The median procedure for n-trees

Let (X,d) be a metric space The functionM:X ^k 2 ^x defined by is the minimum } is called themedian procedure and has been found useful in various applications involving the notion of consensus Here we present axioms that characterizeM whenX is a certain class of trees (hierarchical classifications), andd is the symmetric difference metricWe would like to thank the referees and Editor for helpful comments     

A maximum likelihood methodology for clusterwise linear regression

This paper presents a conditional mixture, maximum likelihood methodology for performing clusterwise linear regression. This new methodology simultaneously estimates separate regression functions and membership inK clusters or groups. A review of related procedures is discussed with an associated critique. The conditional mixture, maximum likelihood methodology is introduced together with the E-M algorithm utilized for parameter estimation. A Monte Carlo analysis is performed via a fractional factorial design to examine the performance of the procedure. Next, a marketing application is presented concerning the evaluations of trade show performance by senior marketing executives. Finally, other potential applications and directions for future research are identified.     

Thresholded consensus for n-trees

A class of (multiple) consensus methods for n-trees (dendroids, hierarchical classifications) is studied. This class constitutes an extension of the so-called median consensus in the sense that we get two numbersm andm such that: If a clusterX occurs ink n-trees of a profileP, withk m, then it occurs in every consensus n-tree ofP. IfX occurs ink n-trees ofP, withm k <m, then it may, or may not, belong to a consensus n-tree ofP. IfX occurs ink n-trees ofP, withk <m then it cannot occur in any consensus n-tree ofP. If these conditions are satisfied, the multiconsensus function is said to be thresholded by the pair (m,m). Two results are obtained. The first one characterizes the pairs of numbers that can be viewed as thresholds for some consensus function. The second one provides a characterization of thresholded consensus methods. As an application a characterization of the quota rules is provided.

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Resume Cet article traite d'une classe de méthodes de consensus (multiples) entre des classifications hiérarchiques. Cette classe est une généralisation du consensus médian dans las mesure oú elle est constituée des méthodes c pour lesquelles il existe deux nombresm etm tels que: Si une classeX appartient ák hiérarchies d'un profilP, aveck m, alorsX appartient á chaque hiérarchie consensus deP. SiX appartient ák hiérarchies deP, avecm k <m, alorsX, peut, ou non, appartenir à une hiérarchie consensus deP. SiX appartient àk hiérarchies deP, aveck <m, alorsX n'appartient á aucune hiérarchie consensus deP. On dit alors que le couple (m,m) est un seuil pour c. Deux résultats sont obtenus. Le premier caractérise les couples de nombres qui sont des seuils de consensus. Le second caractérise les consensus admettant un seuil. Une caractérisation de la régle des quotas est déduite de ce second résultat.

     

A mixture likelihood approach for generalized linear models

A mixture model approach is developed that simultaneously estimates the posterior membership probabilities of observations to a number of unobservable groups or latent classes, and the parameters of a generalized linear model which relates the observations, distributed according to some member of the exponential family, to a set of specified covariates within each Class. We demonstrate how this approach handles many of the existing latent class regression procedures as special cases, as well as a host of other parametric specifications in the exponential family heretofore not mentioned in the latent class literature. As such we generalize the McCullagh and Nelder approach to a latent class framework. The parameters are estimated using maximum likelihood, and an EM algorithm for estimation is provided. A Monte Carlo study of the performance of the algorithm for several distributions is provided, and the model is illustrated in two empirical applications.     

Large-sample results for optimization-based clustering methods

Many common (nonhierarchical) clustering and classification methods are optimization-based methods, in the sense described by Windham (1987) in this Journal. This paper gives some large sample properties for estimates derived by such methods. Under appropriate conditions, such estimates converge with probability one to a limit, and are asymptotically normally distributed around that limiting value. The conditions are satisfied by most of the common examples of optimization-based methods. Prepared for the 2nd International Conference, International Federation of Classification Societies, Charlottesville, VA, 1989. Supported in part by summer research funds, Graduate School of Business Administration, University of Colorado at Denver.     

The mixture method of clustering applied to three-way data

Clustering or classifying individuals into groups such that there is relative homogeneity within the groups and heterogeneity between the groups is a problem which has been considered for many years. Most available clustering techniques are applicable only to a two-way data set, where one of the modes is to be partitioned into groups on the basis of the other mode. Suppose, however, that the data set is three-way. Then what is needed is a multivariate technique which will cluster one of the modes on the basis of both of the other modes simultaneously. It is shown that by appropriate specification of the underlying model, the mixture maximum likelihood approach to clustering can be applied in the context of a three-way table. It is illustrated using a soybean data set which consists of multiattribute measurements on a number of genotypes each grown in several environments. Although the problem is set in the framework of clustering genotypes, the technique is applicable to other types of three-way data sets.     

The Factorial Minimum Spanning Tree as a Reference for a Synthetic Index of Complex Phenomena

This paper is aimed at combining both the properties of factorial subspaces and those of the Minimum Spanning Tree Algorithm (MST) to obtain a reference structure (the Maximum Path) in which the statistical units are in reduced subordering. The coordinates (factor scores) of the statistical units in a multi-factorial subspace through Principal Component Analysis are the basis for the Minimum Spanning Tree. In the MST, we single out a path of maximum length. On the Maximum Path each graduation obtained for the unit can be used as a Synthetic Index of the phenomenon analyzed. Two distinct strategies lead to the choice of the subspace in which we have the best representation of the units in the Maximum Path. The validity of the method is confirmed by results achieved in various applications to real data.     

工程问题的哲学意义

工程是一种有一定规模的建造活动，当今人类正生活在一个由各种有形和无形的工程所关联起来的网络中，人类当代文明就是一种工程文明。工程的普遍化使得工程问题上升到了哲学层面，具有了哲学意义。工程个案和一般工程学科解决工程中的具体问题，但惟独不对“工程本身”发问。对工程的哲学研究则专门追究“工程之所以为工程”的问题。工程问题的哲学意义至少有两种：一是按照哲学研究的惯常方式建构一门新的部门哲学，二是通过对工程问题的特殊性呈现给人类思维方式的变革提供一个契机。任何一项工程都牵涉无数复杂因素，它们之间尽管具有这样那样的逻辑性关联，但总有一些因素之间没有逻辑联系，这就使得工程问题归根到底不可能逻辑地、理论地和哲学地解决。理论和工程之间不可能逻辑地统一起来，这就是工程问题通过哲学而给我们的最特殊的启示。     

The Emergence of Symbolic Algebra as a Shift in Predominant Models

Historians of science find it difficult to pinpoint to an exact period in which symbolic algebra came into existence. This can be explained partly because the historical process leading to this breakthrough in mathematics has been a complex and diffuse one. On the other hand, it might also be the case that in the early twentieth century, historians of mathematics over emphasized the achievements in algebraic procedures and underestimated the conceptual changes leading to symbolic algebra. This paper attempts to provide a more precise setting for the historical context in which this decisive step to symbolic reasoning took place. For that purpose we will consider algebraic problem solving as model-based reasoning and symbolic representation as a model. This allows us to characterize the emergence of symbolic algebra as a shift from a geometrical to a symbolic mode of representation. The use of the symbolic as a model will be situated in the context of mercantilism where merchant activity of exchange has led to reciprocal relations between money and wealth.

Complete linkage as a multiple stopping rule for single linkage clustering

Two commonly used clustering criteria are single linkage, which maximizes the minimum distance between clusters, and complete linkage, which minimizes the maximum distance within a cluster. By synthesizing these criteria, partitions of objects are sought which maximize a combined measure of the minimum distance between clusters and the maximum distance within a cluster. Each combined measure is shown to select a partition in the single linkage hierarchy. Therefore, in effect, complete linkage is used to provide a stopping rule for single linkage. An algorithm is outlined which uses the distance between each pair of objects twice only. To illustrate the method, an example is given using 23 Glamorganshire soil profiles.     

重复元件介导的重组是新嵌合基因形成的一个重要机制

先前的研究提示重复元件在产生新的嵌合基因中具有机制性的作用,这与经典的外显子洗牌模型是一致的,它依赖于非同源重组。而近期一些关于染色体异常的研究结果显示,异位的同源重组可能对于产生新基因也非常重要。本项研究通过对8种果蝇的年轻基因进行筛选和分析,从中识别出了17个重复片段,它们是在最近1200万年中通过异位重组形成的。它们中的大多数已具有功能,并进化出多样的表达类型和嵌合结构。这些结果证实,重复元件介导的非等位同源重组在产生新嵌合基因中起到重要作用。     

晚清筹办北洋海军时引进军事装备的思路与渠道——从一则李鸿章致克虏伯的署名信谈起

光绪六年(1880年)李鸿章致信德国工业巨头阿尔弗雷德.克虏伯,商谈购买战船与火炮之事。信函的内容表明:李鸿章与阿尔弗雷德有直接的书信往来;克虏伯公司力图向北洋推销新式军火;李鸿章曾留意克虏伯所造的毕福脱快船,但是拒绝对方为原有火炮更换新式炮弹的要求;李凤苞和徐建寅被寄予厚望。李鸿章重视与克虏伯等西方军火制造商保持直接的交往,双方相互派员成为北洋引进军事装备和相关技术的重要渠道。     

"世界"是如何可能的?--论康德通过世界问题为科学奠基的策略

"世界"问题是哲学追问的核心问题,因为人类的一切思想活动和实践活动都立足于其在世界中的存在.康德改变了提问方式,追问世界是如何对我们显现的,追问对于我们而言"世界是如何可能的".康德认为感性世界的可能性在于先天纯直观形式与物自体刺激相结合,知性世界的可能性在于范畴对于感性知识的加工.前者是数学作为一门科学的合法性所在,而后者是自然科学作为科学的合法性所在.