Maximum Singular Value Research Articles

A novel method based on Adaptive Periodic Segment Matrix and Singular Value Decomposition for removing EMG artifact in ECG signal

The Electrocardiogram (ECG) signals are usually used to detect and monitor human health. However, the Electromyogram (EMG) artifacts also can be obtained during measurement, these make difficult for doctors in correct diagnosis. In general, ECG signals are periodic while EMG artifacts are non-stationary and overlapped in the frequency domain. According to these characteristics, it is necessary to extract clean ECG signals from EMG artifacts by using the periodic separation method. A novel Adaptive Periodic Segment Matrix (APSM) based on Singular Value Decomposition (SVD) is proposed for extracting clean ECG signals from EMG artifacts. Firstly, a periodic segment estimation method is proposed by obtaining an average periodic length and RR intervals constraint via envelope spectrum of the measured signal. Secondly, the R wave peaks and their positions of the ECG signals are detected by these. After that, APSM with rank one is formed using R wave peaks and the calculated RR intervals constraint, then SVD is processed on this matrix, the restructured ECG signals will be obtained by the first maximal singular value of the formed matrix. The validation of proposed method is made by applying the algorithm to ECG records from different four databases. Quantitative and qualitative analyses have been made and compared with other methods. The results show that the proposed APSM-SVD method is effective for EMG artifacts removal and clean ECG signals extraction. The R peak, P wave, QRS complex and ST segment can be preserved in reconstructed ECG signals.

State-space models of evoked potentials to localize the seizure onset zone.

Surgical removal of the seizure onset zone (SOZ) in epilepsy patients is a potentially curative treatment, but the process heavily relies on accurate localization of the SOZ via visual inspection. SPES (Single-pulse electrical stimulation) is a method recently used to explore inter-areal connectivity in vivo to probe functional brain networks such as language and motor networks, and to a much lesser degree, seizure networks. We hypothesized that a dynamical quantification of the connectivity networks derived from the evoked responses induced by SPES could also be used to localize the SOZ. To test our hypothesis, we used an intracranial EEG (iEEG) data set in which five epilepsy patients underwent extensive SPES evaluation. For each patient, and for each dataset that stimulated a different pair of electrodes, we constructed a state-space model from the patient's data. Specifically, we simultaneously estimated model parameters under an exogenous pulse input to a dynamical system whose state vector consisted of the response iEEG signals. Then, the size of the reachable state space, as quantified by the maximum singular value of the reachability matrix, σmax(R), was computed and denoted as the "largest" network response possible when stimulating the given pair. Our results suggest high agreement between σmax(R) and clinically annotated SOZ for patients with localizable SOZs.Clinical Relevance- Our study applies dynamical systems theory to identify epileptogenic brain regions, creating a novel tool that clinicians may use in surgical planning for medically-refractory epilepsy patients.

Passivity Analysis of Non-autonomous Discrete-Time Inertial Neural Networks with Time-Varying Delays

This paper addresses the passivity problem for delayed non-autonomous discrete-time inertial neural networks (NDINN), including the discrete-time switched inertial neural networks (DSINN) with state-dependent discontinuous right-hand side as its special case. First, we take a linear transformation to transform the original network into first-order difference equations. Second, by utilizing the Lyapunov direct method and with the help of the property of maximum singular value, we present a passivity criterion for the NDINN with delay-dependent linear matrix inequalities. Combining with the characteristic function method, the proposed analytical approach for NDINN is further extended to the DSINN. Finally, two simulation examples validate the efficacy of the analytical results.

Optimization for Deep Convolutional Neural Networks: How Slim Can It Go?

The deep convolutional neural networks (CNN) have a vast amount of parameters, especially in the fully connected (FC) layers, which have become a bottleneck for real-time applications where processing latency is high due to computational cost. In this paper, we propose to optimize the FC layers in CNN via making it much slimmer. We make analysis of the statistical distribution of the weights in FC layer, and observe each column follows Gaussian distribution. Regression model analysis of the weights of FC layer based on Akaike information criteria and Bayesian information criterion demonstrates that they have Granger causality, which means the columns are correlated and they follow colored Gaussian distribution. Based on this distribution, we derive a CNN design and optimization theorem for FC layers from information theory point of view. The theorem provides two design criteria, rank and singular values. Further, we show that FC layer with weights of colored Gaussian is more efficient than that of white Gaussian. The optimization criteria is singular-values-based, so we apply singular value decomposition to find the maximal singular values and QR to identify the corresponding columns in FC layer. We evaluate our optimization approach to AlexNet and apply the slimmer CNN to ImageNet classification. Simulation results show our approach performs much better than random dropout. Specifically, with only around $\text{28}{\%}$ of weights, the AlexNet could perform as well as the original AlexNet in terms of top one error and top five error.

РОЗРОБКА СТЕГАНОГРАФІЧНОГО МЕТОДУ, СТІЙКОГО ДО АТАК ПРОТИ ВБУДОВАНОГО ПОВІДОМЛЕННЯ

Features of modern network communications make it necessary to use in the organization of the hidden channel communication of steganographic algorithms that are resistant to loss compression, and leaving the tasks of developing new effective steganographic methods are relevant. The paper develops a new block steganographic method, which is resistant to attacks against the built-in message, including strong attacks. This method preserves the reliability of the perception of the formed quilting due to the mathematical basis used. It is based on a general approach to the analysis of the state and technology of information systems functioning, matrix analysis, perturbation theory. A digital image is treated as a container. The bandwidth of a hidden link that is built using the developed method is equal to n -2 bpp, n×n is the size of the blocks of the container that are obtained by the standard breakdown of its matrix. Such bandwidth is achieved with any algorithmic implementation of the method. Additional information is a binary sequence, it is the result of pre-coding of the information that is hidden. The embedding of additional information is done by using formal container matrix parameters that are insensitive to perturbation. These are singular values of its small blocks (n≤8). Increasing the maximum singular value of the block, which occurs when embedding additional information, leads to the stability of the method to the perturbing action and to ensure the reliability of the perception of the hip. The magnitude of the increase in the maximum singular value is determined using the values obtained by raising the singular values of the block to a natural degree k. Algorithmic implementation of the method requires additional studies to determine the parameter k.

DOA Estimation of Coherent Signals Based on the Sparse Representation for Acoustic Vector-Sensor Arrays

This paper focuses on the problem of the DOA estimation of coherent signals for the acoustic vector-sensor arrays (AVSAs) in the presence of the isotropic ambient noise. We propose a high-resolution DOA estimation method based on the acoustic intensity principle and the sparse representation technique. First, two cross-covariance matrices are constructed by employing the acoustic pressure and particle velocity components of the AVSA, which eliminates the isotropic noise. Then, in order to fully explore the DOA information of the particle velocity components, an augmented matrix is formed based on the two cross-covariance matrices. We observe an interesting fact that the left singular vector corresponding to the maximum singular value of the augmented cross-covariance matrix is the linear combination of all the signal steering vectors. Based on this fact, a high-resolution DOA estimation algorithm is developed via sparsely representing the left singular vector. This method does not require the prior knowledge of the noise variance or the number of signals to construct the sparse representation model. Simulation and experimental results demonstrate the proposed method outperforms the MUSIC method based on the forward/backward spatial smoothing and some existing sparse representation methods in estimation accuracy and angular resolution, especially in the cases of a low signal-to-noise ratio and/or coherent signals with small angular separations.

Independent controller design for MIMO processes based on extended simplified decoupler and equivalent transfer function

Abstract In this paper, a control system with an extended simplified decoupled network is proposed for controlling the interactive multivariable processes. The decoupler is designed using cofactor matrix of the process and incorporated in the control loop which modifies the multivariable processes into multiple single loops. To design the PI/PID controller for each loop of MIMO processes independently, the Equivalent Transfer Function (ETF) of each loop is determined. The ETF is approximated using the static relative gains and the average propagation time between manipulated and controlled variables of the loops. Subsequently the PI/PID controller settings are calculated using SIMC tuning rules. This approach reduces the complexity in mathematical model approximation of decoupled process and improves the performance of the overall process. The maximum singular value uncertainty model is considered to ensure the robustness of the decoupled control system. Simulation results of different dimensional interactive MIMO processes are included.

Current cycle feedback iterative learning control for tracking control of magnetic levitation system

This paper presents the current cycle feedback iterative learning control (CCF-ILC) augmented with the modified proportional integral derivative (PID) controller to improve the trajectory tracking and robustness of magnetic levitation (maglev) system. Motivated by the need to enhance the point to point control of maglev technology, which is widely used in several industrial applications ranging from photolithography to vibration control, we present a novel CCF-ILC framework using plant inversion technique. Modulating the control signal based on the current tracking error, CCF-ILC reduces the dependency on accurate plant model and significantly improves the robustness of the closed loop system by synthesizing the causal filters to counteract the effect of model uncertainty. To assess the stability, we present a maximum singular value based criterion for asymptotic stability of linear iterative system controlled using CCF-ILC. In addition, we prove the monotonic convergence of output sequence in the neighbourhood of reference trajectory. Finally, the proposed control framework is experimentally validated on a benchmark magnetic levitation system through hardware in loop (HIL) testing. Experimental results substantiate that synthesizing CCF-ILC with the feedback controller can significantly improve the trajectory tracking and robustness characteristics of maglev system.

Improved centralised control system for rejection of loop interaction in coupled tank system

ABSTRACTIn practice, majority of the processes are multivariable in nature and control of these processes is very intricate, due to the presence of non-zero diagonal elements in the system. This problem is addressed in the paper with the proposal of a centralised PI controller for controlling the interactive Two Input and Two Output processes. The proposed controller includes a diagonal PI controller and a decoupler element in off diagonal. To design PI controller, a well-known SISO tuning technique SIMC is considered and decoupler elements of off diagonal are designed using coefficient matching principle. The main diagonal controller improves the system performance, while the decoupler rejects the interaction; this improves the overall system. The designed controller performance is evaluated practically on a coupled tank system. The designed control system performance for both servo and regulatory operation is studied. The robustness analysis of the proposed method was analysed using inverse maximum singular value versus frequency plot by incorporating the multiplicative uncertainty in both input and output of the system.

Robust reconstruction of equivalent source method based near-field acoustic holography using an alternative regularization parameter determination approach.

The core of equivalent source method based near-field acoustic holography is to solve the equivalent source strength with the measured pressure and the transfer matrix, which is a typical ill-posed inverse problem. In this work, an explicit formula is proposed in which the regularization parameter is proportional to the product of the hologram distance and the maximum singular value of the transfer matrix. Utilizing the proposed approach, robust acoustic field reconstruction can be achieved even when the hologram distance is 5 times larger than the average microphone spacing.

The reweighted Landweber scheme for the extrapolation of band-limited signals

The extrapolation of a band-limited signal is in terms of a finite known segment of it in the time interval [−T,T] for T > 0 to determine the unknown part of the signal. Extrapolation in the frequency domain is represented by an integral equation and then discretized as a linear system. If T is small, the theoretical ill-posedness of the extrapolation leads to the linear system having ill-posedness because the condition number of the coefficient matrix is large. The condition number of a matrix equals the maximum singular value of the matrix divided by the minimum singular value. Owing to the large condition number, the solution contains large error, relative to the true solution. We use a reweighting method to improve the condition number for the extrapolation of band-limited signal simulations and propose a reweighted Landweber scheme. Simulations validate the proposed method. Effective reconstructions are obtained from the same number of samples in an appropriately small time interval [−T,T].

Neural Networks-Based Distributed Adaptive Control of Nonlinear Multiagent Systems.

The cooperative control problem of nonlinear multiagent systems is studied in this paper. The followers in the communication network are subject to unmodeled dynamics. A fully distributed neural-networks-based adaptive control strategy is designed to guarantee that all the followers are asymptotically synchronized to the leader, and the synchronization errors are within a prescribed level, where some global information, such as minimum and maximum singular value of graph adjacency matrix, is not necessarily to be known. Based on the Lyapunov stability theory and algebraic graph theory, the stability analysis of the resulting closed-loop system is provided. Finally, an numerical example illustrates the effectiveness and potential of the proposed new design techniques.

Automated detection of Parkinson's disease using minimum average maximum tree and singular value decomposition method with vowels

In this study, a novel method to automatically detect Parkinson's disease (PD) using vowels is proposed. A combination of minimum average maximum (MAMa) tree and singular value decomposition (SVD) are used to extract the salient features from the voice signals. A novel feature signal is constructed from 3 levels of MAMa tree in the preprocessing phase. The SVD operator is applied to the constructed signal for feature extraction. Then 50 most distinctive features are selected using relief feature selection technique. Finally, k nearest neighborhood (KNN) with 10-fold cross validation is used for the classification. We have achieved the highest classification accuracy rate of 92.46% using vowels with KNN classifier. The dataset used consists of 3 vowels for each person. To obtain individual results, post processing step is performed and best result of 96.83% is obtained with KNN classifier. The proposed method is ready to be tested with huge database and can aid the neurologists in the diagnosis of PD using vowels.

Change Point Estimation of the Stationary State in Auto Regressive Moving Average Models, Using Maximum Likelihood Estimation and Singular Value Decomposition-based Filtering

In this paper, for the first time, the subject of change point estimation has been utilized in the stationary state of auto regressive moving average (ARMA) (1, 1). In the monitoring phase, in case the features of the question pursue a time series, i.e., ARMA(1,1), on the basis of the maximum likelihood technique, an approach will be developed for the estimation of the stationary state’s change point. To estimate unidentified parameters following the change point, the dynamic linear model’s filtering was utilized on the basis of the singular decomposition of values. The proposed model has wide applications in several fields such as finance, stock exchange marks and rapid production. The results of simulation showed the suggested estimator’s effectiveness. In addition, a real example on stock exchange market is offered to delineate the application.

An image watermarking method based on visual saliency and contourlet transform

For the purpose of enhancing the imperceptibility and the robustness of watermark, a new image watermarking method based on visual saliency and contourlet transform is proposed. In this algorithm, salient object detection and contourlet transform are operated separately on host image. After dividing the transformed low-pass sub-band into nonoverlapping blocks, the saliency values and the energy distribution of the block determine the quantization step-size of each block together. The logarithmic quantization index modulation is modified so as to gain the robustness against the amplitude scaling attack. Then, in each low-pass sub-band block, the maximum singular value is chosen to embed watermark bits using the modified logarithmic quantization index modulation (MLQIM). The watermarked image is obtained after carrying out the inverse contourlet transform. The results of experiments demonstrate that the presented algorithm possesses satisfactory imperceptibility and is superior to other common algorithms in terms of the robustness against various attacks.

Conditioning of the finite volume element method for diffusion problems with general simplicial meshes

The conditioning of the linear finite volume element discretization for general diffusion equations is studied on arbitrary simplicial meshes. The condition number is defined as the ratio of the maximal singular value of the stiffness matrix to the minimal eigenvalue of its symmetric part. This definition is motivated by the fact that the convergence rate of the generalized minimal residual method for the corresponding linear systems is determined by the ratio. An upper bound for the ratio is established by developing an upper bound for the maximal singular value and a lower bound for the minimal eigenvalue of the symmetric part. It is shown that the bound depends on three factors, the number of the elements in the mesh, the mesh nonuniformity measured in the Euclidean metric, and the mesh nonuniformity measured in the metric specified by the inverse diffusion matrix. It is also shown that the diagonal scaling can effectively eliminates the effects from the mesh nonuniformity measured in the Euclidean metric. Numerical results for a selection of examples in one, two, and three dimensions are presented.

The modified sufficient conditions for echo state property and parameter optimization of leaky integrator echo state network

Leaky integrator echo state network (Leaky-ESN), an improved echo state network, is suitable for learning very slow dynamic systems and replaying the learnt system at different speeds. To ensure the echo state property of Leaky-ESN, spectral radius of reservoir connection weight matrix needs to be less than leaking rate, which means that the output feedback of Leaky-ESN is actually ignored. Leaky-ESN without output feedback is equivalent to being a feedforward type neural network. Therefore, in this paper, we consider Leaky-ESN model with output feedback. Firstly, we give the modified sufficient conditions for echo state property, which are actually some inequality constraints about the control parameters (mainly leaking rate, spectral radius of reservoir connection weight matrix and the scaling of output feedback) and the maximum singular values of feedback and output connection weight matrices. Secondly, to reduce the influence of the initial values of the control parameters on Leaky-ESN, we use the barrier method to optimize the control parameters. The barrier method can convert the constrained optimization problem into the unconstrained optimization problem. Newton’s method and its improve method, for example, eigenvalue modification methods, are further used to solve the unconstrained optimization problem and then obtain the control parameters of Leaky-ESN. Finally, Mackey–Glass chaotic time series prediction is selected to validate the method proposed in this paper. Simulation results show that the method proposed in this paper can make Leaky-ESN model more stable and higher approximation precision.

Vision-Based Adaptive Neural Positioning Control of Quadrotor Aerial Robot

In this paper, a new vision-based adaptive control algorithm is proposed for the positioning of a quadrotor aerial robot (QAR) with an onboard pin-hole camera. First, the transformation between the position tracking error and image projection error is constructed through the spherical projection method, and then the regulation of the position error is achieved indirectly by stabilizing the image projection error. To overcome the challenge that the dynamics of QAR is physically underactuated, a backstepping-based approach that synthesizes the Lipschitz condition and natural saturation of the inverse tangent function is proposed. In the proposed adaptive controller, an optimized adaptive neural network (NN) means is designed, where only the square of the NN weight matrix’s maximum singular value, not the weight matrix itself, is estimated. Moreover, to facilitate practical application, a novel inertial matrix estimator is introduced in the tuning laws, so that the accurate QAR rotation inertial information is not required. By Lyapunov theory, it is proved that the image projection error converges to an adjustable region of zero asymptotically. The effectiveness of the proposed algorithm has been confirmed by the experimental results.

On computing the minimum singular value of a tensor sum

Abstract Recently, the Lanczos bidiagonalization method over tensor space has been proposed for computing the maximum and minimum singular values of a tensor sum T. The method over tensor space is practical in memory and has a simple implementation due to recent developments in tensor computations; however, there is still room for improvement in the convergence to the minimum singular value. This study reconstructed an invert Lanczos bidiagonalization method from vector space to tensor space. The resulting algorithm requires solving linear systems at each iteration step. Using standard direct methods, such as the LU decomposition for solving the linear systems requires a huge memory of O(n 6). Therefore, this paper proposes a tensor-structure-preserving direct methods of T whose memory requirements are of O(n 3), which is equivalent to the order of iterative methods. Numerical examples indicate that the number of iterations tends to be much smaller than that of the conventional method.

Capability evaluation of self-location machining algorithm for ultra-precision workpiece based on SVD

In order to further improve the final precision, efficiency and cost-effectiveness of ultra-precision surface modification, and optimize the process direction and process decision-making of ultra-precision self-positioning processing, this paper studies the point cloud fusion process of self-positioning processing algorithm for ultra-precision workpieces. Based on the evaluation, it proposes a self-positioning processing algorithm capability evaluation method based on SVD. Firstly, based on the kinematics method, the matrix representation of point cloud fusion is established. The transformation matrix representation of self-positioning results is established for the translation, rotation and compound motion, respectively. Then the self-positioning point cloud fusion transformation matrix is obtained. A singular value decomposition is performed to obtain a singular value list of the transformation matrix. finally, the largest singular value in the list is used to characterize the self-positioning processing algorithm. By analyzing the free-precision states of a certain type of ultra-precision blade (a total of 1078 sets of free-standing state) it is found that the proposed evaluation index can correctly characterize self-positioning under the condition of independent translation and independent rotation. For the independent translation, the self-positioning processing algorithm can be positioned normally, and the maximum singular deviation value is also less than the pre-set value. For the independent rotation, when the angle is less than 45°, the self-positioning machining can be correctly performed. The singular value difference also approaches zero. Above 45°, the algorithm's self-positioning machining capability deteriorates, and this feature can be correctly captured by the proposed indicators. For the composite motion consisting of translation and rotation, the proposed index shows that about 35% of the cases can be correctly self-positioned, and the rest can not be correctly self-homing. It indicates that the indicators established by the proposed method can correctly characterize the self-positioning machining algorithm.