit models. In particular, the proposed routine allows user...
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In this article, I provide an illustrative, step-by-step implementation of the expectation-maximization algorithm for the nonparametric estimation of mixed logit models. In particular, the proposed routine allows users to fit straight-forwardly latent-class logit models with an increasing number of mass points so as to approximate the unobserved structure of the mixing distribution.
We consider the problem of event-related desynchronization (ERD) estimation. In existing approaches, model parameters are usually found manually through experimentation, a tedious task that often leads to suboptimal e...
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We consider the problem of event-related desynchronization (ERD) estimation. In existing approaches, model parameters are usually found manually through experimentation, a tedious task that often leads to suboptimal estimates. We propose an expectation-maximization (EM) algorithm for model parameter estimation that is fully automatic and gives optimal estimates. Further, we apply a Kalman smoother to obtain ERD estimates. Results show that the EM algorithm significantly improves the performance of the Kalman smoother. Application of the proposed approach to the motor-imagery EEG data shows that useful ERD patterns can be obtained even without careful selection of frequency bands.
The fluorescence lifetime technique offers an effective way to resolve fluorescent components with overlapping emission spectra. The presence of multiple fluorescent components in biological compounds can hamper their...
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The fluorescence lifetime technique offers an effective way to resolve fluorescent components with overlapping emission spectra. The presence of multiple fluorescent components in biological compounds can hamper their discrimination. The conventional method based on the nonlinear least-squares technique is unable to consistently determine the correct number of fluorescent components in a fluorescence decay profile. This can limit the applications of the fluorescence lifetime technique in biological assays and diagnoses where more than one fluorescent component is typically encountered. We describe the use of an expectation-maximization (EM) method with joint deconvolution to estimate the fluorescence decay parameters, and the Bayesian information criterion (BIC) to accurately determine the number of fluorescent components. A comprehensive simulation and experimental study is carried out to compare the performance and accuracy of the proposed method. The results show that the EMBIC method is able to accurately identify the correct number of fluorescent components in samples with weakly fluorescing components. (C) 2009 Society of Photo-Optical Instrumentation Engineers. [DOI: 10.1117/1.3258835]
Phase distribution in the flow field provides an insight in to the hydrodynamics and heat transfer between the fluids. Void fraction, which is one of the key flow parameters, can be determined by estimating the phase ...
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Phase distribution in the flow field provides an insight in to the hydrodynamics and heat transfer between the fluids. Void fraction, which is one of the key flow parameters, can be determined by estimating the phase boundaries. Electrical impedance tomography (EIT), which has high temporal characteristics, has been used as an imaging modality to estimate the void boundaries, using the prior knowledge of conductivities. The voids formed within the process vessel are not stable and their movement is random in nature, thus dynamic estimation schemes are necessary to track the fast changes. Kalman-type estimators like extended Kalman filter (EKF) assume the knowledge of model parameters, such as the initial states, state transition matrix and the covariance of process and measurement noise. In real situations, we do not have the prior information of the model parameters;therefore, in such circumstances the estimation performance of the Kalman-type filters is affected. In this paper, the expectation-maximization (EM) algorithm is used as an inverse algorithm to estimate the model parameters as well as non-stationary void boundary. The uncertainties caused in Kalman-type filters, due to the inaccurate selection of model parameters are over come using an EM algorithm. The performance of the method is tested with numerical and experimental data. The results show that an EM has better estimation of the void boundary as compared to the conventional EKF. (C) 2010 Elsevier Ltd. All rights reserved.
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