The Young-Householder algorithm and the least squares multidimensional scaling of squared distances

It is shown that replacement of the zero diagonal elements of the symmetric data matrix of approximate squared distances by certain other quantities in the Young-Householder algorithm will yield a least squares fit to squared distances instead of to scalar products. Iterative algorithms for obtaining these replacement diagonal elements are described and relationships with the ELEGANT algorithm (de Leeuw 1975; Takane 1977) are discussed. In large residual situations a penalty function approach, motivated by the ELEGANT algorithm, is adopted. Empirical comparisons of the algorithms are given.An early version of this paper was presented at the Multidimensional Data Analysis Workshop, Pembroke College, Cambridge, July 1985. I want to thank Jan de Leeuw and Yoshio Takane for bringing the ELEGANT algorithm to my attention and for clarifying its rationale and notation. My thanks go also to Stephen du Toit for help with the ALSCAL computations reported in Section 7.     

正多边形的一个性质的推广

将文 [1]给出的正多边形的一个性质推广到了任意多边形和任意多面体 ,从而使文 [1]的结论成了本文得到的一般结论的特例     

汽车甩挂运输最佳运距的研究

汽车甩挂运输是先进的公路运输形式之一。从汽车甩挂运输生产工艺的全过程和昼提高车时利用率出发，提出了适合我国目前推行汽车甩挂运输的最佳单程运距为５３－１００ｋｍ、１３３－２２０ｋｍ和２９３－４６０ｋｍ。     

现存最完整的一份唐代地理全图数据集

中国传统测绘学研究中存在着一个重要问题，就是虽然历史上流传下来大量较高水平的地理全图，但迄今尚未找到一份具体用来绘制这些地图的原始数据集，也不清楚古人如何绘制成这些地图。笔者通过认真分析唐代李吉甫的《元和郡县图志》，发现其中的方向和里程数据就是用来绘制地图的，结合其它文献分析推断：《元和郡县图志》现存最完整的一份唐代地理全图数据集。     

THE HAMMING DISTANCES OF NEGACYCLIC CODES OF LENGTH 2^s OVER GR （2^α, m）

The Hamming distances of all negacyclic codes of length 28 over the Gaiois ring GR （2^α, m） are given. In particular, the Lee distances of all negacyclic codes over Z4 of length 2^s are obtained. The Gray images of such negacyclic codes over Z4 are also determined under the Gray map.     

A validation study of a variable weighting algorithm for cluster analysis

De Soete (1986, 1988) proposed a variable weighting procedure when Euclidean distance is used as the dissimilarity measure with an ultrametric hierarchical clustering method. The algorithm produces weighted distances which approximate ultrametric distances as closely as possible in a least squares sense. The present simulation study examined the effectiveness of the De Soete procedure for an applications problem for which it was not originally intended. That is, to determine whether or not the algorithm can be used to reduce the influence of variables which are irrelevant to the clustering present in the data. The simulation study examined the ability of the procedure to recover a variety of known underlying cluster structures. The results indicate that the algorithm is effective in identifying extraneous variables which do not contribute information about the true cluster structure. Weights near 0.0 were typically assigned to such extraneous variables. Furthermore, the variable weighting procedure was not adversely effected by the presence of other forms of error in the data. In general, it is recommended that the variable weighting procedure be used for applied analyses when Euclidean distance is employed with ultrametric hierarchical clustering methods.     

投影距离的概率峰值效应及其在三维目标识别中的应用

在计算机视觉中，由于物体的几何特性随视线的变化而变化，从而给三维目标识别带来了困难．在设计识别算法时，关键是理解目标重要特征的变化，如角度、距离等的变化．在视线方向各向同性条件下，投影角度和距离的概率密度在其原值附近具有峰值效应，即投影角度及距离接近于原角度及距离．利用投影角度的联合概率函数可识别多面体．在已知距离时，为了便于识别目标，导出了投影距离的密度函数．实验结果证明了该方法的有效性．     

一种改进禁忌搜索的K-medoids聚类算法

针对传统K-medoids聚类算法初始聚类中心随机选择、聚类精度不高、全局搜索能力较差以及禁忌搜索算法对初始值随机选取等问题,提出了一种粒计算与最大距离积法相结合的初始化禁忌搜索初始值算法,将改进后的禁忌搜索算法用来优化K-medoids,以提高聚类算法的性能。通过仿真试验论证了该算法具有较高的效率和准确率以及较强的稳定性。     

非线性热传导反问题数值求解

引入Bregman距离函数,建立了非线性热传导反问题的一种数值求解模式,可对非线性导热系数和边界条件等宗量进行单一和组合识别．所建的有限元正／反演模型分别考虑了非均质和分布参数的影响,并应用同伦算法进行反演求解,探讨了信息测量误差和变量初值对反演结果的影响．数值验证取得了满意的结果．     

小波域梯度准则多焦距图像融合方法的研究

通过介绍小波域不同融合方法的特点,提出一种小波域梯度的改进算法,对多焦距图像采用双正交小波进行分解,对小波系数根据小波域平均梯度进行加权叠加,并通过仿真证明本算法具有很好的效果。