New recursive algorithm for matrix inversion

To reduce the computational complexity of matrix inversion, which is the majority of processing in many practical applications, two numerically efficient recursive algorithms （called algorithms I and II, respectively） are presented. Algorithm I is used to calculate the inverse of such a matrix, whose leading principal minors are all nonzero. Algorithm II, whereby, the inverse of an arbitrary nonsingular matrix can be evaluated is derived via improving the algorithm I. The implementation, for algorithm II or I, involves matrix-vector multiplications and vector outer products. These operations are computationally fast and highly parallelizable. MATLAB simulations show that both recursive algorithms are valid.     

基于非负矩阵分解的复杂网络重构

将网络连边的产生机制和其社团结构结合在一起,基于社团结构决定网络连边的假设推导出节点间的连接概率矩阵并表达为矩阵乘积的形式,然后利用非负矩阵分解得到节点间的连接概率矩阵进行网络重建。设计实验并在几个真实的网络数据上测试,相比基于相似度的网络重构算法,该算法取得了更好的网络重构效果。     

联合互协方差矩阵的快速波达方向估计

针对常规子空间类波达方向(direction-of-arrival, DOA)估计中存在的子空间分解计算量过大问题,提出了基于均匀线阵的联合互协方差矩阵(joint cross covariance matrix,JCCM)DOA估计算法。基于阵列划分和矩阵重构思想,将均匀线阵划分成两个子阵,在求得这两个子阵接收数据互协方差矩阵后,重构一个新的矩阵即JCCM,利用JCCM的部分数据进行线性运算即可得到等价的信号子空间,然后构造多项式并求根,最终实现波达角估计。理论分析和仿真实验证明,算法避开了对协方差矩阵的特征值分解运算,在保证估计精度可接受的同时,有效降低了计算量,取得了更高的估计速度。     

The RCH Method for Computing Minimal Polynomials of Polynomial Matrices

In this paper,a randomized Cayley-Hamilton theorem based method(abbreviated by RCH method) for computing the minimal polynomial of a polynomial matrix is presented.It determines the coefficient polynomials term by term from lower to higher degree.By using a random vector and randomly shifting,it requires no condition on the input matrix and works with probability one.In the case that coefficients of entries of the given polynomial matrix are all integers and that the algorithm is performed in exact computation,by using the modular technique,a parallelized version of the RCH method is also given.Comparisons with other algorithms in both theoretical complexity analysis and computational tests are given to show its effectiveness.     

Computing μ-Bases of Univariate Polynomial Matrices Using Polynomial Matrix Factorization

Journal of Systems Science and Complexity - This paper extends the notion of μ-bases to arbitrary univariate polynomial matrices and present an efficient algorithm to compute a μ-basis...     

线性方程组符号求解Bareiss算法的改进与实现

使用改进后的Bareiss消去法,在求解具有符号系数的线性方程组时可以避免普通Gauss消去法在计算过程中出现所谓中间系数爆炸的问题,还可以求解系数矩阵不是方阵以及系数矩阵奇异的线性方程组的情况.并且以这一改进算法与syzygy算法为基础,给出了求解多项式系数线性方程组的多项式解的算法.已经在自行开发的自动推理平台软件MMP上实现了这个算法.     

Smith Form of Triangular Multivariate Polynomial Matrix

The Smith form of a matrix plays an important role in the equivalence of matrix. It is known that some multivariate polynomial matrices are not equivalent to their Smith forms. In this paper, the authors investigate mainly the Smith forms of multivariate polynomial triangular matrices and testify two upper multivariate polynomial triangular matrices are equivalent to their Smith forms respectively.     

一种组合类别信息的非负矩阵分解方法及其应用

基于非负矩阵分解理论,提出一种新的有监督的特征提取方法,它具有二个特点: 一是在特征提取过程中它直接利用训练样本的类别信息,二是在计算上仍然采用与非负矩阵分解方法相同数学公式,因此这种新特征提取方法被称为组合类别信息的非负矩阵分解(CINMF)方法.另外,在分类时本文提出了基于两种特征融合的分类策略进一步提高CINMF方法的识别率.通过在YALE人脸库和ORL人脸库上进行实验,结果表明本文提出的新方法在识别率方面整体上好于原非负矩阵分解方法,甚至超过常用的主成分分析法(PCA).     

AHP中判断矩阵一致性调整方法研究

提出了两种专家判断矩阵一致性调整的新方法:一般的Hadamard凸组合(Easy-HCC)方法和基于系统聚类分析的Hadamard凸组合(HCC)方法.首先利用判断矩阵的生成元生成一致的正互反生成矩阵,前一种方法对生成矩阵作简单的几何平均;后一种方法通过系统聚类分析,对生成矩阵进行一致性聚类,并以此为基础,按少数服从多数的原则分配权重系数,对生成矩阵进行加权几何平均,获得一致的正互反调整矩阵.然后把这两种方法分别与传统的方法相比较,用同一个算例证明了加法凸组合和前一种方法对判断矩阵调整的无效性,并分析了后一种方法的有效性和实用性.     

基于非负矩阵分解新的人脸识别方法

非负矩阵分解是一个新的特征提取方法,基于非矩阵分解的理论,提出了具有正交性的投影轴的计算方法和具有统计不相关性的投影轴的计算方法。与原非负矩阵分解方法,提出的方法在某种程度上是降低了特征矢量之间的统计相关性,并且提高识别率。通过在ORL人脸库和YALE人脸库上进行实验,结果表明提出的两种特征提取方法在识别率方面整体上好于原非负矩阵分解特征提取(NMF)方法,甚至超过主成分分析(PCA)法。     

On Rank Factorizations and Factor Prime Factorizations for Multivariate Polynomial Matrices

In this paper, rank factorizations and factor left prime factorizations are studied. The authors prove that any polynomial matrix with full row rank has factor left prime factorizations. And for a class of polynomial matrices, the authors give an algorithm to decide whether they have rank factorizations or factor left prime factorizations and compute these factorizations if they exist.     

A NOTE ON THE STOCHASTIC ROOTS OF STOCHASTIC MATRICES

In this paper, we study the stochastic root matrices of stochastic matrices. All stochastic roots of2×2 stochastic matrices are found explicitly.A method based on characteristic polynomial of matrix isdeveloped to find all real root matrices that are functions of the original 3×3 matrix, including allpossible(function)stochastic root matrices. In addition, we comment on some numerical methods forcomputing stochastic root matrices of stochastic matrices.     

正交指数约束的平滑非负矩阵分解方法及应用

提出了一种正交指数约束的平滑非负矩阵分解方法,该方法将非负矩阵分解为基矩阵、列归一化平滑矩阵和系数矩阵之积,同时在目标函数中加入了正交指数约束,保证了低维特征的非负性和局部化,减小了分解误差,提高了稀疏性的调节能力。将该方法应用于数据降维、特征稀疏性比较、有遮挡人脸识别和视频运动特征提取。实验结果表明,该方法比同类方法具有更好的性能。     

L0正则化增量正交投影非负矩阵分解的目标跟踪算法

针对传统跟踪算法不能在复杂场景下进行有效跟踪的问题,提出一种基于L0正则化增量正交投影非负矩阵分解(incremental orthogonal projective non negative matrix factorization,IOPNMF)的目标跟踪算法。在粒子滤波框架下采用IOPNMF算法在线获得跟踪目标基于部分的表示以构建模板矩阵,然后将每帧中的候选样本建立基于模板矩阵的线性表示,对表示系数进行L0正则化约束,并提出快速数值解法,同时引入粒子筛选机制,加快跟踪速度。实验结果表明,新算法能够解决跟踪过程中出现的遮挡、光照变化、运动模糊等影响跟踪性能的因素,具有较高的平均覆盖率和较低的平均中心点误差。     

Characteristic polynomial assignment in F-M model Ⅱ of 2-D systems

The problems of characteristic polynomial assignment in Fornasini-Marchesini (F-M) model Ⅱ of 2-D systems are investigated. The corresponding closed-loop systems described by F-M model Ⅱ are obtained via the state feedback.Using the algebraic geometry method, the characteristic polynomial assignment in the closed-loop systems is discussed. In terms of the theory of algebraic geometry, the problem of characteristic polynomial assignment is transferred to the one whether a rational mapping is onto. Sufficient conditions for almost arbitrary assignment coefficients of characteristic polynomial in F-M model Ⅱ of 2-D systems via state feedback are derived, and they are available for multi-input cases. It also has been shown that this method can be applied to assign the characteristic polynomial with output feedback. The sufficient conditions for almost arbitrary assignment coefficients of characteristic polynomial of multi-input 2-D systems described by F-M model Ⅱ with output feedback are established.     

基于块稀疏矩阵恢复的MIMO雷达扩展目标高分辨成像算法

针对现有多输入多输出(multiple input multiple output,MIM O)雷达稀疏恢复成像算法中存在的运算量大、对扩展目标成像质量低的问题,提出一种基于块稀疏矩阵恢复的MIMO雷达扩展目标高分辨成像算法,通过引入目标块稀疏特征,提高对空间扩展目标的成像质量.首先,通过构造距离向和方位向感知矩阵,建...     

Construction of protograph LDPC codes with circular generator matrices

The application of protograph low density parity check(LDPC) codes involves the encoding complexity problem.Since the generator matrices are dense,and if the positions of "1" s are irregularity,the encoder needs to store every "1" of the generator matrices by using huge chip area.In order to solve this problem,we need to design the protograph LDPC codes with circular generator matrices.A theorem concerning the circulating property of generator matrices of nonsingular protograph LDPC codes is proposed.The circulating property of generator matrix of nonsingular protograph LDPC codes can be obtained from the corresponding quasi-cyclic parity check matrix.This paper gives a scheme of constructing protograph LDPC codes with circulating generator matrices,and it reveals that the fast encoding algorithm of protograph LDPC codes has lower encoding complexity under the condition of the proposed theorem.Simulation results in additive white Gaussian noise(AWGN) channels show that the bit error rate(BER) performance of the designed codes based on the proposed theorem is much better than that of GB20600 LDPC codes and Tanner LDPC codes.     

广义判别正交非负矩阵分解及其应用

提出了一种广义判别正交非负矩阵分解算法。与传统非负矩阵分解算法不同,该算法对目标函数加入了正交约束,保证了低维特征的非负性;也不同于以往的判别非负矩阵分解算法将判别约束加于低维权重上,该算法将判别约束推广到低维特征中,使得低维特征参与模式识别,进一步提高了识别精度。本文给出了算法的推导过程,并将其应用于人脸验证和人脸表情识别。实验结果表明,该算法提高了低维特征的判别能力,具有更好的性能。     

弹道式再入目标跟踪方法对比分析

地基雷达对弹道式再入目标进行滤波跟踪时主要存在两个导致滤波误差增大的不确定因素,一是弹道系数未知,二是不可准确确定过程噪声协方差矩阵。为此,采用交互式多模型无敏滤波（iterative multiple model unscented filter, IMM UF）算法对弹道式再入目标进行跟踪,选取不同的弹道系数初值和过程噪声协方差矩阵构成合适的模型集合进行了仿真分析,并将其滤波结果与扩展卡尔曼滤波（extended Kalman filter, EKF）和无敏滤波（unscented filter, UF）的滤波结果进行了对比分析,同时还分析比较了IMM UF和自治多模型（autonomous multiple model, AMM）UF算法的跟踪滤波性能。从仿真结果可以看出,采用的IMM UF算法和相应的模型集合可以在先验信息缺少的情况实现对弹道式再入目标更高精度的跟踪。