Numerical treatment of restricted gauss-markov model 1

The singular value decomposition (SVD) has been widely used in the ordinary linear model and other statistical problems. In this paper, we shall introduce the generalized singular value decomposition (GSVD) of any two matrices X and H having the same number of columns to moti-vate the numerical treatment of large scale restricted Gauss-Markov model (y,XβHβ = r,σ²1), a situation to reveal the relationship (or restriction) existing among the parameters of the model. Many approaches to restricted linear model are already available. Those approaches apply the generalized inverse of matrices and emphasize the the-oretical solution of the problem rather than the development of efficient and numerical stable algorithm for the computation of estimators. The possible merit of the method present here might lie in the facts that they directly lead to an efficient, numerically stable and easily programmed algorithm for     

On best affine prediction

The theory of best affine prediction (BAP) is extended to the vector case with possibly singular variance matrix of the predictor variable. The theory is then applied to derive Thomson’s classical predictor for factor scores, allowing for a singular variance matrix of the factors. The results are formulated in a free distribution setting. Further, Bartlett’s estimator is considered and compared with Thomson’s predictor. The authors are thankful to the two referees, one for a suggestion that led to the Addendum of the paper, and the other one for several very useful remarks. Research supported by the Spanish grant BEC2000-0983.     

奇异值分解在重构模糊决策系统规则库中的应用

利用SVD技术重构PSG模糊规则库,降低规则的数量。根据矩阵奇异值的性质,适当取舍模糊规则库后件矩阵Ω的奇异值,得到Ω的近似表示Ω,利用Ω重新构建规则库,新规则库的输入变量域的维数比原规则库的维数小,从而有效地降低了模糊规则数。仿真结果证明了该方法是有效的。     

Weighting variables in Kohonen competitive learning algorithms

This paper presents a new variable weight method, called the singular value decomposition (SVD) approach, for Kohonen competitive learning (KCL) algorithms based on the concept of Varshavsky et al. [18 R. Varshavsky, A. Gottlieb, M. Linial, and D. Horn, Novel unsupervised feature filtering of bilogical data, Bioinformatics 22 (2006), pp. 507–513.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]]. Integrating the weighted fuzzy c-means (FCM) algorithm with KCL, in this paper, we propose a weighted fuzzy KCL (WFKCL) algorithm. The goal of the proposed WFKCL algorithm is to reduce the clustering error rate when data contain some noise variables. Compared with the k-means, FCM and KCL with existing variable-weight methods, the proposed WFKCL algorithm with the proposed SVD's weight method provides a better clustering performance based on the error rate criterion. Furthermore, the complexity of the proposed SVD's approach is less than Pal et al. [17 S.K. Pal, R.K. De, and J. Basak, Unsupervised feature evaluation: a neuro-fuzzy approach, IEEE. Trans. Neural Netw. 11 (2000), pp. 366–376.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]], Wang et al. [19 X.Z. Wang, Y.D. Wang, and L.J. Wang, Improving fuzzy c-means clustering based on feature-weight learning, Pattern Recognit. Lett. 25 (2004), pp. 1123–1132.[Crossref], [Web of Science ®] , [Google Scholar]] and Hung et al. [9 W. -L. Hung, M. -S. Yang, and D. -H. Chen, Bootstrapping approach to feature-weight selection in fuzzy c-means algorithms with an application in color image segmentation, Pattern Recognit. Lett. 29 (2008), pp. 1317–1325.[Crossref], [Web of Science ®] , [Google Scholar]].     

Partitioning Pearson's Chi-squared Statistic for Singly Ordered Two-way Contingency Tables

This paper presents a partition of Pearson's chi-squared statistic for singly ordered two-way contingency tables. The partition involves using orthogonal polynomials for the ordinal variable while generalized basic vectors are used for the non-ordinal variable. The benefit of this partition is that important information about the structure of the ordered variable can be identified in terms of locations, dispersion and higher order components. For the non-ordinal variable, it is shown that the squared singular values from the singular value decomposition of the transformed dataset can be partitioned into location, dispersion and higher order components. The paper also uses the chi-squared partition to present an alternative to the maximum likelihood technique of parameter estimation for the log-linear analysis of the contingency table.     

一阶微分方程奇解的存在性及其求法

本文对相当广泛的一类一阶微分方程研究奇解的存在问题,提出一种不借助几何直观,而是用分析方法寻求一阶微分方程的奇解.     

基于矩阵奇异值分解的空间谱估计算法

本文提出了一种利用矩阵奇异值分解来作空间谱估计的方法,即对由天线阵获取的数据所构成的数据矩阵作奇异值分解、删除来自噪声的贡献的诸最小奇异值以改善信噪比,并利用噪声奇异向量和天线阵的方向向量正交的性质来计算空间谱。除了奇异值分解算法本身给计算稳定性带来好处外,本方法的谱估计性能和计算量均优于近几年来国外广泛关注的一种谱估计算法——MUSIC算法。本方法可用于高分辨的测向系统中。     

A stopping rule for structure-preserving variable selection

A stopping rule is provided for the backward elimination process suggested by Krzanowski (1987a) for selecting variables to preserve data structure. The stopping rule is based on perturbation theory for Procrustes statistics, and a small simulation study verifies its suitability. Some illustrative examples are also provided and discussed.     

二维非连续边界元分析积分计算的精确表达式

以二维弹性力学问题为研究对象，采用线性非连续元离散边界积分方程，给出了系数矩阵计算的精确表达式，对二维弹性力学问题进行了数值计算，对非连续边界元配位点对计算结果精度的影响进行了讨论，结果表明准奇异积分计算是配位点影响计算结构精度的主要因素。     

有限奇异酉几何与PBIB设计(Ⅱ)

用有限奇异酉几何中的1维非迷向子空间作处理构作了多个结合类的对称结合方案和相应的一些PBIB设计,并计算了全部参数.