A uniform approach to multidimensional scaling

We present a method and an algorithm that puts interval and ordinal multidimensional scaling at two ends of a continuum. Theory and simulation show that the method compares favorably with classical scaling methods. A parameter is identified that produces scaling that combines benefits of interval, and ordinal scaling.     

The majorization approach to multidimensional scaling for Minkowski distances

The majorization method for multidimensional scaling with Kruskal's STRESS has been limited to Euclidean distances only. Here we extend the majorization algorithm to deal with Minkowski distances with 1≤p≤2 and suggest an algorithm that is partially based on majorization forp outside this range. We give some convergence proofs and extend the zero distance theorem of De Leeuw (1984) to Minkowski distances withp>1.     

A special Jackknife for Multidimensional Scaling

In this paper we develop a version of the Jackknife which seems especially suited for Multidimensional Scaling. It deletes one stimulus at a time, and combines the resulting solutions by a least squares matching method. The results can be used for stability analysis, and for purposes of cross validation.     

Metric unidimensional scaling and global optimization

For the problem of metric unidimensional scaling, the number of local minima is estimated. For locating the globally optimal solution we develop an approach, called the smoothing technique. Although not guaranteed inevitably to locate the global optimum, the smoothing technique did so in all computational experiments where the global optimum was known.     

Convergence of the majorization method for multidimensional scaling

In this paper we study the convergence properties of an important class of multidimensional scaling algorithms. We unify and extend earlier qualitative results on convergence, which tell us when the algorithms are convergent. In order to prove global convergence results we use the majorization method. We also derive, for the first time, some quantitative convergence theorems, which give information about the speed of convergence. It turns out that in almost all cases convergence is linear, with a convergence rate close to unity. This has the practical consequence that convergence will usually be very slow, and this makes techniques to speed up convergence very important. It is pointed out that step-size techniques will generally not succeed in producing marked improvements in this respect.     

Radial basis functions for exploratory data analysis: An iterative majorisation approach for Minkowski distances based on multidimensional scaling

This paper considers the use of radial basis functions for exploratory data analysis. These are used to model a transformation from a high-dimensional observation space to a low-dimensional one. The parameters of the model are determined by optimising a loss function defined to be the stress function in multidimensional scaling. The metric for the low-dimensional space is taken to be the Minkowski metric with order parameter 1<-p<-2. A scheme based on iterative majorisation is proposed.     

GENFOLD2: A set of models and algorithms for the general UnFOLDing analysis of preference/dominance data

A general set of multidimensional unfolding models and algorithms is presented to analyze preference or dominance data. This class of models termed GENFOLD2 (GENeral UnFOLDing Analysis-Version 2) allows one to perform internal or external analysis, constrained or unconstrained analysis, conditional or unconditional analysis, metric or nonmetric analysis, while providing the flexibility of specifying and/or testing a variety of different types of unfolding-type preference models mentioned in the literature including Caroll's (1972, 1980) simple, weighted, and general unfolding analysis. An alternating weighted least-squares algorithm is utilized and discussed in terms of preventing degenerate solutions in the estimation of the specified parameters. Finally, two applications of this new method are discussed concerning preference data for ten brands of pain relievers and twelve models of residential communication devices.     

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.     

Computational solutions for the problem of negative saliences and nonsymmetry in INDSCAL

Carroll and Chang have derived the symmetric CANDECOMP model from the INDSCAL model, to fit symmetric matrices of approximate scalar products in the least squares sense. Typically, the CANDECOMP algorithm is used to estimate the parameters. In the present paper it is shown that negative weights may occur with CANDECOMP. This phenomenon can be suppressed by updating the weights by the Nonnegative Least Squares Algorithm. A potential drawback of the resulting procedure is that it may produce two different versions of the stimulus space matrix. To obviate this possibility, a symmetry preserving algorithm is offered, which can be monitored to produce non-negative weights as well. This work was partially supported by the Royal Netherlands Academy of Arts and Sciences.     

Unidimensional scaling: A linear programming approach minimizing absolute deviations

A Mixed Integer Programming formulation can be developed for the classical unidimensional scaling problem when the measure of goodness-of-fit is thel ₁ norm of the discrepancies rather than the sum of the squares of the discrepancies.The author wishes to thank the editor and the three anonymous referees for their helpful and constructive comments.     

A latent class procedure for the structural analysis of two-way compositional data

This paper develops a new procedure for simultaneously performing multidimensional scaling and cluster analysis on two-way compositional data of proportions. The objective of the proposed procedure is to delineate patterns of variability in compositions across subjects by simultaneously clustering subjects into latent classes or groups and estimating a joint space of stimulus coordinates and class-specific vectors in a multidimensional space. We use a conditional mixture, maximum likelihood framework with an E-M algorithm for parameter estimation. The proposed procedure is illustrated using a compositional data set reflecting proportions of viewing time across television networks for an area sample of households.     

Clustering and clique partitioning: Simulated annealing and tabu search approaches

We study the application of simulated annealing and tabu search to the solution of the clique partitioning problem. We illustrate the effecveness of these techniques by computational results associated not only with randomly generated problems, but also with real-life problems arising from applications concerning the optimal aggregation of binary relations into an equivalence relation. The need for these approaches is emphasized by the example of a special class of instances of the clique partitioning problem for which the most commonly used heuristics perform arbitrarily badly, while tabu search systematically obtains the optimal solution.

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Résumé Nous étudions dans cet article l'application du recuit simulé et de la méthode de recherche tabou dans la résolution du problème de partitionnement de graphes en cliques. Nous illustrons l'efficacité de ces techniques par des résultats numériques associés soit à des problèmes génerés au hasard, soit à des problèmes réels concernant l'agrégation de relations binaires dans une relation d'équivalence. L'intérêt de ces approches est mis en évidence à travers une classe de problèmes pour lesquels les heuristiques les plus connues ont une performance arbitrairement mauvaise, tandis que la méthode de recherche tabou obtient systématiquement des solutions optimales.

     

A tree · a window · a hill; generalization of nearest-neighbor interchange in phylogenetic optimization

The method of nearest-neighbor interchange effects local improvements in a binary tree by replacing a 4-subtree by one of its two alternatives if this improves the objective function. We extend this to k-subtrees to reduce the number of local optima. Possible sequences of k-subtrees to be examined are produced by moving a window over the tree, incorporating one edge at a time while deactivating another. The direction of this movement is chosen according to a hill-climbing strategy. The algorithm includes a backtracking component. Series of simulations of molecular evolution data/parsimony analysis are carried out, fork=4, ..., 8, contrasting the hill-climbing strategy to one based on a random choice of next window, and comparing two stopping rules. Increasing window sizek is found to be the most effective way of improving the local optimum, followed by the choice of hill-climbing over the random strategy. A suggestion for achieving higher values ofk is based on a recursive use of the hill-climbing strategy.Acknowledgments: This work was supported in part by grants to the first author from the Natural Sciences and Engineering Research Council (Canada) and theFonds pour la formation de chercheurs et l'aide à la recherche (Québec), and to the third author from the Danish Research Council. The first author is a fellow of the Canadian Institute for Advanced Research. Much of the research was carried out in the spring of 1991 while the first author was visiting the University of Geneva; warmest thanks are due Professor Claude Weber for this opportunity.     

工业生物过程优化与放大研究中的科学问题——生物过程环境组学与多尺度方法原理研究

本文首先通过实例阐述了基于生物反应器生物过程多尺度分析的过程优化技术和基于细胞生理特性与生物反应器流场特性研究相结合的生物过程放大技术原理和应用方法,并根据生物过程环境对生物细胞生理特性的影响,提出把环境组学作为系统生物学研究的一部分,用系统生物学的方法对生物过程开展全域性（global）研究,即基于生物过程信息处理的生物过程系统工程研究,以期进一步推动我国生物反应器生物过程优化与放大研究的深入开展。     

休闲:一种文化价值观的转变

西方从上古的希伯莱宗教文化和古希腊哲学到中古的基督教神学再到近现代思想与文化的演变中，人们对休闲的意又及其与工作的关系的认识都发生了深刻的变化，这种变化体现了人们文化价值现的转变。各时期西方休闲观中的合理内涵，对在现代社会条件下构建健康的休闲生活方式提供一定的借鉴意义。     

发展基础研究 促进自主创新——在地方基础研究工作研讨会上的报告

同志们:基础研究是原始创新的源泉,是建设创新型国家的关键。《国家中长期科学和技术发展规划纲要(2006—2020)》把基础研究工作放在了重要地位。地方基础研究工作是我国基础研究工作体系的重要组成部分。科技部历来重视地方基础研究工作,于1999—2005年分别在苏州、四川、新疆、湖北和云南等地组织召开了地方基础研究工作会、研讨会和研修班,对促进地方基础研究工作的发展发挥了积极作用。本次会议将传达和学习全国科学技术大会和《国家中长期科学和技术发展规划纲要(2006—2020)》的主要精神;介绍《“十一五”国家基础研究规划》的基本内…     

索利·祖克曼：英国政府首席科学顾问制度的先驱

索利·祖克曼被认为是二十一世纪最重要的科学家之一,他在公共政策相关领域的工作尤为突出,影响深远。祖克曼原是一位动物学家,在1939年二战爆发后进入政府转型为军事顾问,就战时军事计划建言献策,曾参与诺曼底登陆计划的分析工作,为盟军将领选择正确的作战方案提供了支撑。战争结束后,祖克曼继续担任多个政府机构的科学顾问,并成为英国第一任政府首席科学顾问,使"政府首席科学顾问"从历史上临时性的私人聘用转变为制度化的工作职位,成为政府决策过程的核心组成部分。     

心智科学时代的“赫尔墨斯”：弗朗西斯科·瓦雷拉

弗朗西斯科·瓦雷拉是智利著名生物学家、神经科学家、心智科学家和哲学家,也是自创生、具身心智、生成认知以及神经现象学等观念或理论的倡导者和提出者。本文就掌握的史料从瓦雷拉的生平、学术贡献以及评价和影响等三个方面再现了其作为心智科学时代的“赫尔墨斯”形象。     

建设工程公众参与的非正式制度作用机制研究--一种文化视角的解读

公众参与建设工程逐渐被人们重视,但是如何实现高效公众参与仍然是难点。本文以文化为研究视角,分析非正式制度对建设工程公众参与的作用机制。分析表明传统文化对公众参与意识及其制度实施有负面影响,地方文化对公众参与制度实施有着重要作用。以上海磁悬浮事件为案例,证实了反向文化张力下非正式制度降低了公众参与绩效,地方性知识的变化推动了非正式制度的渐进式变迁。最后,指出公众参与文化的形成及地方性知识的变化,是中国公众参与非正式制度的变迁路径。