On a General Transformation Making a Dissimilarity Matrix Euclidean

When a dissimilarity matrix cannot be represented in a Euclidean space, it is possible to make it Euclidean by means of suitable transformations of the original dissimilarity values. In this paper we discuss some interesting properties of a class of transformations based on adding a specific squared Euclidean distance to the initial dissimilarity. An erratum to this article is available at .     

作为方法的空间

传统的空间研究,倾向于将空间视为一种"对象"。这种观念源自传统认识论对于空间属性的确认,即把空间看作绝对的、静止的几何学概念,或是某种先天纯粹的知觉形式,由此造成了空间阐释张力的严重不足。在列斐伏尔和福柯的空间思想引领之下,学界出现了"空间转向"之热潮,改变了研究者们对于空间的既往认识,其不再只是被动的研究对象,还可作为一种方法,成为认识问题的媒介与方式。这种空间方法论的创变,为研究界带来了极富革命性的启思。但就目前来说,空间方法论仍存有不少局限,这需要引起研究者们的及时关注。     

Unfolding a symmetric matrix

Graphical displays which show inter-sample distances are important for the interpretation and presentation of multivariate data. Except when the displays are two-dimensional, however, they are often difficult to visualize as a whole. A device, based on multidimensional unfolding, is described for presenting some intrinsically high-dimensional displays in fewer, usually two, dimensions. This goal is achieved by representing each sample by a pair of points, sayR _i andr _i, so that a theoretical distance between thei-th andj-th samples is represented twice, once by the distance betweenR _i andr _j and once by the distance betweenR _j andr _i. Selfdistances betweenR _i andr _i need not be zero. The mathematical conditions for unfolding to exhibit symmetry are established. Algorithms for finding approximate fits, not constrained to be symmetric, are discussed and some examples are given.     

A reduction algorithm for approximating a (nonmetric) dissimilarity by a tree distance

We propose a development stemming from Roux (1988). The principle is progressively to modify the dissimilarities so that every quadruple satisfies not only the additive inequality, as in Roux's method, but also all triangle inequalities. Our method thus ensures that the results are tree distances even when the observed dissimilarities are nonmetric. The method relies on the analytic solution of the least-squares projection onto a tree distance of the dissimilarities attached to a single quadruple. This goal is achieved by using geometric reasoning which also enables an easy proof of algorithm's convergence. This proof is simpler and more complete than that of Roux (1988) and applies to other similar reduction methods based on local least-squares projection. The method is illustrated using Case's (1978) data. Finally, we provide a comparative study with simulated data and show that our method compares favorably with that of Studier and Keppler (1988) which follows in the ADDTREE tradition (Sattath and Tversky 1977). Moreover, this study seems to indicate that our method's results are generally close to the global optimum according to variance accounted for.We offer sincere thanks to Gilles Caraux, Bernard Fichet, Alain Guénoche, and Maurice Roux for helpful discussions, advice, and for reading the preliminary versions of this paper. We are grateful to three anonymous referees and to the editor for many insightful comments. This research was supported in part by the GREG and the IA² network.     

Selection of a Representative Sample

Sometimes a larger dataset needs to be reduced to just a few points, and it is desirable that these points be representative of the whole dataset. If the future uses of these points are not fully specified in advance, standard decision-theoretic approaches will not work. We present here methodology for choosing a small representative sample based on a mixture modeling approach.     

作为世界假设的语境论

美国哲学家Pepper的根隐喻理论是形式论、机械论、有机论和语境论这些世界假设的基础。形式论的根隐喻是形式的相似性，机械论的根隐喻是机器，有机论的根隐喻是有机生长，语境论的根隐喻是历史事件。语境论是Pepper极力倡导的一种重要的整体论哲学学说，“变化”和“新奇”是其主要概念，并由这两个概念衍生出一套亚概念，用来说明事件的变化和发展。语境论的优点在于着眼于现实目标的分析，缺点是分析范围广，精确性弱。     

Mathematics as a Quasi-Empirical Science

The present paper aims at showing that there are times when set theoretical knowledge increases in a non-cumulative way. In other words, what we call ‘set theory’ is not one theory which grows by simple addition of a theorem after the other, but a finite sequence of theories T ₁, ..., T _n in which T _i+1, for 1 ≤ i < n, supersedes T _i . This thesis has a great philosophical significance because it implies that there is a sense in which mathematical theories, like the theories belonging to the empirical sciences, are fallible and that, consequently, mathematical knowledge has a quasi-empirical nature. The way I have chosen to provide evidence in favour of the correctness of the main thesis of this article consists in arguing that Cantor–Zermelo set theory is a Lakatosian Mathematical Research Programme (MRP).     

Tree enumeration modulo a consensus

The number of trees withn labeled terminal vertices grows too rapidly withn to permit exhaustive searches for Steiner trees or other kinds of optima in cladistics and related areas Often, however, structured constraints are known and may be imposed on the set of trees to be scanned These constraints may be formulated in terms of a consensus among the trees to be searched We calculate the reduction in the number of trees to be enumerated as a function of properties of the imposed consensusThis work was supported in part by the Natural Sciences and Engineering Research Council of Canada through operating grant A8867 to D Sankoff and infrastructure grant A3092 to D Sankoff, R J Cedergren and G Lapalme We are grateful to William H E Day for much encouragement and many helpful suggestions     

作为人文科学的心理学

心理学中一直存在自然科学和人文科学两种研究取向，前者是主流，后者是非主流。自然科学研究取向的心理学对整个世界心理学的发展作出了重要贡献，但它也存在一些偏差。人文科学研究取向的心理学对心理学研究中“科学主义”的超越以及它的方法论原则凸显了其存在的合理性与必要性。     

What is a Definition?

According to the standard view of definition, all defined terms are mere stipulations, based on a small set of primitive terms. After a brief review of the Hilbert-Frege debate, this paper goes on to challenge the standard view in a number of ways. Examples from graph theory, for example, suggest that some key definitions stem from the way graphs are presented diagramatically and do not fit the standard view. Lakatos's account is also discussed, since he provides further examples that suggest many definitions are much more than mere convenient abbreviations. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

论作为知识的技术标准

如何认识技术标准是有关技术标准研究的最基本问题,已有研究主要从经济学、社会学等视角来认识技术标准,往往忽略技术发展规律对技术标准的影响。本文从技术知识论角度,将技术标准看作一种技术知识,具体探讨技术标准作为编码化知识的特征以及技术标准与人工制品之间的关系,从而开拓对技术标准认识的全新视角,为解决技术标准研究领域的问题提供新的思路。     

自然辩证法:从恩格斯的一本书到马克思主义中国化的一门学科

从恩格斯的《自然辩证法》一书的出版、传播和研究,到1956年新中国第一个科学技术发展远景规划把自然辩证法定位为"哲学和自然科学之间"的一门科学,便成为一门学科在建设和发展中。今天,自然辩证法在中国已成为马克思主义学说的一个组成部分和马克思主义中国化的一门学科。     

Estimating the Cluster Tree of a Density by Analyzing the Minimal Spanning Tree of a Sample

runt pruning , a new clustering method that attempts to find modes of a density by analyzing the minimal spanning tree of a sample. The method exploits the connection between the minimal spanning tree and nearest neighbor density (e.g. normal mixture) or about the geometric shapes of the clusters, and is computationally feasible for large data sets.     

如何理解先验知识?

先验知识是一种"独立于经验"的知识。它所独有的特征是排除将感观世界作为其知识的基石或理由,而通过非感知理性获得,如直觉,纯理性和反省等等。本论文基于当代分析哲学家对康德先验知识概念的重新解读,修正和提炼,分析先验概念的消极描述,积极描述以及探讨不可修正性是否可作为其特征,进一步论证先验辩护即为先验的本质,赋予其时代特征。这一概念能为我们提供结合先验和经验各自优点的更好评价,同时也让我们更好地理解经验是如何与先验保持和谐,至少在原则上保持和谐的。     

“化学物质”是一个必要的术语

例举化学物质一词的使用情况，讨论界定化学物质一词的必要性，提出：化学物质是以原子及其聚集体（核-电子体系）为微观实体的，构成占有空间的宏观物体（气体、液体、固体）的东西。建议在辞书里增添化学物质为一词条，建议教学中讨论化学物质的概念。     

“化学物质”是一个必要的术语

例举化学物质一词的使用情况，讨论界定化学物质一词的必要性,提出：化学物质是以原子及其聚集体（核-电子体系）为微观实体的，构成占有空间的宏观物体（气体、液体、固体）的东西。建议在辞书里增添化学物质为一词条,建议教学中讨论化学物质的概念。     

Towards a Darwinian Approach to Mathematics

In the past decades, recent paradigm shifts in ethology, psychology, and the social sciences have given rise to various new disciplines like cognitive ethology and evolutionary psychology. These disciplines use concepts and theories of evolutionary biology to understand and explain the design, function and origin of the brain. I shall argue that there are several good reasons why this approach could also apply to human mathematical abilities. I will review evidence from various disciplines (cognitive ethology, cognitive psychology, cognitive archaeology and neuropsychology) that suggests that the human capacity for mathematics is a category-specific domain of knowledge, hard-wired in the brain, which can be explained as the result of natural selection.