Simultaneous (M,N) Singular Value Decomposition of Matrices

A necessary and sufficient condition for the existence of simultaneous (M,N)singular value decomposition of matrices is given.Some properties about the weighted partial ordering are discussed with the help of the decomposition.

Precise integration method for a class of singular two-point boundary value problems

In this paper we present a precise integration method based on high order multiple perturbation method and reduction method for solving a class of singular twopoint boundary value problems.Firstly,by employing the method of variable coefficient dimensional expanding,the non-homogeneous ordinary differential equations（ODEs） are transformed into homogeneous ODEs.Then the interval is divided evenly,and the transfer matrix in every subinterval is worked out using the high order multiple perturbation method,and a set of algebraic equations is given in the form of matrix by the precise integration relation for each segment,which is worked out by the reduction method.Finally numerical examples are elaboratedd to validate the present method.

Singular Integral Equations with Cosecant Kernel in Solutions with Singularities of High Order

We have discussed and solved the boundary value problem with period 2aπ and the singular integral equation with kernel csc t-tv/a in solution having singularities of high order, where the smooth contour of integration is in the strip 0<Rez<aπ.

High order multiplication perturbation method for singular perturbation problems

This paper presents a high order multiplication perturbation method for sin- gularly perturbed two-point boundary value problems with the boundary layer at one end. By the theory of singular perturbations, the singularly perturbed two-point boundary value problems are first transformed into the singularly perturbed initial value problems. With the variable coefficient dimensional expanding, the non-homogeneous ordinary dif- ferential equations （ODEs） are transformed into the homogeneous ODEs, which are then solved by the high order multiplication perturbation method. Some linear and nonlinear numerical examples show that the proposed method has high precision.

A UNIFORM HIGH-ORDER METHOD FOR A SINGULAR PERTURBATION PROBLEM IN CONSERVATIVE FORM

A uniform high-order method is. presented for the numerical solution of a singular perturbation problem in conservative form. We firest replace the original second-order problem (1.1) by two equivalent first-order problems ( 1.4), i.e., the solution of (1.1) is a linear combination of the solutions of (1.4). Then we derive a uniformly O (hm+1) accurate scheme for the first-order problems (1.4), where m is an arbitrary nonnegative integer, so we can get a uniformly O (hm+1) accurate solution of the original problem (1.1) by relation (1.3). Some illustrative numerical results are also given.

FAST ALGORITHMS FOR HIGHER-ORDER SINGULAR VALUE DECOMPOSITION FROM INCOMPLETE DATA

Higher-order singular value decomposition （HOSVD） is an efficient way for data reduction and also eliciting intrinsic structure of multi-dimensional array data. It has been used in many applications, and some of them involve incomplete data. To obtain HOSVD of the data with missing values, one can first impute the missing entries through a certain tensor completion method and then perform HOSVD to the reconstructed data. However, the two-step procedure can be inefficient and does not make reliable decomposition. In this paper, we formulate an incomplete HOSVD problem and combine the two steps into solving a single optimization problem, which simultaneously achieves imputation of missing values and also tensor decomposition. We also present one algorithm for solving the problem based on block coordinate update （BCU）. Global convergence of the algorithm is shown under mild assumptions and implies that of the popular higher-order orthogonality iteration （HOOI） method, and thus we, for the first time, give global convergence of HOOI. In addition, we compare the proposed method to state-of-the-art ones for solving incom- plete HOSVD and also low-rank tensor completion problems and demonstrate the superior performance of our method over other compared ones. Furthermore, we apply it to face recognition and MRI image reconstruction to show its practical performance.

Distributed Monitoring of Power System Oscillations Using Multiblock Principal Component Analysis and Higher-order Singular Value Decomposition

The primary goal in the analysis of hierarchical distributed monitoring and control architectures is to study the spatiotemporal patterns of the interactions between areas or subsystems.In this paper,a novel conceptual framework for distributed monitoring of power system oscillations using multiblock principal component analysis(MB-PCA)and higher-order singular value decomposition(HOSVD)is proposed to understand,characterize,and visualize the global behavior of the power system.The proposed framework can be used to evaluate the influence of a given area or utility on the oscillatory behavior,uncover low-dimensional structures from high-dimensional data,and analyze the effects of heterogeneous data on the modal characteristics and interpretation of power system.The metrics are then investigated to examine the relationships between the dynamic patterns and participation of individual data blocks in the global behavior of the system.Practical application of these techniques is demonstrated by case studies of two systems:a 14-machine test system and a 5449-bus 635-generator equivalent model of a large power system.

Expansion of the Decoupled Discreet-Time Jacobian Eigenvalue Approximation for Model-Free Analysis of PMU Data

This paper proposes an extension of the algorithm in [1], as well as utilization of the wavelet transform in event detection, including High Impedance Fault (HIF). Techniques to analyze the abundant data of PMUs quickly and effectively are paramount to increasing response time to events and unstable parameters. With the amount of data PMUs output, unstable parameters, tie line oscillations, and HIFs are often overlooked in the bulk of the data. This paper explores model-free techniques to attain stability information and determine events in real-time. When full system connectivity is unknown, many traditional methods requiring other bus measurements can be impossible or computationally extensive to apply. The traditional method of interest is analyzing the power flow Jacobian for singularities and system weak points, attained by applying singular value decomposition. This paper further develops upon the approach in [1] to expand the Discrete-Time Jacobian Eigenvalue Approximation (DDJEA), giving values to significant off-diagonal terms while establishing a generalized connectivity between correlated buses. Statistical linear models are applied over large data sets to prove significance to each term. Then the off diagonal terms are given time-varying weights to account for changes in topology or sensitivity to events using a reduced system model. The results of this novel method are compared to the present errors of the previous publication in order to quantify the degree of improvement that this novel method imposes. The effective bus eigenvalues are briefly compared to Prony analysis to check similarities. An additional application for biorthogonal wavelets is also introduced to detect event types, including the HIF, for PMU data.

Unified parametric approaches for high-order integral observer design for matrix second-order linear systems

A type of high-order integral observers for matrix second-order linear systems is proposed on the basis of generalized eigenstructure assignment via unified parametric approaches. Through establishing two general parametric solutions to this type of generalized matrix second-order Sylvester matrix equations, two unified complete parametric methods for the proposed observer design problem are presented. Both methods give simple complete parametric expressions for the observer gain matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the fight factorization of the system, and allows eigenvalues of the error system to be set undetermined and sought via certain optimization procedures. A spring-mass-dashpot system is utilized to illustrate the design procedure and show the effect of the proposed approach.

High-Order Supervised Discriminant Analysis for Visual Data

In practical applications, we often have to deal with high-order data, for example, a grayscale image and a video clip are intrinsically a 2nd-order tensor and a 3rd-order tensor, respectively. In order to satisty these high-order data, it is conventional to vectorize these data in advance, which often destroys the intrinsic structures of the data and includes the curse of dimensionality. For this reason, we consider the problem of high-order data representation and classification, and propose a tensor based fisher discriminant analysis （FDA）, which is a generalized version of FDA, named as GFDA. Experimental results show our GFDA outperforms the existing methods, such as the 2-directional 2-dimensional principal component analysis （（2D）2pCA）, 2-directional 2-dimensional linear discriminant analysis （（2D）2LDA）, and multilinear discriminant analysis （MDA）, in high-order data classification under a lower compression ratio.

高机动目标的改进强跟踪CKF自适应IMM算法

为提升高机动目标跟踪精度,提出了一种改进的强跟踪CKF自适应交互多模型跟踪算法。在IMM算法运动模型集中引入CS-Jerk模型,增强对高机动目标的适应能力,采用奇异值分解(SVD)算法解决模型集中因模型扩维而导致CKF算法无法Cholesky分解的问题;提出了一种改进的强跟踪CKF算法,降低强跟踪CKF算法的计算量;利用模型的后验信息对IMM算法模型转移概率进行自适应调整,提高跟踪精度。仿真结果表明,基于所提算法目标的位置均方根误差均值和速度均方根误差均值较IMM-CKF算法分别降低了22.50%和16.58%,有效提高了目标跟踪精度。

奇异值分解五阶容积卡尔曼滤波汽车状态估计

针对三阶滤波对高维汽车非线性模型估计精度有限的问题,以电动汽车为研究对象,提出了一种基于奇异值分解的五阶容积卡尔曼滤波(SVD-FCKF)车辆状态估计器。首先基于Dugoff轮胎模型,构建高维非线性7自由度车辆动力学模型。然后根据三阶球面-径向容积规则将CKF拓展到五阶,使其具有五阶泰勒级数展开精度,同时利用奇异值分解代替传统Cholesky分解,提高估计器的鲁棒性。最后利用Carsim和Matlab/Simulink联合仿真平台对SVD-FCKF进行验证,结果表明:改进的SVD-FCKF估计器能够有效提高电动汽车纵向速度、侧向速度、质心侧偏角和四轮转速的估计精度和稳定性,多工况适应能力强,整体估计效果优于CKF估计器。研究结果为电动汽车主动安全研究提供了理论支撑,具有实际应用价值。

基于POD降维外推差分算法的热传导模型研究

针对一维热传导问题,基于奇异值分解和特征投影本征分解(proper orthogonal decomposition,POD)法通过提取特征模态,建立了一种极少自由度、较高精度的降维外推仿真模型。给出模型降维近似解分量的数学推导、算法过程以及误差分析,实现了温度场的快速计算。最后,通过数值例子,将POD计算结果与有限差分法(FDM)计算结果进行了对比。结果表明:POD方法在不同的时间步长、空间步长及定解条件下,均能捕捉到传热过程的准确信息,平均计算速度比传统有限差分法计算速度提高了200倍,有效缩短了计算机模拟时间。考核了低阶模型的准确性,并说明了低阶方程可以定性的反映原高维系统的传热特性。同时,POD所得结果与FDM结果间的最大相对误差为0.15%,满足工程计算精度要求。所提出的POD降维外推算法方案,不但扩展了POD特征空间,而且可以逐步改进数值求解步骤,弥补了POD方法的不足,验证了利用POD降维算法研究传热问题的可行性与有效性。对于实现复杂传热模型的高效准确的分析与仿真数值求解过程有一定的理论参考价值。

基于MB-LBP和张量HOSVD的人脸识别算法

融合多尺度分块局部二值模式和张量高阶奇异值分解提出一种人脸识别算法。优选不同尺度的MB-LBP算子组合提取图像纹理特征,构造人脸图像的3阶张量模型;利用HOOI算法进行张量高阶奇异值分解;基于HOSVD分解结果采用最邻近算法设计识别分类器。运用Yale数据库和自制数据库进行算法对比实验,验证算法的有效性,实验结果表明,基于Yale数据库,提出算法与LBP-深度置信网络算法的识别精度一样高,均为98.667%;基于自制人脸数据库,该算法识别精度为100%。综上提出算法是一种有效的、可行的识别算法。

对偶P-分解及偏序

文章应用对偶奇异值分解建立对偶复矩阵的P-分解,得到该分解的若干性质,应用该分解建立D-GL二元关系,并证明该二元关系是一类偏序。

基于HOSVD分类的非特定人脸表情识别算法

由于人脸外观、光照、姿势变化等对人脸表情特征提取的影响,非特定人脸表情识别率普遍较低。针对上述问题,提出一种基于高阶奇异值分解(HOSVD)分类的非特定人脸表情识别算法。算法融合局部方向模式(LDP)全脸特征和中心化二值模式(CBP)局部特征,以增强人脸表情特征的鉴别力,引入HOSVD建立表情子空间进行分类识别,从而减少人脸外观对表情特征的影响,同时利用HOSVD求解区域能量用于精确匹配。在JAFFE数据库上的非特定人脸表情实验结果表明,HOSVD分类算法相比传统最近邻算法更能区分表情图像的特征,识别率提高了18%,此外,LDP融合CBP特征相比LDP特征和CBP特征更能准确描述人脸表情,识别率分别提高了17%和12.2%。由此可见,上述方法对解决非特定人表情识别问题具有更好的识别效果。

一种奇异值分解与子空间加权联合的改进MUSIC算法

在低信噪比、小快拍数等非理想条件下,经典DOA估计算法对邻近目标的分辨率严重下降,甚至失去分辨能力。针对这一问题,提出了一种将重构的接收信号协方差矩阵进行奇异值分解并与改进的加权子空间方法相结合的改进算法。该算法充分利用互相关信息构建新的接收信号协方差矩阵,并对噪声子空间信息采用新的校正方法,对噪声特征值进行改造,之后对噪声子空间进行加权,最后与信号子空间加权技术相联合。仿真实验证明,改进算法在低信噪比和小快拍数条件下可以分辨间隔4°的相邻目标,统计分析表明该算法的分辨率明显优于经典MUSIC算法。

高维矩阵奇异值分解的快速计算方法对比分析及应用

为在大数据环境下处理高维矩阵和应用奇异值分解提供更高效的解决方案,从而加速数据分析和处理速度,通过研究随机投影以及Krylov子空间投影理论下关于高维矩阵求解特征值特征向量(奇异值奇异向量)问题,分别总结了6种高效计算方法并对其相关应用研究进行对比分析。结果表明,在谱聚类的应用上,通过降低核心步骤SVD(Singular Value Decomposition)的复杂度,使优化后的算法与原始谱聚类算法的精度相近,但大大缩短了运行时间,在1200维的数据下计算速度相较原算法快了10倍以上。同时,该方法应用于图像压缩领域,能有效地提高原有算法的运行效率,在精度不变的情况下,运行效率得到了1~5倍的提升。

基于PSO-SVM的高温炉变频电机局部放电预警监测方法

在高温炉加热过程中,非均匀的暂态随机状态会影响高温炉变频电机局部放电信号时间特性,导致时间一幅值关系的离散变量不能确定而影响监测效率,为此提出基于PSO-SVM的高温炉变频电机局部放电预警监测方法。首先,采用奇异值分解(SVD)抑制高温炉变频电机局部放电信号中的窄带干扰,获取有用信号;其次,利用局部线性嵌入(LLE)算法提取降维信号中的局部放电特征参数;最后,将其作为输入特征向量构建基于粒子群优化的支持向量机分类函数(PSO-SVM),完成对高温炉变频电机局部放电类型的识别和监测,并以此为依据求出局部放电阈值预警参数和趋势预警缺陷水平,实现对高温炉变频电机局部放电的预警监测。实验结果表明,所提方法能够有效抑制局部放电窄带干扰,并在一定程度上提高了高温炉电机局部放电信号的识别精度和预警监测效率。

一种改进的HOSVD降噪的信道预测算法

基于高阶奇异值分解(High Order Singular Value Decomposition,HOSVD)降噪的信道预测算法对天线数较少引起的秩不足问题比较敏感,同时也难以应付较大多普勒频移的情况,从而引起信道估计性能和预测性能的急剧下降、损失信道容量.针对这一问题,提出了一种改进的使用HOSVD降噪的信道预测算法.该算法先利用多输入多输出(Multiple-input Multiple-Output,MIMO)信道固有的空时相关性对采样得到的信道状态信息(Channel State Information,CSI)进行矩阵重排和数据平滑处理,随后基于信道的多维结构特性,使用HOSVD降低噪声的影响,继而重构信道矩阵,最后利用递归最小二乘滤波器对未来时刻的信道状态进行预测.仿真表明,所提算法的估计误差和预测误差性能均明显优于对比算法,这是因为所提算法通过矩阵重排和空时平滑,虚拟地增加了天线数,降低了秩缺失问题对估计和预测精度的影响,从而有效补偿了因误差所致的信道容量的损失.同时,对比天线数和多普勒频移对不同算法性能的影响可见,所提算法也能在大多普勒频移和天线数较少等不利条件下提供较好预测性能和信道容量,具有一定的优越性.