基于准范数与零范数的矩阵恢复

针对高维度矩阵的低秩恢复问题中核范数与l₁范数过惩罚导致的结果偏差,提出一种矩阵恢复方法。使用准范数代替低秩恢复问题中常用的核范数约束,使用零范数代替l₁范数约束。对于准范数的求解问题,采用与准范数等价的Frobenius/核混合范数进行替代,提出基于交替近似的线性最小化方法对目标函数进行求解。在合成数据与真实数据上的实验结果表明,该算法在主观视觉效果与客观数值比较上都能获得更好的结果。     

基于泊松方程实现点云的表面重构

根据测量的数据点集,由梯度关系得到采样点和指示函数的积分关系,根据积分关系用划分块的方法获得点集的向量场,计算指示函数梯度场的逼近,构成泊松方程.根据泊松方程使用矩阵迭代求出近似解,采用移动立方体算法提取等值面,对所测数据点集重构出被测物体的模型,泊松方程在边界处的误差为零,因此得到的模型不会存在假的表面框.     

线性投影非负矩阵分解方法及应用

针对线性投影结构非负矩阵分解迭代方法比较复杂的问题,提出了一种线性投影非负矩阵分解方法.从投影和线性变换角度出发,将Frobenius范数作为目标函数,利用泰勒展开式,严格导出基矩阵和线性变换矩阵的迭代算法,并证明了算法的收敛性.实验结果表明:该算法是收敛的;相对于非负矩阵分解等方法,该方法的基矩阵具有更好的正交性和稀疏性;人脸识别结果说明该方法具有较高的识别率.线性投影非负矩阵分解方法是有效的.     

基于Ranking的泊松矩阵分解兴趣点推荐算法

随着基于位置社交网络(location-based social network, LBSN)的发展,兴趣点推荐成为满足用户个性化需求、减轻信息过载问题的重要手段.然而,已有的兴趣点推荐算法存在如下的问题：1)多数已有的兴趣点推荐算法简化用户签到频率数据,仅使用二进制值来表示用户是否访问一个兴趣点;2)基于矩阵分解的兴趣点推荐算法把签到频率数据和传统推荐系统中的评分数据等同看待,使用高斯分布模型建模用户的签到行为;3)忽视用户签到数据的隐式反馈属性.为解决以上问题,提出一个基于Ranking的泊松矩阵分解兴趣点推荐算法.首先,根据LBSN中用户的签到行为特点,利用泊松分布模型替代高斯分布模型建模用户在兴趣点上签到行为;然后采用BPR(Bayesian personalized ranking)标准优化泊松矩阵分解的损失函数,拟合用户在兴趣点对上的偏序关系;最后,利用包含地域影响力的正则化因子约束泊松矩阵分解的过程.在真实数据集上的实验结果表明：基于Ranking的泊松矩阵分解兴趣点推荐算法的性能优于传统的兴趣点推荐算法.     

混合本征模型的多视SAR影像海冰密度检测

目的 SAR影像中像素光谱测度的空间相关性蕴含着海洋表面和海冰更加丰富的空间特性及其变化信息,因此合理建模这种相关性是高分辨率SAR影像海冰精准解译的关键。提出一种利用随机模型及空间统计学测度刻画海冰空间结构的方法。方法 本文首先,在空间统计学框架下,SAR影像被表示为多值Gamma模型和泊松线Mosaic模型线性加权构建的混合模型,其中多值Gamma模型用于描述海洋表面雷达信号背向散射变化的连续性,而泊松线Mosaic模型则用于表征不同类型海冰表面雷达信号背向散射变化的区域性。利用上述混合模型的一阶、二阶变异函数,建模蕴含在SAR影像中海冰空间结构的变化。结果 对RADARSAT-1影像海冰结构建模并反演其密度。实验区域真实海冰密度分别为20%,80%等,运用本文方法反演所得海冰密度与真实海冰密度误差正负不超过10%。结论 本文提出混合本征模型用以刻画SAR强度影像中海冰像素强度变化的空间关系,能够较好地反演Ungava湾海冰密度分布。为利用遥感影像检测空间机构提供一种全新的方法。     

线性流形上广义自反矩阵的最佳逼近算法研究

本文讨论的是线性流行上广义自反矩阵的最佳逼近,给出了解这个问题的一般表达方法。此外,在对应的这一类型问题中,Frobenius范数的一个给定自反矩阵的最佳逼近矩阵的一般表达式已被得到。     

基于Hessian矩阵范数正则化方法的共聚焦图像复原

对于泊松噪声污染下的模糊共聚焦图像复原问题,为解决传统方法中存在的阶梯效应,提出了一种基于Hessian矩阵范数的正则化方法.在泊松概率模型的基础上,该方法引入Hessian矩阵范数作为正则条件,并应用交替方向乘子法和梯度投影方法求解最优化模型.在激光扫描共聚焦显微镜实验中,所获得的复原图像质量优于传统方法,此结果证明了该方法可以有效地复原泊松噪声污染下的模糊共聚焦图像.     

基于MWH模型的新闻视频语义挖掘

根据新闻视频伴随文本及关键帧图像多模异构特征,构建多翼Harmoniums模型,该模型包括多元文本泊松分布和多元颜色直方图高斯分布2个子模型。通过研究隐含主题与观测输入之间的双向依存关系,将其扩展为双层随机场模型,从而对新闻视频进行语义挖掘。在CCTV新闻视频集上进行测试,实验结果验证了该模型的有效性。     

奇异非线性系统基于等价空间的故障检测

研究一类用Takagi-Sugeno(T-S)模糊模型描述的离散奇异系统基于等价空间的故障检测问题,引入反映故障先验信息的参考故障模型,提出一个基于Frobenius范数的残差产生器设计性能指标,将故障检测问题归结为求解一个最小化问题,并给出等价矩阵的线性矩阵不等式求法.该算法能保证残差在实现故障检测的同时对干扰具有最大的鲁棒性.最后,算例仿真验证了所提出方法的有效性.     

基于凸函数理论的Hopfield网络稳定性分析

讨论连接权值不对称或激活函数非单调的离散时间Hopfield网络稳定性分析。引入新的能量函数,利用凸函数的性质证明随状态的更新网络能量函数单调下降从而得出网络收敛的充分条件。对于激活函数为非单调的连续函数而网络连接权值对称,则当网络连接权值矩阵的最大特征值和神经元激活函数的导数下确界之积大于-1时,网络全并行收敛。对于网络激活函数为单调连续函数,网络连接权值为非对称矩阵时,神经元激活函数导数的最大值和连接权值矩阵的2-范数之积小于1时,网络全并行收敛。     

区间矩阵稳定的新充分必要条件

本文讨论了对称区间矩阵的稳定性并给出了一个简单的充分必要条件，同时还讨论了线性时变区间矩阵和非线性时变区间矩阵的稳定性。     

关于确定加权矩阵的两个定理

给定一线性连续或离散时间系统以及与其对应的二次型性能指标函数,文中证明了在系统的开、闭环特征多项式,系统的系数矩阵以及二次型性能指标函数中的加权矩阵之间存在一组确定的显式关系.根据这组关系,满足期望闭环特征值要求的加权矩阵的确定问题变为求解一组具有二次变量的非线性方程组.对于高阶系统,用数值方法求解该方程组也是十分方便的.     

基于循环核矩阵的自适应目标跟踪算法

针对现在存在的基于分类的目标跟踪算法难以实现自适应目标大小变化的问题,提出并实现了基于循环核矩阵的自适应目标跟踪算法。算法首先在包含目标的感兴趣区域内采集所有的训练样本以构成一个循环矩阵结构,再使用高斯核函数构造出循环核矩阵,最后通过基于循环核矩阵的分类器的封闭形式的解进行训练和检测。同时,将比较成熟的循环矩阵理论与傅里叶分析建立连接,从而实现了在快速傅里叶变换下进行快速学习和检测。在此基础上,通过分类器对目标响应度的变化,实现自适应目标大小的变化。与一些经典的和较新的自适应目标跟踪算法进行比较,实验结果表明该算法在一定场景下能够更加准确和有效地表达目标的变化。     

An analytical algorithm for generalized low-rank approximations of matrices

The algorithm for generalized low-rank approximations of matrices (GLRAM) has been developed recently. In this paper, the optimality property of GLRAM is revealed. Accordingly, an analytical method for GLRAM is proposed. The proposed method is non-iterative. Moreover, the relationship between 2DPCA and GLRAM is shown.     

SDF classifier revisited

This paper is addressing problems related to the construction of classifiers based on the Similarity Discriminant Function (SDF), in which the traditional vector representation of a pattern is replaced with matrix data. We introduce potential modifications of the matrix data structure and propose new variants of the SDF. The algorithms that we present were tested on images of handwritten digits and on photographs of human faces, taken from the ORL and CMU‐PIE databases. The results of experiments show that our modifications significantly improved the performance of the original SDF classifier.     

On the quadratic stability of switched linear systems associated with symmetric transfer function matrices

In this paper we give necessary and sufficient conditions for weak and strong quadratic stability of a class of switched linear systems consisting of two subsystems, associated with symmetric transfer function matrices. These conditions can simply be tested by checking the eigenvalues of the product of two subsystem matrices. This result is an extension of the result by Shorten and Narendra for strong quadratic stability, and the result by Shorten et al. on weak quadratic stability for switched linear systems. Examples are given to illustrate the usefulness of our results.     

Computation of functions of Hamiltonian and skew-symmetric matrices

In this paper we consider numerical methods for computing functions of matrices being Hamiltonian and skew-symmetric. Analytic functions of this kind of matrices (i.e., exponential and rational functions) appear in the numerical solutions of ortho-symplectic matrix differential systems when geometric integrators are involved. The main idea underlying the presented techniques is to exploit the special block structure of a Hamiltonian and skew-symmetric matrix to gain a cheaper computation of the functions. First, we will consider an approach based on the numerical solution of structured linear systems and then another one based on the Schur decomposition of the matrix. Splitting techniques are also considered in order to reduce the computational cost. Several numerical tests and comparison examples are shown.     

Simultaneously controllable fuzzy matrices

Let F be a set of n × n fuzzy matrices. F is called simultaneously controllable if there exists a permutation matrix P such that for each A ε F, C = [c_ij] = P A P^T satisfies c_ij ≥ c_ji for i > j, where is the max-min composition. In this paper, the necessary and sufficient conditions for a set of n × n fuzzy matrices to be simultaneously controllable will be established. A constructive algorithm which can determine a simultaneously controllable set of n × n fuzzy matrices is presented as well.     

Eigen-solving via reduction to DPR1 matrices

Highly effective polynomial root-finders have been recently designed based on eigen-solving for DPR1 (that is diagonal + rank-one) matrices. We extend these algorithms to eigen-solving for the general matrix by reducing the problem to the case of the DPR1 input via intermediate transition to a TPR1 (that is triangular + rank-one) matrix. Our transforms use substantially fewer arithmetic operations than the QR classical algorithms but employ non-unitary similarity transforms of a TPR1 matrix, whose representation tends to be numerically unstable. We, however, operate with TPR1 matrices implicitly, as with the inverses of Hessenberg matrices. In this way our transform of an input matrix into a similar DPR1 matrix partly avoids numerical stability problems and still substantially decreases arithmetic cost versus the QR algorithm.     

Computation of the structured stability radius via matrix sign function

Robustness of perturbed state space models of the form is considered, where B, C are given matrices, A is an asymptotically stable matrix and D is the unknown perturbation matrix. An efficient algorithm to compute the complex structured stability radius, which is based on the properties of the matrix sign function, is presented. A comparison with previous algorithms shows the efficiency of the new algorithm