Time series modeling of surface EMG based hand manipulation identification via expectation maximization algorithm

Classification of Hand Manipulation Using BP Neural Network and Support Vector Machine Based on Surface Electromyography Signal

Many diseases show dichotomous phenotypic variation but do not follow a simple Mendelian pattern of inheritance. Variances of these binary diseases are presumably controlled by multiple loci and environmental variants. A least-squares method has been developed for mapping such complex disease loci by treating the binary phenotypes (0 and 1) as if they were continuous. However, the least-squares method is not recommended because of its ad hoc nature. Maximum Likelihood (ML) and Bayesian methods have also been developed for binary disease mapping by incorporating the discrete nature of the phenotypic distribution. In the ML analysis, the likelihood function is usually maximized using some complicated maximization algorithms (e.g. the Newton-Raphson or the simplex algorithm). Under the threshold model of binary disease, we develop an Expectation Maximization (EM) algorithm to solve for the maximum likelihood estimates (MLEs). The new EM algorithm is developed by treating both the unobserved genotype and the disease liability as missing values. As a result, the EM iteration equations have the same form as the normal equation system in linear regression. The EM algorithm is further modified to take into account sexual dimorphism in the linkage maps. Applying the EM-implemented ML method to a four-way-cross mouse family, we detected two regions on the fourth chromosome that have evidence of QTLs controlling the segregation of fibrosarcoma, a form of connective tissue cancer. The two QTLs explain 50-60% of the variance in the disease liability. We also applied a Bayesian method previously developed (modified to take into account sex-specific maps) to this data set and detected one additional QTL on chromosome 13 that explains another 26% of the variance of the disease liability. All the QTLs detected primarily show dominance effects.

This paper proposes a method for obtaining nonlinear models of distribution grid based on available measurements from the power grid. We formulate a maximum likelihood estimation (MLE) problem that estimates unknown line parameters—specifically, the impedance between nodes—using measured voltage magnitudes and net active and reactive power injections at each node. The nonlinear model for the distribution grid uses a nonlinear approximation of the DistFlow model, which includes line losses and is parameterized by the unknown line impedances. We solve the resulting MLE problem using an expectation maximization (EM) algorithm, tailored for the nonlinear model, and provide a numerically robust implementation. The proposed method is demonstrated on the IEEE 37-node test network, and we compare it with the state-of-the-art methods. The proposed method achieves a 70% reduction in voltage error and an error for state variables that is more than 10000 times smaller. A final comparison uses data from a real network, and the proposed method achieves parameter estimates with errors 100 times smaller than competing methods.

This paper introduces structural identification using expectation maximization (STRIDE), a novel application of the expectation maximization (EM) algorithm and approach for output-only modal identification. The EM algorithm can be used to estimate the maximum likelihood parameters of a state-space model. In this context, the state-space model represents the equation of motion for a linear dynamic system. STRIDE is an iterative procedure that uses Kalman filtering and Rauch-Tung-Striebel (RTS) smoothing equations to produce estimates of the unobserved states; these calculations are based on the observed data and prior estimates of the state-space parameters. With this information, the conditional likelihood of the model is maximized and the state-space parameters are updated at each iteration. Once an iteration meets user-prescribed convergence criterion, the algorithm ends—yielding maximum likelihood estimates (MLE) for the state-space model parameters. The modal properties of the structure are th...

In this work, an expectation maximization (EM) algorithm is derived for maximum likelihood estimation of the autocorrelation function of a linear distortion channel as well as the level of additive noise, under the assumption that the source signal comes from a mixture of Gaussian sources. To facilitate parameter initialization in the EM algorithm, a correlation-matching based estimation algorithm is developed for the channel autocorrelation function. The proposed EM algorithm was evaluated on speech-derived simulated data of multiple autoregressive Gaussian sources and real speech of isolated digits under signal-to-noise ratios (SNRs) of 20 dB down to 0 dB. The algorithm is shown to produce convergent estimation results as well as estimates of signal statistics that lead to significantly improved classification accuracy under additive and convolutive noise conditions.

A stochastic version of Expectation Maximization algorithm for better estimation of Hidden Markov Model

A classical technique for reconstruction of emission tomography (ET) images from measured projections is based on the maximum likelihood (ML) estimation, achieved with the expectation maximization (EM) algorithm. We incorporate the wavelet transform (WT) and total variation (TV) based penalties into the ML framework, and compare performance of the EM algorithm and the previously proposed conjugate barrier (CB) algorithm. Using the WT- and TV-based penalties allows one to embed regularization procedures into the iterative process. In the case of the WT-based penalty, we impose a subset of wavelet coefficients with a desired resolution on the objective function. It appears that the CB algorithm outperforms substantially the EM algorithm in penalized reconstruction. The properties of the optimization algorithms along with WTand TV-based regularization are demonstrated on image reconstructions of a synthetic brain phantom, and the quality of reconstruction is compared with standard methods.

Time series subject to regime shifts have attracted much interest in domains such as econometry, finance or meteorology. For discrete-valued regimes, models such as the popular Hidden Markov Chain (HMC) describe time series whose state process is unknown at all time-steps. Sometimes, time series are annotated. Thus, another category of models handles the case with regimes observed at all time-steps. We present a novel model which addresses the intermediate case: (i) state processes associated to such time series are modelled by Partially Hidden Markov Chains (PHMCs); (ii) a multivariate linear autoregressive (MLAR) model drives the dynamics of the time series, within each regime. We describe a variant of the expectation maximization (EM) algorithm devoted to PHMC-MLAR model learning. We propose a hidden state inference procedure and a forecasting function adapted to the semi-supervised framework. We first assess inference and prediction performances, and analyze EM convergence times for PHMC-MLAR, using simulated data. We show the benefits of using partially observed states as well as a fully labelled scheme with unreliable labels, to decrease EM convergence times. We highlight the robustness of PHMC-MLAR to labelling errors in inference and prediction tasks. Finally, using turbofan engine data from a NASA repository, we show that PHMC-MLAR outperforms or largely outperforms other models: PHMC and MSAR (Markov Switching AutoRegressive model) for the feature prediction task, PHMC and five out of six recent state-of-the-art methods for the prediction of machine useful remaining life.

Finite mixtures of multivariate skew t (MST) distributions have proven to be useful in modelling heterogeneous data with asymmetric and heavy tail behaviour. Recently, they have been exploited as an effective tool for modelling flow cytometric data. A number of algorithms for the computation of the maximum likelihood (ML) estimates for the model parameters of mixtures of MST distributions have been put forward in recent years. These implementations use various characterizations of the MST distribution, which are similar but not identical. While exact implementation of the expectation-maximization (EM) algorithm can be achieved for `restricted' characterizations of the component skew t-distributions, Monte Carlo (MC) methods have been used to fit the `unrestricted' models. In this paper, we review several recent fitting algorithms for finite mixtures of multivariate skew t-distributions, at the same time clarifying some of the connections between the various existing proposals. In particular, recent results have shown that the EM algorithm can be implemented exactly for faster computation of ML estimates for mixtures with unrestricted MST components. The gain in computational time is effected by noting that the semi-infinite integrals on the E-step of the EM algorithm can be put in the form of moments of the truncated multivariate non-central t-distribution, similar to the restricted case, which subsequently can be expressed in terms of the non-truncated form of the central t-distribution function for which fast algorithms are available. We present comparisons to illustrate the relative performance of the restricted and unrestricted models, and demonstrate the usefulness of the recently proposed methodology for the unrestricted MST mixture, by some applications to three real datasets.

Recently, the expectation maximisation (EM) algorithm has been applied to a lot of problems of estimating parameters and learning and there are some theoretical analyses, however, prediction error is not mentioned yet. We are trying to evaluate the learning error when a machine learns with the EM algorithm and the probability distribution of the estimated parameters is mentioned here as the first step for the learning curve.

Left Ventricular Diastolic Dysfunction (LVDD) is a decompensatory change in the relaxation properties of the heart, the risk for which increases with age. Currently, physicians use a decision-tree-like algorithm to distinguish between discrete LVDD levels. This approach, based on cut-off thresholds, can potentially lead to information loss and possibly to misdiagnosis. This paper aims to explore an alternative diagnostic method to determine LVDD risk level, taking into account a wide variety of attributes available in patient records, without pre-setting cut-off thresholds. Using a large dataset derived from the Baltimore Longitude Study of Aging (BLSA), and adjusting the data for age and gender, we employ the Chi Square test and the information gain criterion to identify attributes that correlate well with the physician-assigned grades; such attributes are referred to as distinguishing attributes. We then apply the expectation maximization (EM) algorithm, as well as the K-Means, in order to cluster records that are represented using distinguishing attributes. While clusters resulting from the K-Means are not stable, three stable and tightly-formed clusters, which are obtained from the EM algorithm, roughly correspond to the physician-assigned categories. Based on the results from the EM algorithm, we can compute a patient's probability to have low, high or no risk for LVDD, and use this probability as a basis for defining a risk score to determine the patient's LVDD severity.

Objective: Data being missed is an unavoidable problem in cohort studies. This paper compares the imputation effect of eight common missing data imputation methods involved in cutting longitudinal data through simulation study to provide a valuable reference for the treatment of missing data in longitudinal studies. Methods: The simulation study is based on R language software and generates missing longitudinal data by the Monte Carlo method. By comparing the average absolute deviation, average relative deviation, and TypeⅠerror from the regression analysis of different imputation methods, the imputation effect of varying imputation methods on missing longitudinal data and the influence on subsequent multivariate analysis are evaluated. Results: The mean imputation, k nearest neighbor (KNN), regression imputation, and random forest all have a similar imputation effect, which is also steady. However, the hot deck is inferior to the above imputation methods. K-means clustering and expectation maximization (EM) algorithm are among the worst and unstable. Mean imputation, EM algorithm, random forest, KNN, and regression imputation can control TypeⅠerror. Still, multiple imputations, hot deck, and K-means clustering cannot effectively manage the TypeⅠerror. Conclusions: For missing data in longitudinal studies, mean imputation, KNN, regression imputation, and random forest can be used as better imputation methods under the mechanism of missing at random. When the missing ratio is not too large, multiple imputations and hot deck can also perform well, but K-means clustering and EM algorithm are not recommended.

Methodology for PET system modeling using image-space techniques in the expectation maximization (EM) algorithm is presented. The approach, applicable to both list-mode data and projection data, is of particular significance to EM algorithm implementations which otherwise only use basic system models (such as those which calculate the system matrix elements on the fly). A basic version of the proposed technique can be implemented using image-space convolution, in order to include resolution effects into the system matrix, so that the EM algorithm gradually recovers the modeled resolution with each update. The improved system modeling (achieved by inclusion of two convolutions per iteration) results in both enhanced resolution and lower noise, and there is often no need for regularization-other than to limit the number of iterations. Tests have been performed with simulated list-mode data and also with measured projection data from a GE Advance PET scanner, for both [/sup 18/F]-FDG and [/sup 124/I]-NaI. The method demonstrates improved image quality in all cases when compared to the conventional FBP and EM methods presently used for clinical data (which do not include resolution modeling). The benefits of this approach for /sup 124/I (which has a low positron yield and a large positron range, usually resulting in noisier and poorer resolution images) are particularly noticeable.

We are interested in an estimate of the usual residents in the Netherlands. Capture-recapture estimation with three registers enables us to estimate the size of the total population, of which the usual residents are a part. However, usual residence cannot be used as a covariate because it is not available in one of the registers. We approach this as a missing data problem. There are different methods available to handle missing data. In this manuscript we use Expectation Maximization (EM) algorithm and Predictive Mean Matching (PMM). The EM algorithm is often used in categorical data analysis, but PMM has the advantage of flexibility in the choice for a specific part of the observed data used for the imputation of the missing data. Four scenarios have been identified where the missing data are completed via either the EM algorithm or PMM imputation, resulting in different population size estimates for usual residence. It was found that the different scenarios lead to different population size estimates. Even small changes in the completed data lead to different population size estimates. In this study PMM imputation performs best according flexibility and it is theoretically better motivated.

Due to the lack of information about the causes of outages, the estimation of the interactions between component failures that capture the general outage propagation patterns is a typical parameter estimation problem with incomplete data. In this paper, we estimate these interactions by the expectation maximization (EM) algorithm. The proposed method is validated with simulated cascading failure data from the AC OPA model on the IEEE 118-bus system. The EM algorithm can accurately estimate the interactions and identify the key links and key components using only a small number of the original cascades from a detailed cascading blackout model, which is critical for online cascading failure analysis and decision making. Compared with AC OPA simulation, the highly probabilistic interaction model simulation based on the proposed interaction estimation method can achieve a speed-up of 100.61.