Detection of cardiomyopathy using multilayered perceptron network

Motivated by applications of distributed linear estimation, distributed control, and distributed optimization, we consider the question of designing linear iterative algorithms for computing the average of numbers in a network. Specifically, our interest is in designing such an algorithm with the fastest rate of convergence given the topological constraints of the network. As the main result of this paper, we design an algorithm with the fastest possible rate of convergence using a nonreversible Markov chain on the given network graph. We construct such a Markov chain by transforming the standard Markov chain, which is obtained using the Metropolis-Hastings method. We call this novel transformation <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">pseudo-lifting</i> . We apply our method to graphs with geometry, or graphs with doubling dimension. Specifically, the convergence time of our algorithm (equivalently, the mixing time of our Markov chain) is proportional to the diameter of the network graph and hence optimal. As a byproduct, our result provides the fastest mixing Markov chain given the network topological constraints, and should naturally find their applications in the context of distributed optimization, estimation and control.

Pegasos is a popular and reliable machine learning algorithm for making linear Support Vector Machines solvable at the larger scale. It benefits from the strongly convex optimization objective, faster convergence rates and lower computational and memory costs. In this paper we devise a new weighted formulation of the Pegasos algorithm which favors from the different coordinate-wise λ i regularization parameters. Together with the proposed extension we give a brief theoretical justification of its convergence to an optimal solution and analyze at a glance its computational costs. We conclude our paper with the numerical results obtained for UCI datasets and demonstrate the merits and the importance of our approach for achieving a better classification accuracy and convergence rates in the partially or fully stochastic setting.

For various data-based bandwidth selectors for a kernel density estimator, the relative rate of convergence of the selected bandwidth is considered. Several methods have recently been found which have the very fast rate of convergence of the square root of the sample size. Such a fast rate of convergence is quite surprising, in view of those usually encountered in nonparametric curve estimation problems. A survey and comparison of methods with this very fast rate of convergence is given.

Consensus conditions and convergence speeds are crucial for distributed consensus algorithms of networked systems. Based on a basic first-order average-consensus protocol with time-varying topologies and additive noises, this paper first investigates its critical consensus condition on network topology by stochastic approximation frameworks. A new joint-connectivity condition called extensible joint-connectivity that contains a parameter $\delta$ (termed the extensible exponent) is proposed. With this and a balanced topology condition, we show that a critical value of $\delta$ for consensus is $1/2$ . Optimization on convergence rate of this protocol is further investigated. It is proved that the fastest convergence rate, which is the theoretic optimal rate among all controls, is of the order $1/t$ for the best topologies, and is of the order $1/t^{1-2\delta }$ for the worst topologies, which are balanced and satisfy the extensible joint-connectivity condition. For practical implementation, certain open-loop control strategies are introduced to achieve consensus with a convergence rate of the same order as the fastest convergence rate. Furthermore, a consensus condition is derived for nonstationary and strongly correlated random topologies. The algorithms and consensus conditions are applied to distributed consensus computation of mobile ad-hoc networks; and their related critical exponents are derived from relative velocities of mobile agents for guaranteeing consensus.

We study in this paper a revenue-management problem with add-on discounts. The problem is motivated by the practice in the video game industry by which a retailer offers discounts on selected supportive products (e.g., video games) to customers who have also purchased the core products (e.g., video game consoles). We formulate this problem as an optimization problem to determine the prices of different products and the selection of products for add-on discounts. In the base model, we focus on an independent demand structure. To overcome the computational challenge of this optimization problem, we propose an efficient fully polynomial-time approximation scheme (FPTAS) algorithm that solves the problem approximately to any desired accuracy. Moreover, we consider the problem in the setting in which the retailer has no prior knowledge of the demand functions of different products. To solve this joint learning and optimization problem, we propose an upper confidence bound–based learning algorithm that uses the FPTAS optimization algorithm as a subroutine. We show that our learning algorithm can converge to the optimal algorithm that has access to the true demand functions, and the convergence rate is tight up to a certain logarithmic term. We further show that these results for the independent demand model can be extended to multinomial logit choice models. In addition, we conduct numerical experiments with the real-world transaction data we collect from a popular video gaming brand’s online store on Tmall.com. The experiment results illustrate our learning algorithm’s robust performance and fast convergence in various scenarios. We also compare our algorithm with the optimal policy that does not use any add-on discount. The comparison results show the advantages of using the add-on discount strategy in practice. This paper was accepted by J. George Shanthikumar, big data analytics.

Electrocardiogram is an electrical representation of heart activities that provide vital information on the cardiac condition. Development of reliable intelligent systems through analysis of cardiac rhythms has been paramount for automated classification of cardiac diseases. Bundle branch block is an arrhythmia caused by defects in the conduction pathways that alters the flow and speed of electrical impulses, leading to loss of cardiac output, and in severe cases, death. This paper proposes and investigates HMLP network for classification of bundle branch block arrhythmias. Samples of normal, right bundle branch block, and left bundle branch block beats were obtained from the PTB Diagnostic ECG database. Initially, the original signal underwent a filtering process and the baseline drift were rectified using the polynomial curve fitting technique. Five morphological features were then extracted through median threshold method for a total of 150 beat samples. The features were then used for training of the single hidden layer HMLP network. The training stage employed four different learning algorithms for four hidden node implementations. Results show that the Polak-Ribiere conjugate gradient algorithm achieved the best convergence speed with 100% classification accuracy. Overall, the various HMLP network structures managed to attain 99.6% average classification accuracy.

The capacitated arc routing problem (CARP) is a classical NP-Hard combinatorial optimization problem. In this paper, we present a memetic algorithm based on Extension step and Statistical filtering for Large-Scale CARP (ESMAENS) which has improvements in both the global search strategy and the local search strategy. Firstly, ESMAENS adopts the Route Distance Grouping decomposition scheme (RDG) to decompose the large-scale CARP into some independent sub-problems. Then, the initial population would evolve into a new group by using the Evolutionary Algorithm. Furthermore, ESMAENS introduces the extension step search strategy to search the potential solutions around the current solution. As a result, with the increase of the iteration number, it avoids getting to the premature convergence. Meanwhile, the diversity of the population can be increased. Finally, in the local search strategy, the statistical filter is used to filter out some solutions and make the algorithm get the lower bound at a faster convergence rate with a high stability. Compared with RDG-MAENS, experimental results on Beullen’C, D, E, F, egl and EGL-G test set show that ESMAENS has a better convergence rate, and the stability of solutions obtained is improved. Furthermore, ESMAENS achieves a global search for the solutions. Especially for the large-scale EGL-G test set, ESMAENS can converge to a lower bound at a faster convergence rate, and it is suitable for solving large-scale CARP.

This study aims to provide a robust trajectory tracking controller which guarantees the prescribed performance of a robot manipulator, both in transient and steady-state modes, experiencing parametric uncertainties. The main core of the controller is designed based on the adaptive finite-time sliding mode control (SMC) and extreme learning machine (ELM) methods to collectively estimate the parametric model uncertainties and enhance the quality of tracking performance. Accordingly, the global estimation with a fast convergence rate is achieved while the tracking error and the impact of chattering on the control input are mitigated significantly. Following the control design, the stability of the overall control system along with the finite-time convergence rate is proved, and the effectiveness of the proposed method is investigated via extensive simulation studies. The results of simulations confirm that the prescribed transient and steady-state performances are obtained with enough accuracy, fast convergence rate, robustness, and smooth control input which are all required for practical implementation and applications.

Motivated by classical vortex blob methods for the Euler equations, we develop a numerical blob method for the aggregation equation. This provides a counterpoint to existing literature on particle methods. By regularizing the velocity field with a mollifier or “blob function”, the blob method has a faster rate of convergence and allows a wider range of admissible kernels. In fact, we prove arbitrarily high polynomial rates of convergence to classical solutions, depending on the choice of mollifier. The blob method conserves mass and the corresponding particle system is energy decreasing for a regularized free energy functional and preserves the Wasserstein gradient flow structure. We consider numerical examples that validate our predicted rate of convergence and illustrate qualitative properties of the method.

A generalisation of the ecm algorithm (Meng & Rubin, 1993), which is itself an extension of the em algorithm (Dempster, Laird & Rubin, 1977), can be obtained by replacing some CM-steps of ECM, which maximise the constrained expected complete-data loglikelihood function, with steps that maximise the correspondingly constrained actual likelihood function. This algorithm, which we call ecme algorithm, for Expectation/Conditional Maximisation Either, shares with both em and ecm their stable monotone convergence and basic simplicity of implementation relative to competing faster converging methods. Moreover, ecme can have a substantially faster convergence rate than either EM or ECM, measured using either the number of iterations or actual computer time. There are two reasons for this improvement. First, in some of ECME'S maximisation steps, the actual likelihood is being conditionally maximised, rather than a current approximation to it, as with EM and ECM. Secondly, ecme allows faster converging numerical methods to be used on only those constrained maximisations where they are most efficacious. Illustrative ecme algorithms are presented with both closed-form and iterative CM-steps, which demonstrate the faster rate of convergence and the associated easier assessment of convergence. Also, theoretical expressions are presented and illustrated regarding the rate of convergence of ecme. Finally, relationships with Markov chain Monte Carlo methods are discussed.

This article investigates the problem of distributed hypothesis testing over networks. By introducing double and triple cumulations of historical observations, two novel distributed learning algorithms are developed to solve the considered problem. Within this framework, we study the convergence rates of the proposed algorithms. More specifically: 1) It is proven that the algorithm with double cumulation of historical observations has a faster convergence rate than those of the existing algorithms. 2) Furthermore, it is proven that the algorithm with triple cumulation of historical observations can be further accelerated. Especially, based on the theoretical results, this article shows that a tradeoff among convergence rate, transient performance, and memory burden exists in the proposed algorithms. Finally, simulation examples verify the theoretical results.

This paper proposes a new method to detect and identify foreign matter mixed in a plastic bottle filled with transfusion solution. A spin-stop mechanism and mixed illumination style are applied to obtain high contrast images between moving foreign matter and a static transfusion background. The Gaussian mixture model is used to model the complex background of the transfusion image and to extract moving objects. A set of features of moving objects are extracted and selected by the ReliefF algorithm, and optimal feature vectors are fed into the back propagation (BP) neural network to distinguish between foreign matter and bubbles. The mind evolutionary algorithm (MEA) is applied to optimize the connection weights and thresholds of the BP neural network to obtain a higher classification accuracy and faster convergence rate. Experimental results show that the proposed method can effectively detect visible foreign matter in 250-mL transfusion bottles. The misdetection rate and false alarm rate are low, and the detection accuracy and detection speed are satisfactory.

Noise and interference are the two most common and basic problems in wireless communication systems. The noise in wireless communication channels has the characteristics of randomness and impulsivity, so the performance of adaptive filtering algorithms based on geometric algebra (GA) and second-order statistics is greatly reduced in the wireless communication systems. In order to improve the performance of adaptive filtering algorithms in wireless communication systems, this paper proposes two novel GA-based adaptive filtering algorithms, which are deduced from the robust algorithms based on the minimum error entropy (MEE) criterion and the joint criterion (MSEMEE) of the MEE and the mean square error (MSE) with the help of GA theory. The noise interference in wireless communication is modeled by alpha-stable distribution which is in good agreement with the actual data in this paper. Simulation results show that for the mean square deviation (MSD) learning curve, the GA-based MEE (GA-MEE) algorithm has faster convergence rate and better steady-state accuracy compared to the GA-based maximum correntropy criterion algorithm (GA-MCC) under the same generalized signal-to-noise ratio (GSNR). The GA-MEE algorithm reduces the convergence rate, but improves the steady-state accuracy by 10–15 dB compared to the adaptive filtering algorithms based on GA and second-order statistics. For GA-based MSEMEE (GA-MSEMEE) algorithm, when GA-MSEMEE and the adaptive filtering algorithms based on GA and second-order statistics keep the same convergence rate, its steady-state accuracy is improved by 10–15 dB, and when GA-MSEMEE and GA-MEE maintain approximately steady-state accuracy, its convergence rate is improved by nearly 100 iterations. In addition, when the algorithms are applied to noise cancellation, the average recovery error of the two proposed algorithms is 7 points lower than that of other GA-based adaptive filtering algorithms. The results validate the effectiveness and superiority of the GA-MEE and GA-MSEMEE algorithms in the alpha-stable noise environment, providing new methods to deal with multi-channel interference in wireless networks.

In this paper, we build bounded error observers for a common class of partially known bioreactor models. The main idea is to construct hybrid bounded observers "between" high gain observer, which has an adjustable convergence rate but requires perfect knowledge of the model, and asymptotic observer which is very robust towards uncertainty but has a fixed convergence rate. An hybrid bounded error observer which reconstructs the two state variables is constructed considering two steps: first step is similar to a high gain observer meaning that fast convergence rate but error depending on the knowledge of the model are obtained; second step is a switch to an observer similar to the asymptotic one meaning that fixed convergence rate towards an error as small as desired is obtained. Thus, a better convergence rate of estimated variables than the classical asymptotic observer is obtained.

The modes in the electrocardiogram (ECG) signal can be divided into stable modes and unstable modes. The unstable modes are of great significance for signal analysis and classification. When the traditional dynamic mode decomposition (DMD) method is directly applied to these signals, it is difficult to effectively extract these key modes due to the rank mismatch problem of the data matrix. In order to better capture and analyze unstable modes, this study introduced the Hankel matrix to expand ECG data and used it as the input of DMD to propose the Hankel dynamic mode decomposition (HDMD) method. Although HDMD has been applied in other physiological signal processing, this study is the first to successfully apply it to multi-lead ECG signal analysis. By optimizing the delay parameters of the Hankel matrix and retaining the modes that account for 90% of the singular value decomposition energy, we significantly improve the effectiveness of feature extraction. Each type of abnormal ECG signal data is classified on the PTB Diagnostic ECG database. The experimental results of the proposed model are compared with the direct use of DMD for modal extraction. The highest classification accuracy of multi-modal ECG signal data extracted by HDMD is more than 10% higher than that using DMD. At the same time, the mean squared error (MSE) of the reconstruction using HDMD is 0.282 lower than that of DMD, indicating a significant improvement in reconstruction accuracy. Further illustrating the proposed method, the HDMD method can better capture and analyze the unstable modes in the ECG signal, thereby significantly improving the accuracy and robustness of signal classification. Future work will focus on further optimizing the parameter selection of the HDMD model and exploring its application potential in real-time heart disease monitoring and early warning systems.