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In order to solve the problem of the low action recognition accuracy of passengers' unsafe behaviors caused by redundant joints, this study proposes an efficient recognition method based on a Kinect sensor. The method uses the pelvis as the starting point of the vector and high-frequency bone joints as the end point to construct the recognition feature vector. The joint angle difference between actions is obtained by using the cosine law, and the initial test result is converted into action similarity combined with the DTW similarity algorithm. Considering the combination of 3 angle features and 4 joint feature selection methods, 12 combined recognition models are formed. A comparative experiment was carried out to identify five types of unsafe behaviors of metro passengers-punch, one-armed call for help, arms for help, trip forward and trip backwards. The results show that the overall selection of joints has a poor similarity effect and cannot achieve the purpose of recognition. The overall recognition model effect of the local "pelvis divergence method" is higher than that of the local "adjacent joint method", and the local "pelvis divergence method" has the highest recognition result of the maximum angle difference model, and the recognition results of the five unsafe behaviors are 86.9%, 89.2%, 85.5%, 86.7%, and 88.3%, respectively, and the recognition accuracy of this method is 95.7%, indicating the feasibility of the model. The recognition results are more concentrated and more stable, which significantly improves the recognition rate of metro passengers' unsafe behavior.

This paper presents a hybrid variational quantum algorithm that finds a random eigenvector of a unitary matrix with a known quantum circuit. The algorithm is based on the SWAP test on trial states generated by a parametrized quantum circuit. The eigenvector is described by a compact set of classical parameters that can be used to reproduce the found approximation to the eigenstate on demand. This variational eigenvector finder can be adapted to solve the generalized eigenvalue problem, to find the eigenvectors of normal matrices and to perform quantum principal component analysis on unknown input mixed states. These algorithms can all be run with low-depth quantum circuits, suitable for an efficient implementation on noisy intermediate-scale quantum computers and, with some restrictions, on linear optical systems. In full-scale quantum computers, where there might be optimization problems due to barren plateaus in larger systems, the proposed algorithms can be used as a primitive to boost known quantum algorithms. Limitations and potential applications are discussed. [ABSTRACT FROM AUTHOR]

Real partially symmetric tensors arise from the strong ellipticity condition problem in solid mechanics and the entanglement problem in quantum physics. In this paper, we try to compute the smallest V-singular value of partially symmetric tensors with orders (p, q). This is a unified notion in a broad sense that, when (p , q) = (2 , 2) , the V-singular value coincides with the notion of M-eigenvalue. To do that, we propose a generalized inverse power method with a shift variable to compute the smallest V-singular value and eigenvectors. Global convergence of the algorithm is established. Furthermore, it is proven that the proposed algorithm always converges to the smallest V-singular value and the associated eigenvectors. Several numerical experiments show the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The quantum phase estimation algorithm has been utilized by a variety of quantum algorithms, most notably Shor's algorithm, to obtain information regarding the period of a function that is appropriately encoded into a unitary operator. In many cases, it is desired to estimate whether a specific state exhibits a certain pattern quickly. In this paper, we exhibit a methodology based on the QPE algorithm to identify certain patterns. In particular, starting from a properly encoded state, we demonstrate how to construct unitary operators whose eigenvectors correspond to states with proper diagonals. QPE will then output an eigenphase equal to zero with certainty for these states, thereby identifying this class of matrices. For partial matches, our algorithm, based on the tolerance threshold used, will show areas of high similarity, and it will outperform classical ones when the number of mismatches defined by the tolerance is significantly low when compared to the size of the diagonal. [ABSTRACT FROM AUTHOR]

Currently, magnetic gradient tensor-based localization methods face challenges such as significant errors in geomagnetic field estimation, susceptibility to local optima in optimization algorithms, and inefficient performance. In addressing these issues, this article propose a two-point localization method under the constraint of overlaying geometric invariants. This method initially establishes the relationship between the target position and the magnetic gradient tensor by substituting an intermediate variable for the magnetic moment. Exploiting the property of the eigenvector corresponding to the minimum absolute eigenvalue being perpendicular to the target position vector, this constraint is superimposed to formulate a nonlinear system of equations of the target's position. In the process of determining the target position, the Nara method is employed for obtaining the initial values, followed by the utilization of the Levenberg–Marquardt algorithm to derive a precise solution. Experimental validation through both simulations and experiments confirms the effectiveness of the proposed method. The results demonstrate its capability to overcome the challenges faced by a single-point localization method in the presence of some errors in geomagnetic field estimation. In comparison to traditional two-point localization methods, the proposed method exhibits the highest precision. The localization outcomes under different noise conditions underscore the robust noise resistance and resilience of the proposed method. [ABSTRACT FROM AUTHOR]

A novel unconstrained optimization model named weighted trace-penalty minimization (WTPM) is proposed to address the extreme eigenvalue problem arising from the full configuration interaction (FCI) method. Theoretical analysis shows that the global minimizers of the WTPM objective function are the desired eigenvectors, rather than the eigenspace. Analyzing the condition number of the Hessian operator in detail contributes to the determination of a near-optimal weight matrix. With the sparse feature of FCI matrices in mind, the coordinate descent (CD) method is adapted to WTPM and results in the WTPM-CD method. The reduction of computational and storage costs in each iteration shows the efficiency of the proposed algorithm. Finally, the numerical experiments demonstrate the capability to address large-scale FCI matrices. [ABSTRACT FROM AUTHOR]

An ordered pair Σ = (Σu, σ) is called the signed graph, where Σu = (V,E) is a underlying graph and σ is a signed mapping, called signature, from E to the sign set {+, -}. The splitting signed graph Γ(Σ) of a signed graph Σ is defined as, for every vertex u ∈ V (Σ), take a new vertex u′. Join u′ to all the vertices of Σ adjacent to u such that σΓ(u′v) = σ(u′v), u ∈ N(v). The objective of this paper is to propose an algorithm for the generation of a splitting signed graph, a splitting root signed graph from a given signed graph using Matlab. Additionally, we conduct a spectral analysis of the resulting graph. Spectral analysis is performed on the adjacency and laplacian matrices of the splitting signed graph to study its eigenvalues and eigenvectors. A relationship between the energy of the original signed graph Σ and the energy of the splitting signed graph Γ(Σ) is established. [ABSTRACT FROM AUTHOR]

The locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm is a popular approach for computing a few smallest eigenvalues and the corresponding eigenvectors of a large Hermitian positive definite matrix A . In this work, we propose a mixed precision variant of LOBPCG that uses a (sparse) Cholesky factorization of A computed in lower precision as the preconditioner. To further enhance performance, a mixed precision orthogonalization strategy is proposed. To analyze the impact of reducing precision in the preconditioner on performance, we carry out a rounding error and convergence analysis of PINVIT, a simplified variant of LOBPCG. Our theoretical results predict and our numerical experiments confirm that the impact on convergence remains marginal. In practice, our mixed precision LOBPCG algorithm typically reduces the computation time by a factor of 1.4 – 2.0 on both CPUs and GPUs. [ABSTRACT FROM AUTHOR]

Graph matching aims at finding the vertex correspondence between two unlabeled graphs that maximizes the total edge weight correlation. This amounts to solving a computationally intractable quadratic assignment problem. In this paper, we propose a new spectral method, graph matching by pairwise eigen-alignments (GRAMPA). Departing from prior spectral approaches that only compare top eigenvectors, or eigenvectors of the same order, GRAMPA first constructs a similarity matrix as a weighted sum of outer products between all pairs of eigenvectors of the two graphs, with weights given by a Cauchy kernel applied to the separation of the corresponding eigenvalues, then outputs a matching by a simple rounding procedure. The similarity matrix can also be interpreted as the solution to a regularized quadratic programming relaxation of the quadratic assignment problem. For the Gaussian Wigner model in which two complete graphs on n vertices have Gaussian edge weights with correlation coefficient 1 - σ 2 , we show that GRAMPA exactly recovers the correct vertex correspondence with high probability when σ = O (1 log n) . This matches the state of the art of polynomial-time algorithms and significantly improves over existing spectral methods which require σ to be polynomially small in n. The superiority of GRAMPA is also demonstrated on a variety of synthetic and real datasets, in terms of both statistical accuracy and computational efficiency. Universality results, including similar guarantees for dense and sparse Erdős–Rényi graphs, are deferred to a companion paper. [ABSTRACT FROM AUTHOR]

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In a recent paper, a new method was proposed to find the common invariant subspaces of a set of matrices. This paper investigates the more general problem of putting a set of matrices into block triangular or block-diagonal form simultaneously. Based on common invariant subspaces, two algorithms for simultaneous block triangularization and block diagonalization of sets of matrices are presented. As an alternate approach for simultaneous block diagonalization of sets of matrices by an invertible matrix, a new algorithm is developed based on the generalized eigenvectors of a commuting matrix. Moreover, a new characterization for the simultaneous block diagonalization by an invertible matrix is provided. The algorithms are applied to concrete examples using the symbolic manipulation system Maple. [ABSTRACT FROM AUTHOR]

Solving eigenproblem of the Laplacian matrix of a fully connected weighted graph has wide applications in data science, machine learning, and image processing, etc. However, this is very challenging because it involves expensive matrix operations. Here, an efficient quantum algorithm is proposed to solve it. Specifically, the optimal Hamiltonian simulation technique based on the block‐encoding framework is adopted to implement the quantum simulation of the Laplacian matrix. Then, the eigenvalues and eigenvectors of the Laplacian matrix are extracted by the quantum phase estimation algorithm. The core of this entire algorithm is to construct a block‐encoding of the Laplacian matrix. To achieve this, how to construct block‐encoding of operators containing the information of the weight matrix and the degree matrix, respectively are shown in detail, and the block‐encoding of the Laplacian matrix is further obtained. Compared with its classical counterpart, this algorithm has a polynomial speedup on the number of vertices and an exponential speedup on the dimension of each vertex. It is also shown that this algorithm can be extended to solve the eigenproblem of symmetric (non‐symmetric) normalized Laplacian matrix. [ABSTRACT FROM AUTHOR]

We propose a wave operator method to calculate eigenvalues and eigenvectors of large parameter-dependent matrices using an adaptative active subspace. We consider a Hamiltonian that depends on external adjustable or adiabatic parameters, using adaptative projectors that follow the successive eigenspaces when the adjustable parameters are modified. The method can also handle non-Hermitian Hamiltonians. An iterative algorithm is derived and tested through comparisons with a standard wave operator algorithm using a fixed active space and with a standard block-Davidson method. The proposed approach is competitive; it converges within a few dozens of iterations at constant memory cost. We first illustrate the abilities of the method on a 4D-coupled oscillator model Hamiltonian. A more realistic application to molecular photodissociation under intense laser fields with varying intensity or frequency is also presented. Maps of photodissociation resonances of H 2 + in the vicinity of exceptional points are calculated as an illustrative example. [ABSTRACT FROM AUTHOR]

We introduce an approach for exploring eigenvector localization phenomena for a class of (unbounded) selfadjoint operators. More specifically, given a target region and a tolerance, the algorithm identifies candidate eigenpairs for which the eigenvector is expected to be localized in the target region to within that tolerance. Theoretical results, together with detailed numerical illustrations of them, are provided that support our algorithm. A partial realization of the algorithm is described and tested, providing a proof of concept for the approach. [ABSTRACT FROM AUTHOR]

We describe a strategy for solving nonlinear eigenproblems numerically. Our approach is based on the approximation of a vector‐valued function, defined as solution of a non‐homogeneous version of the eigenproblem. This approximation step is carried out via the minimal rational interpolation method. Notably, an adaptive sampling approach is employed: the expensive data needed for the approximation is gathered at locations that are optimally chosen by following a greedy error indicator. This allows the algorithm to employ computational resources only where where "most of the information" on not‐yet‐approximated eigenvalues can be found. Then, through a post‐processing of the surrogate, the sought‐after eigenvalues and eigenvectors are recovered. Numerical examples are used to showcase the effectiveness of the method. [ABSTRACT FROM AUTHOR]

In max-plus algebra, some algorithms for determining the eigenvector of irreducible matrices are the power algorithm and the Kleene star algorithm. In this research, a modified Kleene star algorithm will be discussed to compensate for the disadvantages of the Kleene star algorithm. The Kleene star algorithm's time complexity is O (n (n !)) , and the new Kleene star algorithm's time complexity is O (n 4) , while the power algorithm's time complexity cannot be calculated. This research also applies max-plus algebra in a railroad network scheduling problem, constructing a graphical user interface to perform schedule calculations quickly and easily. [ABSTRACT FROM AUTHOR]

This article presents a maximum torque per ampere strategy for a five-phase synchronous reluctance drive. The approach is developed considering general machine parameters and is formalized as a constrained optimization problem. The optimal solution is found analytically by using Lagrange’s multipliers method and is based on the computation of the eigenvalues and eigenvectors of the inductance derivatives matrix. The proposed approach is evaluated both numerically and experimentally. It is also compared with other current references control strategies, effectively showing a reduction of the machine rms currents for the same developed torque. The same approach can also be extended to machines with a different number of phases. [ABSTRACT FROM AUTHOR]

Point cloud data model can be obtained by 3D laser scanning technology, but due to the roughness, surface texture and measurement environment of the object, the original point cloud data model usually contains a large number of noise points. Aiming at the problem that the complex noises in point cloud data model are difficult to remove, a point cloud denoising algorithm with geometric feature preservation is proposed. Firstly, the tensor voting matrix of points and their neighboring points in point cloud was calculated, and the eigenvalues and eigenvectors of the matrix were solved; secondly, the diffusion tensor based on the eigenvalues and eigenvectors was constructed, and the anisotropic diffusion equation based on the diffusion tensor was adopted to filter the noises so as to realize the initial denoising of point cloud; thirdly, the curvature factor and the density of data points in the initial denoising point cloud were defined, and the objective function of fuzzy c-means (FCM) clustering method was constructed by weighting the degree factor. Finally, the feature weighted FCM algorithm was used to further delete the noises in the point cloud, and the final accurate denoising was achieved. The experimental results show that the geometric feature preserving denoising algorithm has good denoising effect on both public point cloud, cultural relic point cloud and outdoor point cloud, so the proposed denoising algorithm is an effective point cloud denoising algorithm. [ABSTRACT FROM AUTHOR]

An anomaly detection algorithm combining eigenvalues and eigenvectors in random matrix is proposed, which can solve the problem that present algorithms based on random matrix theory overly rely on eigenvalues and ignore useful information contained in eigenvectors. Firtsly, the time window method is used to select the original data of rolling bearing, and the sampling feature matrix is constructed by extracting bearing feature. Secondly, the eigenvalues and principal eigenvector of sampling feature matrix are investigated and combined to construct comprehensive feature index and its corresponding threshold. Finally, an anomaly detection based on comprehensive feature index is proposed to detect the early anomaly of rolling bearing. The application research is carried out by using bearing datasets of intelligent maintenance center and Xi'an Jiaotong University; the result shows that compared with the single eigenvalue index and kurtosis index, the algorithm based on the comprehensive feature index can detect the abnormal condition of bearing earlier. And the accuracy and effectiveness of the anomaly detection algorithm are proved through spectrum analysis, which provides guidance and basis for fault warning and equipment maintenance. [ABSTRACT FROM AUTHOR]

This article proposes a low-latency parallel Jacobi-method-based algorithm for computing eigenvalues and eigenvectors of $n\times n$ -sized real-symmetric matrix. It is a coordinate rotations digital-computer (CORDIC)-based iterative algorithm that comprises multiple rotations and hence the key contribution of our work is to reduce the time cost of each rotation. Thus, alleviating the total latency for computing eigenvalues and eigenvectors using the parallel Jacobi method. Based on this proposed algorithm and additional architectural optimizations, a new low-latency and highly accurate VLSI-architecture has been presented in this manuscript for computing eigenvalues and eigenvectors of real-symmetric matrix. Subsequently, this work proposes a reconfigurable algorithm and its VLSI-architecture for computing eigenvalues and eigenvectors of complex Hermitian (CH), complex skew-Hermitian (CSH), and real skew-symmetric (RSS) matrices. Performance analysis of the proposed architectures has demonstrated minimal error-percentage of 0.0106% which is adequate for the wide range of real-time applications. The proposed architectures are hardware implemented on Zynq Ultrascale+ field-programmable gate array (FPGA)-board that consumed short latency of $9.377~\mu \text{s}$ while operating at maximum clock frequency of 172.75 MHz. Comparison of our implementation results with the reported works showed that the proposed architecture incurs 43.75% lower latency and 89.4% better accuracy than the state-of-the-art implementation. [ABSTRACT FROM AUTHOR]

Compressive covariance estimation has arisen as a class of techniques whose aim is to obtain second-order statistics of stochastic processes from compressive measurements. Recently, these methods have been used in various image processing and communications applications, including denoising, spectrum sensing, and compression. Notice that estimating the covariance matrix from compressive samples leads to ill-posed minimizations with severe performance loss at high compression rates. In this regard, a regularization term is typically aggregated to the cost function to consider prior information about a particular property of the covariance matrix. Hence, this paper proposes an algorithm based on the projected gradient method to recover low-rank or Toeplitz approximations of the covariance matrix from compressive measurements. The proposed algorithm divides the compressive measurements into data subsets projected onto different subspaces and accurately estimates the covariance matrix by solving a single optimization problem assuming that each data subset contains an approximation of the signal statistics. Furthermore, gradient filtering is included at every iteration of the proposed algorithm to minimize the estimation error. The error induced by the proposed splitting approach is analytically derived along with the convergence guarantees of the proposed method. The proposed algorithm estimates the covariance matrix of hyperspectral images from synthetic and real compressive samples. Extensive simulations show that the proposed algorithm can effectively recover the covariance matrix of hyperspectral images from compressive measurements with high compression ratios ($8-15\%$ approx) in noisy scenarios. Moreover, simulations and theoretical results show that the filtering step reduces the recovery error up to twice the number of eigenvectors. Finally, an optical implementation is proposed, and real measurements are used to validate the theoretical findings. [ABSTRACT FROM AUTHOR]

It is common for communities in real-world networks to possess hierarchical and overlapping structures, which make community detection even more challenging. In this paper, by investigating consensus process of the classical DeGroot model in opinion dynamics, we propose a novel method based on the cumulative opinion distance (COD) to discover hierarchical and overlapping communities. It is shown that this method is different from those classical algorithms relying on static fitness metrics that depict the inhomogeneous connectivity across the network. The proposed method is validated from two aspects. First, by estimating the eigenvectors of adjacency matrices, we investigate the detectability limit of our algorithms on random networks, which together with the results concerning the convergence speed of consensus guarantees the performance of our method theoretically. Second, experiments on both large scale real-world networks and artificial benchmarks show that our method is very effective and competitive on hierarchical modular graphs. In particular, it outperforms the state-of-the-art algorithms on overlapping community detection. [ABSTRACT FROM AUTHOR]

We describe an algorithm to compute the extremal eigenvalues and corresponding eigenvectors of a symmetric matrix which is based on solving a sequence of Quadratic Binary Optimization problems. This algorithm is robust across many different classes of symmetric matrices; It can compute the eigenvector/eigenvalue pair to essentially any arbitrary precision, and with minor modifications, can also solve the generalized eigenvalue problem. Performance is analyzed on small random matrices and selected larger matrices from practical applications. [ABSTRACT FROM AUTHOR]

We study and derive algorithms for nonlinear eigenvalue problems, where the system matrix depends on the eigenvector, or several eigenvectors (or their corresponding invariant subspace). The algorithms are derived from an implicit viewpoint. More precisely, we change the Newton update equation in a way that the next iterate does not only appear linearly in the update equation. Although the modifications of the update equation make the methods implicit, we show how corresponding iterates can be computed explicitly. Therefore, we can carry out steps of the implicit method using explicit procedures. In several cases, these procedures involve a solution of standard eigenvalue problems. We propose two modifications, one of the modifications leads directly to a well-established method (the self-consistent field iteration) whereas the other method is to our knowledge new and has several attractive properties. Convergence theory is provided along with several simulations which illustrate the properties of the algorithms. [ABSTRACT FROM AUTHOR]

We describe an implementation of a polynomial system solver to compute the approximate solutions of a 0-dimensional polynomial system with finite precision p-adic arithmetic. We also describe an improvement to an algorithm of Caruso, Roe, and Vaccon for calculating the eigenvalues and eigenvectors of a p-adic matrix. [ABSTRACT FROM AUTHOR]

In this article, we proposed a multiparameter joint estimation algorithm based on the dual-polarized cylindrical conformal array (DCCA) in the presence of mutual coupling. Using the characteristic of the dual-polarized cylindrical conformal array, 2D direction-of-arrival (DOA) estimation can be divided into 1D estimations of elevation and azimuth. Sensors on the boundary of the DCCA are set as auxiliary sensors to eliminate the influence of mutual coupling. Then, elevation can be estimated by the generalized eigenvalues utilizing signal subspace eigenvectors (GEESE). After that, polarization sensitivity can be eliminated by projection transformation and the proposed dual-polarized forward-backward smoothing algorithm. Consequently, a dual-polarized spatial spectrum can be developed to estimate the azimuth based on the estimated elevation. Furthermore, the angles of the signals can be reestimated to improve the accuracy of DOA estimation. Simulation results confirm the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The generalized eigenvalue (GE) problems are of particular importance in various areas of science engineering and machine learning. We present a variational quantum algorithm for finding the desired generalized eigenvalue of the GE problem, A | ψ ⟩ = λ B | ψ ⟩ , by choosing suitable loss functions. Our approach imposes the superposition of the trial state and the obtained eigenvectors with respect to the weighting matrix B on the Rayleigh quotient. Furthermore, both the values and derivatives of the loss functions can be calculated on near-term quantum devices with shallow quantum circuit. Finally, we propose a full quantum generalized eigensolver (FQGE) to calculate the minimal generalized eigenvalue with quantum gradient descent algorithm. As a demonstration of the principle, we numerically implement our algorithms to conduct a 2-qubit simulation and successfully find the generalized eigenvalues of the matrix pencil (A , B) . The numerically experimental result indicates that FQGE is robust under Gaussian noise. [ABSTRACT FROM AUTHOR]

The quartic eigenvalue problem (λ4A+λ3B+λ2C+λD+E)x = 0 naturally arises in a plethora of applications, such as when solving the Orr–Sommerfeld equation in the stability analysis of the Poiseuille flow, in theoretical analysis and experimental design of locally resonant phononic plates, modeling a robot with electric motors in the joints, calibration of catadioptric vision system, or, for example, computation of the guided and leaky modes of a planar waveguide. This article proposes a new numerical method for the full solution (all eigenvalues and all left and right eigenvectors) that, starting with a suitable linearization, uses an initial, structure-preserving reduction designed to reveal and deflate a certain number of zero and infinite eigenvalues before the final linearization is forwarded to the QZ algorithm. The backward error in the reduction phase is bounded column wise in each coefficient matrix, which is advantageous if the coefficient matrices are graded. Numerical examples show that the proposed algorithm is capable of computing the eigenpairs with small residuals, and that it is competitive with the available state-of-the-art methods. [ABSTRACT FROM AUTHOR]

As we all know, the model mismatch, primarily when the desired signal exists in the training data, or when the sample data is used for training, will seriously affect algorithm performance. This paper combines the subspace algorithm based on direction of arrival (DOA) estimation with the adaptive beamforming. It proposes a reconstruction algorithm based on the interference plus noise covariance matrix (INCM). Firstly, the eigenvector of the desired signal is obtained according to the eigenvalue decomposition of the subspace algorithm, and the eigenvector is used as the estimated value of the desired signal steering vector (SV). Then the INCM is reconstructed according to the estimated parameters to remove the adverse effect of the desired signal component on the beamformer. Finally, the estimated desired signal SV and the reconstructed INCM are used to calculate the weight. Compared with the previous work, the proposed algorithm not only improves the performance of the adaptive beamformer but also dramatically reduces the complexity. Simulation experiment results show the effectiveness and robustness of the proposed beamforming algorithm. [ABSTRACT FROM AUTHOR]

Finding the common principal component (CPC) for ultra-high dimensional data is a multivariate technique used to discover the latent structure of covariance matrices of shared variables measured in two or more k conditions. Common eigenvectors are assumed for the covariance matrix of all conditions, only the eigenvalues being specific to each condition. Stepwise CPC computes a limited number of these CPCs, as the name indicates, sequentially and is, therefore, less time-consuming. This method becomes unfeasible when the number of variables p is ultra-high since storing k covariance matrices requires O (k p 2) memory. Many dimensionality reduction algorithms have been improved to avoid explicit covariance calculation and storage (covariance-free). Here we propose a covariance-free stepwise CPC, which only requires O (k n) memory, where n is the total number of examples. Thus for n < < p , the new algorithm shows apparent advantages. It computes components quickly, with low consumption of machine resources. We validate our method CFCPC with the classical Iris data. We then show that CFCPC allows extracting the shared anatomical structure of EEG and MEG source spectra across a frequency range of 0.01–40 Hz. [ABSTRACT FROM AUTHOR]

We consider extrapolation of the Arnoldi algorithm to accelerate computation of the dominant eigenvalue/eigenvector pair. The basic algorithm uses sequences of Krylov vectors to form a small eigenproblem which is solved exactly. The two dominant eigenvectors output from consecutive Arnoldi steps are then recombined to form an extrapolated iterate, and this accelerated iterate is used to restart the next Arnoldi process. We present numerical results testing the algorithm on a variety of cases and find on most examples it substantially improves the performance of restarted Arnoldi. The extrapolation is a simple post-processing step which has minimal computational cost. [ABSTRACT FROM AUTHOR]

It is crucial to generate random graphs with specific structural properties from real graphs, which could anonymize graphs or generate targeted graph data sets. The state-of-the-art method called spectral graph forge (SGF) was proposed at INFOCOM 2018. This method uses a low-rank approximation of the matrix by throwing away some spectrums, which provides privacy protection after distributing graphs while ensuring data availability to a certain extent. As shown in SGF, it needs to discard at least 20% spectrum to defend against deanonymous attacks. However, the data availability will be significantly decreased after more spectrum discarding. Thus, is there a way to generate a graph that guarantees maximum spectrum and anonymity at the same time? To solve this problem, this paper proposes graph nonlinear scaling (GNS). We firmly prove that GNS can preserve all eigenvectors meanwhile providing high anonymity for the forged graph. Precisely, the GNS scales the eigenvalues of the original spectrum and constructs the forged graph with scaled eigenvalues and original eigenvectors. This approach maximizes the preservation of spectrum information to guarantee data availability. Meanwhile, it provides high robustness towards deanonymous attacks. The experimental results show that when SGF discards only 10% of the spectrum, the forged graph has high data availability. At this time, if the distance vector deanonymity algorithm is used to attack the forged graph, almost 100% of the nodes can be identified, while when achieving the same availability, only about 20% of the nodes in the forged graph obtained from GNS can be identified. Moreover, our method is better than SGF in capturing the real graph's structure in terms of modularity, the number of partitions, and average clustering. [ABSTRACT FROM AUTHOR]

Purpose: Qualitative methods are not suitable to process high volumes of policy texts for exploring policy evolution. Therefore, it is hard to use qualitative methods to systematically analyze the characteristics of complex policy networks. So the authors propose a bibliometric research study for exploring policy evolution from time–agency–theme perspectives to excavate the rules and existing problems of China's medical informatization policy and to provide suggestions for formulating and improving the future medical informatization policies. Design/methodology/approach: Initially, 615 valid samples are obtained by retrieving related China's medical informatization policy documents, and the joint policy-making agency network and the co-occurrence network models of medical informatization policies are defined, and then the authors research China's medical informatization policies from single-dimension and multi-dimension view. Findings: The analysis results reveal that China's medical informatization policy process can be divided into four stages; the policy-making agencies are divided into four subgroups by community detection analysis according to the fast unfolding algorithm; the core policy theme keywords are identified based on the eigenvector centrality of the nodes in those networks; the focuses of theme terms are varied in different stages and the correlations between agencies and themes are gradually decentralized. Practical implications: These findings provide experience and evidence on leveraging informatics in the medical and healthcare field of China. Also, they can help scholars and practitioners better understand the current status and future directions of medical and healthcare informatics development in China and provide a reference to formulate and improve China's future medical informatization policies. Originality/value: This study proposes a quantitative bibliometric-based research framework to describe transitions and trends of China's medical informatization policy. [ABSTRACT FROM AUTHOR]

Based on the spectral divide‐and‐conquer algorithm by Nakatsukasa and Higham [SIAM J. Sci. Comput., 35(3):A1325–A1349, 2013], we propose a new algorithm for computing all the eigenvalues and eigenvectors of a symmetric banded matrix with small bandwidth, with the eigenvectors given implicitly as a product of orthonormal matrices stored in the so‐called hierarchically off‐diagonal low‐rank (HODLR) format. For this purpose, we combine our previous work on the fast computation of spectral projectors in the HODLR format, with a novel technique for extracting a basis for the range of such a HODLR matrix. Preliminary numerical experiments demonstrate that our algorithm exhibits quasi‐linear complexity for matrices that can be efficiently represented in the HODLR format throughout the divide‐and‐conquer algorithm, and allows for conveniently dealing with such large‐scale matrices. [ABSTRACT FROM AUTHOR]

In the block version of the classical two-sided Jacobi method for the Hermitian eigenvalue problem, the off-diagonal elements of iterated matrix A (k) converge to zero. However, this fact alone does not necessarily guarantee that A (k) converges to a fixed diagonal matrix. The same is true for the matrix of accumulated unitary transformations Q (k). We prove that under certain assumptions A (k) indeed converges to a fixed diagonal matrix, whose diagonal elements are the eigenvalues of the input matrix A. Next it is shown that for a simple eigenvalue the corresponding column of Q (k) converges to the corresponding eigenvector. For a multiple eigenvalue or a cluster of eigenvalues, we prove that the orthogonal projectors constructed from the corresponding columns of Q (k) converge to the orthogonal projector onto the eigenspace corresponding to those eigenvalues. Moreover, the appropriate convergence bounds are obtained for all discussed cases. Convergence results are also valid for the parallel block-Jacobi method with dynamic ordering. The developed theory is illustrated by numerical example. [ABSTRACT FROM AUTHOR]

As collaborative filtering recommendation algorithm relies on user data, there is a great risk of privacy leakage. Differential privacy protection technology can provide strict privacy protection effects, but most recommendation algorithms based on differential privacy do not consider implicit feedback data. To solve the problem, this paper proposed a new collaborative filtering recommendation algorithm based on differential privacy protection. Firstly, it performed matrix decomposition on the implicit feedback matrix to obtain the implicit eigenvectors of users and items. Then it merged the implicit eigenvectors into the solution of explicit feedback model. The algorithm satisfied e-differential privacy protection by adding mean perturbation and gradient perturbation to the model. Finally this paper applied this algorithm to predict the score, and evaluated the effectiveness of the algorithm on the MovieLens dataset. Experimental results show that the algorithm can achieve an effective balance between the accuracy of recommendation results and privacy protection of users. [ABSTRACT FROM AUTHOR]

An (n, d, λ)-graph is a d regular graph on n vertices in which the absolute value of any nontrivial eigenvalue is at most λ. For any constant d ≥ 3, ϵ > 0 and all sufficiently large n we show that there is a deterministic poly(n) time algorithm that outputs an (n, d, λ)-graph (on exactly n vertices) with λ ≤ 2 d − 1 + ϵ . For any d=p + 2 with p ≡ 1 mod 4 prime and all sufficiently large n, we describe a strongly explicit construction of an (n, d, λ)-graph (on exactly n vertices) with λ ≤ 2 (d − 1) + d − 2 + o (1) (< (1 + 2) d − 1 + o (1)) , with the o(1) term tending to 0 as n tends to infinity. For every ϵ> 0, d> d0(ϵ) and n>n0(d, ϵ) we present a strongly explicit construction of an (m, d, λ)-graph with λ < (2 + ϵ) d and m = n + o(n). All constructions are obtained by starting with known Ramanujan or nearly Ramanujan graphs and modifying or packing them in an appropriate way. The spectral analysis relies on the delocalization of eigenvectors of regular graphs in cycle-free neighborhoods. [ABSTRACT FROM AUTHOR]

Resolvent analysis identifies the most responsive forcings and most receptive states of a dynamical system, in an input–output sense, based on its governing equations. Interest in the method has continued to grow during the past decade due to its potential to reveal structures in turbulent flows, to guide sensor/actuator placement and for flow control applications. However, resolvent analysis requires access to high-fidelity numerical solvers to produce the linearized dynamics operator. In this work, we develop a purely data-driven algorithm to perform resolvent analysis to obtain the leading forcing and response modes, without recourse to the governing equations, but instead based on snapshots of the transient evolution of linearly stable flows. The formulation of our method follows from two established facts: (i) dynamic mode decomposition can approximate eigenvalues and eigenvectors of the underlying operator governing the evolution of a system from measurement data, and (ii) a projection of the resolvent operator onto an invariant subspace can be built from this learned eigendecomposition. We demonstrate the method on numerical data of the linearized complex Ginzburg–Landau equation and of three-dimensional transitional channel flow, and discuss data requirements. Presently, the method is suitable for the analysis of laminar equilibria, and its application to turbulent flows would require disambiguation between the linear and nonlinear dynamics driving the flow. The ability to perform resolvent analysis in a completely equation-free and adjoint-free manner will play a significant role in lowering the barrier of entry to resolvent research and applications. [ABSTRACT FROM AUTHOR]

Large-scale social graph data poses significant challenges for social analytic tools to monitor and analyze social networks. The information-theoretic distance measure, namely, resistance distance, is a vital parameter for ranking influential nodes or community detection. The superiority of resistance distance and Kirchhoff index is that it can reflect the global properties of the graph fairly, and they are widely used in assessment of graph connectivity and robustness. There are various measures of network criticality which have been investigated for underlying networks, while little is known about the corresponding metrics for mixed networks. In this paper, we propose the positive walk algorithm to construct the Hermitian matrix for the mixed graph and then introduce the Hermitian resistance matrix and the Hermitian Kirchhoff index which are based on the eigenvalues and eigenvectors of the Hermitian Laplacian matrix. Meanwhile, we also propose a modified algorithm, the directed traversal algorithm, to select the edges whose removal will maximize the Hermitian Kirchhoff index in the general mixed graph. Finally, we compare the results with the algebraic connectivity to verify the superiority of the proposed strategy. [ABSTRACT FROM AUTHOR]

The spectral clustering (SC) method has a good clustering effect on arbitrary structure datasets because of its solid theoretical basis. However, the required time complexity is high, thus limiting the application of SC in big datasets. To reduce time complexity, we propose an SC algorithm based on OptiSim Selection (SCOSS) in this study. This new algorithm starts from selecting a representative subset by using an optimizable k-dissimilarity selection algorithm (OptiSim) and then uses the Nystrom method to approximate the eigenvectors ¨ of the similarity matrix. Theoretical deductions and experiment results show that the proposed algorithm can use less clustering time to achieve a good clustering result. [ABSTRACT FROM AUTHOR]

Classical Floquet theory describes motion near a periodic orbit. But comparing Floquet theory to action angle methods shows which Jordan form is desirable. A new eigenvector algorithm is developed ensuring a canonical transform and handling the typical for the case of repeated eigenvalues, a chronic problem in conservative Hamiltonian systems. This solution also extends the Floquet decomposition to adjacent trajectories, and is fully canonical. This method yields the matrix of frequency partial derivatives, extending the solution's validity. Some numerical examples are offered. [ABSTRACT FROM AUTHOR]

In max-min fuzzy algebra, the study of eigenvectors is important because it can help us to recognize the steady states of systems working in discrete steps. This paper investigates the properties of steady states described by max-min matrices and vectors with interval coefficients. The characteristics of the eigenspace structure and polynomial-time algorithms for recognition of tolerable and weakly-tolerable interval eigenvectors in max-min algebra are described. This research is a continuation of an earlier investigation concerning strongly-tolerable interval eigenvectors. [ABSTRACT FROM AUTHOR]

The computation of the eigenvalue decomposition of matrices is one of the most investigated problems in numerical linear algebra. In particular, real nonsymmetric tridiagonal eigenvalue problems arise in a variety of applications. In this paper the problem of computing an eigenvector corresponding to a known eigenvalue of a real nonsymmetric tridiagonal matrix is considered, developing an algorithm that combines part of a sweep and part of a sweep, both with the shift equal to the known eigenvalue. The numerical tests show the reliability of the proposed method. [ABSTRACT FROM AUTHOR]

In recent years, the reduced biquaternion algebras have been widely used in color image processing problems and in the field of electromagnetism. This paper studies eigen-problems of reduced biquaternion matrices by means of a complex representation of a reduced biquaternion matrix and derives new algebraic algorithms to find the eigenvalues and eigenvectors of reduced biquaternion matrices. This paper also concludes that the number of eigenvalues of an n × n reduced biquaternion matrix is infinite. In addition, the proposed algebraic algorithms are shown to be effective in application to a color face recognition problem. • The eigen-problems of reduced biquaternion matrices are further studied based on the complex representation form. • Propose new algebraic algorithms for finding the eigenvalues and the eigenvectors of a reduced biquaternion matrix. • An n × n reduced biquaternion matrix has infinite eigenvalues. • There are multiple eigenvalues corresponding to the same eigenvector of a reduced biquaternion matrix. • The proposed method is more comprehensive and can find more eigenvalues of a reduced biquaternion matrix. [ABSTRACT FROM AUTHOR]

We study the de Casteljau subdivision algorithm for Bezier curves and the Lane-Riesenfeld algorithm for uniform B-spline curves over the integers mod m , where m > 2 is an odd integer. We place the integers mod m evenly spaced around a unit circle so that the integer k mod m is located at the position on the unit circle at e 2 π ki / m = cos (2 k π / m) + i sin (2 k π / m) ↔ (cos (2 k π / m) , sin (2 k π / m)). Given a sequence of integers (s 0 , ... , s m) mod m , we connect consecutive values s j s j + 1 on the unit circle with straight line segments to form a control polygon. We show that if we start these subdivision procedures with the sequence (0 , 1 , ... , m) mod m , then the sequences generated by these recursive subdivision algorithms spawn control polygons consisting of the regular m -sided polygon and regular m -pointed stars that repeat with a period equal to the minimal integer k such that 2 k = ± 1 m o d m. Moreover, these control polygons represent the eigenvectors of the associated subdivision matrices corresponding to the eigenvalue 2 − 1 m o d m. We go on to study the effects of these subdivision procedures on more general initial control polygons, and we show in particular that certain control polygons, including the orbits of regular m -sided polygons and the complete graphs of m -sided polygons, are fixed points of these subdivision procedures. [Display omitted] [ABSTRACT FROM AUTHOR]

Purpose: To obtain efficient operation modes of transmit array (TxArray) coils using a general design technique based on the eigenmode analysis of the scattering matrix. Methods: We introduce the concept of modal reflected power and excitation eigenmodes, which are calculated as the eigenvalues and eigenvectors of SHS, where the superscript H denotes the Hermitian transpose. We formulate the normalized reflected power, which is the ratio of the total reflected power to the total incident power of TxArray coils for a given excitation signal as the weighted sum of the modal reflected power. By minimizing the modal reflected power of TxArray coils, we increase the excitation space with a low total reflection. The algorithm was tested on 4 dual‐row TxArray coils with 8 to 32 channels. Results: By minimizing the modal reflected power, we designed an 8‐element TxArray coil to have a low reflection for 7 out of 8 dimensions of the excitation space. Similarly, the minimization of the modal reflected power of a 16‐element TxArray coil enabled us to enlarge the dimension of the excitation space by 50% compared with commonly employed design techniques. Moreover, we demonstrated that the low total reflected power for some critical excitation modes, such as the circularly polarized mode, can be achieved for all TxArray coils even with a high level of coupling. Conclusion: Eigenmode analysis is an efficient method that intuitively provides a quantitative and compact representation of the coil's power transmission capabilities. This method also provides insight into the excitation modes with low reflection. [ABSTRACT FROM AUTHOR]

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Copyright of Journal of Harbin Institute of Technology. Social Sciences Edition / Haerbin Gongye Daxue Xuebao. Shehui Kexue Ban is the property of Harbin Institute of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)