Minimum Eigenvalue Research Articles

An Adaptive Covariance Matrix Based on Combined Fully Blind Self Adapted Method for Cognitive Radio Spectrum Sensing

The main aim of this paper is to analysis and simulate existing methods such as energy detection, Maximum–Minimum Eigen value detectors (MME), MME with blind two stage detector and compare with the proposed adaptive covariance threshold method. This comparison is being made keeping in mind the complexity and accurateness in the terms of the sensing receiver operating characteristics curve. The influence of signal bandwidth of signal in comparison to the bandwidth of observation is done for every detector. As of the MME detector, the ratio between the bandwidth of the signal and the bandwidth of the observation is observed to be 0.5 when the reasonable values are used. The performance of the adaptive covariance threshold with combined full blind self-adapted detector are simulated on Matlab. The proposed method of detector shows a superior performance values when compared to three individual detectors. The performance metrics of proposed method are performed better than other three individual detector.

Nonlinear form-finding of symmetric cable–strut structures using stiffness submatrices associated with full symmetry subspace

An efficient and nonlinear form-finding method is proposed for symmetric cable–strut structures with complex geometry or many nodes. Expressed in the symmetry-adapted coordinate system, the first block matrix of the symmetry-adapted tangent stiffness matrix is extracted using the full symmetry subspace, which is much smaller-sized and associated with the first irreducible representation of a symmetry group. Then, this stiffness submatrix and the principle of minimum potential energy are adopted for the fast but stable convergence of the initial configuration to the stable configuration. During the form-finding process, the generalized inverse of a matrix and modification for the minimum eigenvalues are employed, to guarantee the positive definiteness of the stiffness submatrix. The form-finding process can start from an arbitrary initial configuration, whereas only certain symmetry group, and the connectivity pattern and the initial lengths of the members should be given in advance. A few numerical examples are illustrated to show the efficiency and accuracy of the form-finding method for cable–strut structures with complex geometry and different symmetry.

A potential post-perovskite province in D″ beneath the Eastern Pacific: evidence from new analysis of discrepant SKS–SKKS shear-wave splitting

SUMMARY Observations of seismic anisotropy in the lowermost mantle—D″—are abundant. As seismic anisotropy is known to develop as a response to plastic flow in the mantle, constraining lowermost mantle anisotropy allows us to better understand mantle dynamics. Measuring shear-wave splitting in body wave phases which traverse the lowermost mantle is a powerful tool to constrain this anisotropy. Isolating a signal from lowermost mantle anisotropy requires the use of multiple shear-wave phases, such as SKS and SKKS. These phases can also be used to constrain azimuthal anisotropy in D″: the ray paths of SKS and SKKS are nearly coincident in the upper mantle but diverge significantly at the core–mantle boundary. Any significant discrepancy in the shear-wave splitting measured for each phase can be ascribed to anisotropy in D″. We search for statistically significant discrepancies in shear-wave splitting measured for a data set of 420 SKS–SKKS event–station pairs that sample D″ beneath the Eastern Pacific. To ensure robust results, we develop a new multiparameter approach which combines a measure derived from the eigenvalue minimization approach for measuring shear-wave splitting with an existing splitting intensity method. This combined approach allows for easier automation of discrepant shear-wave splitting analysis. Using this approach we identify 30 SKS–SKKS event–station pairs as discrepant. These predominantly sit along a backazimuth range of 260°–290°. From our results we interpret a region of azimuthal anisotropy in D″ beneath the Eastern Pacific, characterized by null SKS splitting, and mean delay time of $1.15 \, \mathrm{ s}$ in SKKS. These measurements corroborate and expand upon previous observations made using SKS–SKKS and S–ScS phases in this region. Our preferred explanation for this anisotropy is the lattice-preferred orientation of post-perovskite. A plausible mechanism for the deformation causing this anisotropy is the impingement of subducted material from the Farallon slab at the core–mantle boundary.

Image restoration based on adaptive switching between synthesis and analysis sparse regularisation

Both synthesis and analysis sparse regularisation have been successfully applied to solve various inverse vision problems. The authors find an optimisation model to combine the power of the dual sparse prior models for image restoration. Specifically, for each local patch, adaptive switching on using synthesis or analysis sparse regularisation is performed for better restoration quality. In addition, cluster-specific synthesis and analysis sub-dictionary learning, based on principal component analysis method and sequential minimal eigenvalues algorithm, is incorporated into the joint sparse models to achieve maximum indices gains. The efficient alternating strategy is exploited to solve the optimisation problem. Experimental results highlight the superiority of the proposed approach compared with the state-of-the-art methods, especially in terms of better image structures preservation.

Sensing and throughput analysis of a MU-MIMO based cognitive radio scheme for the Internet of Things

State-of-the-art energy detection (ED) based spectrum sensing requires perfect knowledge of noise power and is vulnerable to noise uncertainty. An eigenvalue-based spectrum sensing approach performs well in such an uncertain environment, but does not mitigate the spectrum scarcity problem, which evolves with the future Internet of Things (IoT) rollout. In this paper, we propose a multi-user multiple-input and multiple-output (MU-MIMO) based cognitive radio scheme for the Internet of Things (CR-IoT) with weighted-eigenvalue detection (WEVD) for the analysis of sensing, system throughput, energy efficiency and expected lifetime. In this scheme, each CR-IoT user is being equipped with MIMO antennas; we calculate the WEVD ratio, which is defined as the ratio between the difference of the maximum eigenvalue and minimum eigenvalue to the sum of the maximum eigenvalue and minimum eigenvalue. This mitigates against the spectrum scarcity problem, enhances system throughput, improves energy efficiency, prolongs expected lifetime and lowers error probability. Simulation results confirm the effectiveness of the proposed scheme; here the WEVD technique demonstrates a better detection gain and enhanced system throughput in comparison to the conventional scheme with eigenvalue based detection (EVD) and ED techniques in a noise uncertainty environment (i.e. SNR < -28). Furthermore, the proposed scheme has a lower energy consumption, prolonged expected lifetime and achieves a low error probability when compared with other schemes like the conventional single-input and single-output (SISO) based CR-IoT scheme with EVD and ED spectrum sensing.

New Metric for Minimum Variance Analysis Validation in the Study of Interplanetary Magnetic Clouds

The aim of this article is to study the minimum variance analysis (MVA) degeneration problem based on the variance space geometry. We propose a mathematical metric to evaluate the separation of the eigenvalues. In the MVA method, a variance space is obtained geometrically using an ellipsoid where the axes are equal to the square root of the eigenvalues of the covariance matrix. The metric is defined as the product between the geometric flattening of the ellipsoid with respect to the three axes. In this article, we present a statistical analysis applied to the distribution of the eigenvalue ratios and the mathematical metric focussed on the study of several interplanetary coronal mass ejections with and without magnetic clouds (MCs). The results show the non-applicability of the ratio between the intermediate and minimum eigenvalues, as well as that around $90\%$ of MC events have values in the $[4.5,19.5]$ range for the defined metric. Our metric is compared with others and we show its robustness in indicating the usefulness of the MVA method to identify the axes of MCs.

A machine learning approach on multiscale texture analysis for breast microcalcification diagnosis

BackgroundScreening programs use mammography as primary diagnostic tool for detecting breast cancer at an early stage. The diagnosis of some lesions, such as microcalcifications, is still difficult today for radiologists. In this paper, we proposed an automatic binary model for discriminating tissue in digital mammograms, as support tool for the radiologists. In particular, we compared the contribution of different methods on the feature selection process in terms of the learning performances and selected features.ResultsFor each ROI, we extracted textural features on Haar wavelet decompositions and also interest points and corners detected by using Speeded Up Robust Feature (SURF) and Minimum Eigenvalue Algorithm (MinEigenAlg). Then a Random Forest binary classifier is trained on a subset of a sub-set features selected by two different kinds of feature selection techniques, such as filter and embedded methods. We tested the proposed model on 260 ROIs extracted from digital mammograms of the BCDR public database. The best prediction performance for the normal/abnormal and benign/malignant problems reaches a median AUC value of 98.16% and 92.08%, and an accuracy of 97.31% and 88.46%, respectively. The experimental result was comparable with related work performance.ConclusionsThe best performing result obtained with embedded method is more parsimonious than the filter one. The SURF and MinEigen algorithms provide a strong informative content useful for the characterization of microcalcification clusters.

Stiffness analysis of cable-driven parallel mechanisms with cables having large sustainable strains

A cable-driven parallel mechanism is driven by a group of cables. Cable-driven parallel mechanisms can use various cables (e.g. steel cables, nylon cables, isoprene rubber cables, and extension springs) with different sustainable strains. This paper studies the stiffness of cable-driven parallel mechanisms with cables having large sustainable strains, aiming to achieve significantly adjustable overall stiffness. The overall stiffness of a cable-driven parallel mechanism can be decomposed into the constant base stiffness and the adjustable strain stiffness. This paper proposes and mathematically proves a theorem that guarantees that the overall stiffness of a cable-driven parallel mechanism at an arbitrary stable pose can be dominated by the adjustable strain stiffness when cable strains are larger than 100%. The theorem employs the minimum eigenvalues of stiffness matrices to characterize the stiffness of cable-driven parallel mechanism. The theorem provides a sufficient condition that guarantees that the overall stiffness of a cable-driven parallel mechanism at an arbitrary stable pose can be significantly adjusted (i.e. the adjustable strain stiffness contributes more than the constant base stiffness in determining the overall stiffness). The theorem is verified through the simulation of a cable-driven parallel mechanism with six degrees of freedom and seven cables.

On the lower bounds for the minimum eigenvalue of the Hadamard product of an M-matrix and its inverse

Abstract Recently, some authors have established a number of inequalities involving the minimum eigenvalue for the Hadamard product of M-matrices. In this paper, we improve these results and give some new lower bounds on the minimum eigenvalue for the Hadamard product of an M-matrix A and its inverse A - 1 {A^{-1}} . Finally, it is shown by the numerical examples that our bounds are also better than some previous results.

New estimation methods for autoregressive process in the presence of white observation noise

This paper presents four new methods for estimating the parameters of an autoregressive (AR) process based on observations corrupted by white noise. The first three methods are iterative, while the last one is non-iterative. One method is designed to achieve an unbiased estimation of the AR parameters by undermining the destructive impact of observation noise in terms of utilizing the null space of the AR parameter vector. Another one uses both low- and high-order Yule-Walker equations to construct a constrained least squares optimization problem, in which the variance of observation noise is estimated by alternating between two equations. One more method exploits an approximation which leads to reducing the problem of estimating the AR parameters with arbitrary order p to estimating just two parameters, while the last one estimates the variance of the observation noise using the minimum eigenvalue of the enlarged autocorrelation matrix. The performance of the proposed methods is evaluated in terms of various numerical examples, which demonstrate their superiority in terms of accuracy and robustness against the observation noise compared to state-of-the-art existing methods in most simulation examples. It makes the proposed methods a good fit for practical analysis of data contaminated by observation noise, when AR modeling is applicable, and gives a range of choices of methods for different data analysis situations.

Symmetric Peaks-Based Spectrum Sensing Algorithm for Detecting Modulated Signals

Cognitive radio is considered an effective solution to spectrum shortages, which has been a significant issue in the next generation of wireless communications. In this paper, we focus on spectrum sensing under a low signal-to-noise-ratio (SNR) and noise fluctuation and propose a symmetric peaks-based spectrum sensing algorithm for modulated signals. First, we analyze the characteristics of the cyclic autocorrelation function of modulated signals, and construct a detection domain for detecting primary users based on the characteristics of the cyclic autocorrelation function of primary signals. Then, we introduce the significance level factor into the spectrum sensing, and develop a symmetric peaks criterion. Following this criterion, we propose a symmetric peaks-based spectrum sensing algorithm. Finally, we give the probabilities of detection and false alarm of the spectrum sensing algorithm, discuss the effect of the significance level factor on the spectrum sensing performance, and compare the complexity of the algorithm with that of other algorithms. The spectrum sensing algorithm proposed does not require any prior knowledge of primary user signals or noise in the systems, and can sense modulated signals under very low SNR. Simulation results are provided to verify the performance of the algorithm proposed under a low SNR and noise fluctuation. Compared with the maximum and minimum eigenvalue (MME) algorithm, frequency domain autocorrelation-based (FD-AC) algorithm and statistical knowledge autocorrelation-based (SKAB) algorithm, it improves about 4 dB margin in SNR.

A Comparative Study of Feature Detection Techniques for Navigation of Visually Impaired Person in an Indoor Environment

A development of automatic location identification and tracking system for visually impaired/ challenged person is a very challenging task in an indoor environment. In this paper, the comprehensive study of different feature detection and matching techniques namely, Minimum Eigenvalue (MinEigen) algorithm, Harris–Stephens (Harris) algorithm, Speeded Up Robust Features (SURF), Features from Accelerated Segment Test (FAST), Binary Robust Invariant Scalable Keypoints (BRISK) and Maximally Stable Extremal Regions (MSER) is presented. These algorithms are employed to detect and match the features of an image and retrieve the best matched image. Based on our experiments, we compare those algorithms on parameters such as sum of square difference (SDD), precision, recall, number of detected, matched features and processing time. Empirically, we have found that SURF algorithm produce minimum SSD score to achieve best matching. The MSER and MinEign algorithm extracts high and low number of features respectively. In respect of processing time, BRISK takes maximum and FAST method takes minimum time when compared to the other algorithms.

Robust adaptive beamforming for MIMO radar in the presence of covariance matrix estimation error and desired signal steering vector mismatch

Owing to covariance matrix estimation error, desired signal steering vector mismatch, and the existence of target signal in training samples, most of adaptive beamforming algorithms suffer from a great performance degradation. Aim at this, this study proposes a robust adaptive beamforming algorithm for multiple-input-multiple-output radar. To be specific, the sample covariance matrix is replaced by the reconstructed covariance matrix, to narrow the difference between the maximum and minimum noise eigenvalues. In addition, the diagonal loading technique is applied to correct the mismatched desired signal steering vector by maximising the output signal-to-interference-plus-noise ratio of adaptive beamformer, and a simple closed-form solution to loading factor can be further obtained. Computer simulation results demonstrate that the proposed algorithm can efficiently improve the robustness of adaptive beamformer against both covariance matrix estimation error and desired signal steering vector mismatch.

On the Matrix Condition of Phylogenetic Tree.

Phylogenetic comparative analyses use trees of evolutionary relationships between species to understand their evolution and ecology. A phylogenetic tree of n taxa can be algebraically transformed into an n by n squared symmetric phylogenetic covariance matrix C where each element in C represents the affinity between extant species i and extant species j. This matrix C is used internally in several comparative methods: for example, it is often inverted to compute the likelihood of the data under a model. However, if the matrix is ill-conditioned (ie, if , defined by the ratio of the maximum eigenvalue of C to the minimum eigenvalue of C, is too high), this inversion may not be stable, and thus neither will be the calculation of the likelihood or parameter estimates that are based on optimizing the likelihood. We investigate this potential issue and propose several methods to attempt to remedy this issue.

Improving the condition number of estimated covariance matrices

High dimensional error covariance matrices and their inverses are used to weight the contribution of observation and background information in data assimilation procedures. As observation error covariance matrices are often obtained by sampling methods, estimates are often degenerate or ill-conditioned, making it impossible to invert an observation error covariance matrix without the use of techniques to reduce its condition number. In this paper, we present new theory for two existing methods that can be used to ‘recondition’ any covariance matrix: ridge regression and the minimum eigenvalue method. We compare these methods with multiplicative variance inflation, which cannot alter the condition number of a matrix, but is often used to account for neglected correlation information. We investigate the impact of reconditioning on variances and correlations of a general covariance matrix in both a theoretical and practical setting. Improved theoretical understanding provides guidance to users regarding method selection, and choice of target condition number. The new theory shows that, for the same target condition number, both methods increase variances compared to the original matrix, with larger increases for ridge regression than the minimum eigenvalue method. We prove that the ridge regression method strictly decreases the absolute value of off-diagonal correlations. Theoretical comparison of the impact of reconditioning and multiplicative variance inflation on the data assimilation objective function shows that variance inflation alters information across all scales uniformly, whereas reconditioning has a larger effect on scales corresponding to smaller eigenvalues. We then consider two examples: a general correlation function, and an observation error covariance matrix arising from interchannel correlations. The minimum eigenvalue method results in smaller overall changes to the correlation matrix than ridge regression but can increase off-diagonal correlations. Data assimilation experiments reveal that reconditioning corrects spurious noise in the analysis but underestimates the true signal compared to multiplicative variance inflation.

A hybrid PSO-ABC algorithm for optimal load shedding and improving voltage stability

In this paper, a hybrid method is proposed for reducing the amount of load shedding and voltage collapse. The hybrid method is the combination of particle swarm optimisation (PSO) algorithm and artificial bee colony (ABC) algorithm. Both algorithms equally contribute in the paper to determine the optimal load shed values for improving the voltage stability of the power system. Here, PSO is used to determine the weak buses in the system whereas ABC computes the optimal amount of load shed value to be cut for voltage stability purpose. They work on different fitness functions as per the requirements of their purpose. The appropriate buses for load shedding are selected based on the sensitivity of minimum eigenvalue of load flow Jacobian with respect to the load shed. The proposed method based on PSO and ABC is implemented in MATLAB working platform and its performance is tested with six bus and IEEE 14 bus bench mark test systems. From the simulations, the performance of the proposed method is analysed and compared with various techniques in terms of sensitivity of minimum eigenvalues, voltage profile and load power. Through comparison performance, it is showed that the proposed method ensures voltage stability with minimum load shedding.

A Design Method of Optimal PID-Based Repetitive Control Systems

This paper is concerned with the design of a PID-based repetitive control strategy for a strictly proper plant with requirements of high-precision tracking performance for periodic signals and good rejecting performance for an external disturbance with a finite frequency range. The PID-based controller consists of a PID controller and a repetitive controller connected in series, and its control parameters are optimized to meet the performance requirements. First, utilizing Youla–Kucera Parameterization, the necessary and sufficient conditions for the existence of the PID-based repetitive controller are derived. Second, from the requirements of the control performance and the analysis of the sensitivity function, the description of the PID-based repetitive controller is deduced. Third, the design of PID control parameters depends on the stability of closed-loop system and the attenuation performance. By introducing an arbitrarily small relaxation variable and applying the $H_\infty $ control method, the design problem is transformed into a generalized eigenvalue minimization problem (GVEP) under linear matrix inequality (LMI) constraints. In addition, the largest cutoff frequency in the repetitive controller is also achieved by solving a GVEP. Finally, simulations are applied to examine the validity and efficacy of the proposed method.

SAR Images Co-registration Based on Gradient Descent Optimization

The target of the registration process is to get the disagreement between two captured images for the same area to candidate the transformation matrix that is used to map the points in one image to its congruent in the other image for the same area. A dynamic method is demonstrated in this paper to improve registration process of SAR images. At first, smoothing filtering is used for noise reduction based on gaussian-kernel filter to set aside the pursue-up amplification of noise. Then; area based matching method, cross correlation, is used to perform a coarse registration. The output of the coarse registration is directly applied to the regular step gradient descent (RSGD) optimizer as a fine registration process. The performance of the demonstrated method was evaluated via comparison with the common used corner detectors (Harris, Minimum Eigenvalues, and FAST). Mean square error (MSE) and peak signal-to-noise ratio (PSNR) are the main factors for the comparison. The results show that the demonstrated approach preserves the robustness of the registration process and minimizes the image noise.

Interaction Matrix Based Analysis and Asymptotic Cooperative Control of Multi-agent Systems

In this paper, we investigate a decentralized asymptotic cooperative control problem of multi-agent systems with leader-follower configuration. We firstly develop a new method using a proposed “interaction matrix” for the analysis of cooperation convergence of multi-agent systems, i.e. both consensus of the agents states and trajectory tracking of the whole group can be instantaneously concluded only by observing the minimum eigenvalue of the interaction matrix. For a multi-agent system, the external given desired trajectory can be partially obtained (through sensing or detecting) by the leaders, but higher-order derivatives such as acceleration and jerk of the desired trajectory cannot be obtained. In this case, by using some conventional control methods, the trajectory tracking performance is always not satisfactory when a trajectory varies aggressively w.r.t. time. For the sake of asymptotic tracking of an arbitrary given external trajectory of a multi-agent system, we develop a nonlinear cooperative controller based on the robust integral of signum of cooperative error (RISCE) technique, where the interaction matrix is used. The simulation results show asymptotic convergence of cooperation by using the proposed control, and better performance compared to composited nonlinear feedback based PD (CNF-PD) control.

On alternating paths and the smallest positive eigenvalue of trees

In this article, we consider the class of tress on a fixed number of vertices. We consider the problem of finding trees with first four minimum smallest positive eigenvalues. First we obtain the upper and lower bounds on number of alternating paths in a tree. It is shown that the smallest positive eigenvalue of a tree is related to the number of alternating paths in it. With the help of combinatorial arguments, the trees with the maximum, second maximum and third maximum number of alternating paths are derived. Subsequently, the unique trees with the second minimum, third minimum and fourth minimum smallest positive eigenvalue are characterized.