面向社团结构划分的最短路径相异性指数算法

用最短路径距离取代网络中用布朗微粒衡量的两节点之间的距离,在此基础上提出了基于最短路径的相异性指数算法.对算法实现过程进行描述,并将算法应用于存在的研究算法分析实例上,说明该算法可行性.把该算法应用于本文构造的虚拟企业网络的社团划分上,划分结果与预期相符.     

Cross-sectional approach for clustering time varying data

Cluster analysis is to be performed on a three-mode data matrix of type: units, variables, time. A general model for calculating the distance between two units varying in time is proposed. One particular model is developed and used in an example concerned with clustering of 23 European countries according to the similarity of energy consumption in the years 1976–1982.Supported in part by the Research Council of Slovenia, Yugoslavia.     

Numerical classification of proximity data with assignment measures

An approach to numerical classification is described, which treats the assignment of objects to types as a continuous variable, called an assignment measure. Describing a classification by an assignment measure allows one not only to determine the types of objects, but also to see relationships among the objects of the same type and among the types themselves.A classification procedure, the Assignment-Prototype algorithm, is described and evaluated. It is a numerical technique for obtaining assignment measures directly from one-mode, two-way proximity matrices.     

Structural Classification Analysis of Three-Way Dissimilarity Data

The paper presents a methodology for classifying three-way dissimilarity data, which are reconstructed by a small number of consensus classifications of the objects each defined by a sum of two order constrained distance matrices, so as to identify both a partition and an indexed hierarchy. Specifically, the dissimilarity matrices are partitioned in homogeneous classes and, within each class, a partition and an indexed hierarchy are simultaneously fitted. The model proposed is mathematically formalized as a constrained mixed-integer quadratic problem to be fitted in the least-squares sense and an alternating least-squares algorithm is proposed which is computationally efficient. Two applications of the methodology are also described together with an extensive simulation to investigate the performance of the algorithm.     

Partial dissimilarities with application to clustering

We consider dissimilarities which are defined only on some pairs of items. Such situations may occur in some problems like unfolding or merging, or can be encountered as an intermediate step of a more general transformation. We give necessary and sufficient conditions for the existence of extensions with good properties and characterize the family of such extensions. Using partial dissimilarities we construct a dissimilarity-into-distance transformation family.The author thanks the editor and two anonymous referees for their suggestions and their helpful comments.     

Three-way distances

In this paper, dissimilarity relations are defined on triples rather than on dyads. We give a definition of a three-way distance analogous to that of the ordinary two-way distance. It is shown, as a straightforward generalization, that it is possible to define three-way ultrametric, three-way star, and three-way Euclidean distances. Special attention is paid to a model called the semi-perimeter model. We construct new methods analogous to the existing ones for ordinary distances, for example: principal coordinates analysis, the generalized Prim (1957) algorithm, hierarchical cluster analysis.     

关于溴水氧化酮糖问题的探讨

本文以多次实验事实为依据,在剖析酮糖结构和外部因素的基础上,得出了一个比较圆满的结论:在酸性条件下,溴水能直接氧化酮糖,而在碱性条件下,溴水能间接地氧化酮糖。从而对某些有机文献的叙述进行修正和补充。     

模糊集上度量的若干注记

给一个度量空间Ｓ上的两个模糊集ｕ 和ｖ,Ｃｈａｕｄｈｕｒｉ和Ｒｏｓｅｎｆｅｌｄ 定义了ｕ、ｖ 之间的Ｈａｕｓｄｏｒｆｆ距离。该定义只适应于ｕ 和ｖ 取离散值或连续值的情形。在更一般的情况下,定义了新的Ｈａｕｓｄｏｒｆｆ距离     

A computationally efficient approximation to the nearest neighbor interchange metric

The nearest neighbor interchange (nni) metric is a distance measure providing a quantitative measure of dissimilarity between two unrooted binary trees with labeled leaves. The metric has a transparent definition in terms of a simple transformation of binary trees, but its use in nontrivial problems is usually prevented by the absence of a computationally efficient algorithm. Since recent attempts to discover such an algorithm continue to be unsuccessful, we address the complementary problem of designing an approximation to the nni metric. Such an approximation should be well-defined, efficient to compute, comprehensible to users, relevant to applications, and a close fit to the nni metric; the challenge, of course, is to compromise these objectives in such a way that the final design is acceptable to users with practical and theoretical orientations. We describe an approximation algorithm that appears to satisfy adequately these objectives. The algorithm requires O(n) space to compute dissimilarity between binary trees withn labeled leaves; it requires O(n logn) time for rooted trees and O(n ² logn) time for unrooted trees. To help the user interpret the dissimilarity measures based on this algorithm, we describe empirical distributions of dissimilarities between pairs of randomly selected trees for both rooted and unrooted cases.The Natural Sciences and Engineering Research Council of Canada partially supported this work with Grant A-4142.     

Metric and Euclidean properties of dissimilarity coefficients

We assemble here properties of certain dissimilarity coefficients and are specially concerned with their metric and Euclidean status. No attempt is made to be exhaustive as far as coefficients are concerned, but certain mathematical results that we have found useful are presented and should help establish similar properties for other coefficients. The response to different types of data is investigated, leading to guidance on the choice of an appropriate coefficient.The authors wish to thank the referees, one of whom did a magnificent job in painstakingly checking the detailed algebra and detecting several slips.