Fitting a distance model to homogeneous subsets of variables: Points of view analysis of categorical data

An approach is presented for analyzing a heterogeneous set of categorical variables assumed to form a limited number of homogeneous subsets. The variables generate a particular set of proximities between the objects in the data matrix, and the objective of the analysis is to represent the objects in lowdimensional Euclidean spaces, where the distances approximate these proximities. A least squares loss function is minimized that involves three major components: a) the partitioning of the heterogeneous variables into homogeneous subsets; b) the optimal quantification of the categories of the variables, and c) the representation of the objects through multiple multidimensional scaling tasks performed simultaneously. An important aspect from an algorithmic point of view is in the use of majorization. The use of the procedure is demonstrated by a typical example of possible application, i.e., the analysis of categorical data obtained in a free-sort task. The results of points of view analysis are contrasted with a standard homogeneity analysis, and the stability is studied through a Jackknife analysis.     

虚拟现实技术系统的美学分析

虚拟现实技术系统通常是指以计算机技术为主,利用并综合三维图形技术、多媒体技术、仿真技术等诸多技术的新技术形态。虚拟现实技术系统所营造的"虚拟现实",开辟了人类的新一维生存空间,提供了新的生存方式。其所具有的媒介功能、去蔽功能、虚拟性、互动性、沉浸性、超越性,与艺术实践活动中展现的艺术特性相融通,彰显出技术与艺术的本质同一性。     

媒介与人类的互动延伸——麦克卢汉主义人本的进化的媒介技术本体论批判

"媒介是人的延伸"与"人是媒介的延伸"两个逆转性的命题,是西方麦克卢汉主义媒介技术哲学的核心命题,也是对该学派人本的进化的媒介技术本体论进行梳理评判的最佳切入点,其媒介与人互动延伸的隐喻性本体论蕴含着必然的逻辑悖论。     

The analysis of free-sorting data: Beyond pairwise cooccurrences

Free-sorting data are obtained when subjects are given a set of objects and are asked to divide them into subsets. Such data are usually reduced by counting for each pair of objects, how many subjects placed both of them into the same subset. The present study examines the utility of a group of additional statistics. the cooccurrences of sets of three objects. Because there are dependencies among the pair and triple cooccurrences, adjusted triple similarity statistics are developed. Multidimensional scaling and cluster analysis — which usually use pair similarities as their input data — can be modified to operate on three-way similarities to create representations of the set of objects. Such methods are applied to a set of empirical sorting data: Rosenberg and Kim's (1975) fifteen kinship terms.The author thanks Phipps Arabie, Lawrence Hubert, Lawrence Jones, Ed Shoben, and Stanley Wasserman for their considerable contributions to this paper.     

What has Philosophy to Offer to Chemistry?

The paper asks about the reasons for the neglect of chemistry in modern philosophy of science and investigates in how far this science can be the object of an autonomous philosophical reflection. It is argued that from a culturalistic point of view chemistry indeed offers a field of interesting questions ranging from the reconstruction of its epistemological objects to the elucidation of the semantic functions of terms like "atom" or "molecule". It is further argued that the philosophical reflection upon chemistry has important consequences for the didactic, the history and even the ethics of this science, making thus philosophy to a partner of chemistry in fulfilling its purposes in human society. This revised version was published online in July 2006 with corrections to the Cover Date.     

Fixed points approach to clustering

Assume that a dissimilarity measure between elements and subsets of the set being clustered is given. We define the transformation of the set of subsets under which each subset is transformed into the set of all elements whose dissimilarity to it is not greater than a given threshold. Then a cluster is defined as a fixed point of this transformation. Three well-known clustering strategies are considered from this point of view: hierarchical clustering, graph-theoretic methods, and conceptual clustering. For hierarchical clustering generalizations are obtained that allow for overlapping clusters and/or clusters not forming a cover. Three properties of dissimilarity are introduced which guarantee the existence of fixed points for each threshold. We develop the relation to the theory of quasi-concave set functions, to help give an additional interpretation of clusters.     

Degenerating Families of Dendrograms

Dendrograms used in data analysis are ultrametric spaces, hence objects of nonarchimedean geometry. It is known that there exist p-adic representations of dendrograms. Completed by a point at infinity, they can be viewed as subtrees of the Bruhat-Tits tree associated to the p-adic projective line. The implications are that certain moduli spaces known in algebraic geometry are in fact p-adic parameter spaces of dendrograms, and stochastic classification can also be handled within this framework. At the end, we calculate the topology of the hidden part of a dendrogram.     

Perceiving the Infinite and the Infinitesimal World: Unveiling and Optical Diagrams in Mathematics

Many important concepts of the calculus are difficult to grasp, and they may appear epistemologically unjustified. For example, how does a real function appear in “small” neighborhoods of its points? How does it appear at infinity? Diagrams allow us to overcome the difficulty in constructing representations of mathematical critical situations and objects. For example, they actually reveal the behavior of a real function not “close to” a point (as in the standard limit theory) but “in” the point. We are interested in our research in the diagrams which play an optical role –microscopes and “microscopes within microscopes”, telescopes, windows, a mirror role (to externalize rough mental models), and an unveiling role (to help create new and interesting mathematical concepts, theories, and structures). In this paper we describe some examples of optical diagrams as a particular kind of epistemic mediator able to perform the explanatory abductive task of providing a better understanding of the calculus, through a non-standard model of analysis. We also maintain they can be used in many other different epistemological and cognitive situations.     

The generation of random,binary unordered trees

Several techniques are given for the uniform generation of trees for use in Monte Carlo studies of clustering and tree representations. First, general strategies are reviewed for random selection from a set of combinatorial objects with special emphasis on two that use random mapping operations. Theorems are given on how the number of such objects in the set (e.g., whether the number is prime) affects which strategies can be used. Based on these results, methods are presented for the random generation of six types of binary unordered trees. Three types of labeling and both rooted and unrooted forms are considered. Presentation of each method includes the theory of the method, the generation algorithm, an analysis of its computational complexity and comments on the distribution of trees over which it samples. Formal proofs and detailed algorithms are in appendices.     

N-trees as nestings: Complexity,similarity, and consensus

Interpreting a taxonomic tree as a set of objects leads to natural measures of complexity and similarity, and sets natural lower bounds on a consensus tree Interpretations differing as to the kind of objects constituting a tree lead to different measures and consensus Subset nesting is preferred over the clusters (strict consensus) and even the triads interpretations because of its superior expression of shared structure Algorithms for computing the complexity and similarity of trees, as well as a consensus index onto [0,1], are presented for this interpretation The full consensus is defined as the only tree which includes all the nestings shared in a profile of rival trees and whose clusters reflect only nestings shared in the profile The full consensus is proved to exist uniquely for each profile, and to equal the Adams consensusThe author is grateful for the many helpful comments on presentation from Frances McA Adams, William H E Day, and Christopher A Meacham     

FINDCLUS: Fuzzy INdividual Differences CLUStering

ADditive CLUStering (ADCLUS) is a tool for overlapping clustering of two-way proximity matrices (objects?×?objects). In Simple Additive Fuzzy Clustering (SAFC), a variant of ADCLUS is introduced providing a fuzzy partition of the objects, that is the objects belong to the clusters with the so-called membership degrees ranging from zero (complete non-membership) to one (complete membership). INDCLUS (INdividual Differences CLUStering) is a generalization of ADCLUS for handling three-way proximity arrays (objects?×?objects?×?subjects). Here, we propose a fuzzified alternative to INDCLUS capable to offer a fuzzy partition of the objects by generalizing in a three-way context the idea behind SAFC. This new model is called Fuzzy INdividual Differences CLUStering (FINDCLUS). An algorithm is provided for fitting the FINDCLUS model to the data. Finally, the results of a simulation experiment and some applications to synthetic and real data are discussed.     

也谈腐殖酸与“黑漆古”镜表面呈色的关系

有学者认为，战国汉唐青铜镜表面并未镀锡，其“黑漆古”表层是高锡青铜基体在腐殖酸作用下自然形成的。该文依据有关试验和文献资料，提出了一些不同的看法：（１）现有腐殖酸处理试样从颜色、光泽到表面成分和表层结构，与古镜“黑漆古”都是不同的；（２）“腐殖酸富集说”解释不了“水银沁”镜、“花背”镜等的表面现象，以及一般铜镜的加工工艺；（３）它没有一条文献记载可以为据。笔者依旧认为：“黑漆古”是古镜镀锡表层自然腐蚀的结果，这是既有实物资料，也有文献记载为凭的。     

Reality,Systems and Impure Systems

Impure systems contain Objects and Subjects: Subjects are human beings. We can distinguish a person as an observer (subjectively outside the system) and that by definition is the Subject himself, and part of the system. In this case he acquires the category of object. Objects (relative beings) are significances, which are the consequence of perceptual beliefs on the part of the Subject about material or energetic objects (absolute beings) with certain characteristics.The IS (Impure System) approach is as follows: Objects are perceptual significances (relative beings) of material or energetic objects (absolute beings). The set of these objects will form an impure set of the first order. The existing relations between these relative objects will be of two classes: transactions of matter and/or energy and inferential relations. Transactions can have alethic modality: necessity, possibility, impossibility and contingency. Ontic existence of possibility entails that inferential relations have Deontic modality: obligation, permission, prohibition, faculty and analogy. We distinguished between theorems (natural laws) and norms (ethical, legislative and customary rules of conduct).     

Distributed Morality: Externalizing Ethical Knowledge in Technological Artifacts

Technology moves us to a better world. We contend that through technology people can simplify and solve moral tasks when they are in presence of incomplete information and possess a diminished capacity to act morally. Many external things, usually inert from the moral point of view, can be transformed into the so-called moral mediators. Hence, not all of the moral tools are inside the head, many of them are shared and distributed in “external” objects and structures which function as ethical devices.

隐性知识转移的特征与模式分析

本研究分析了隐性知识的特点、知识转移的特点和隐性知识转移的特征，指出人和技术是隐性知识转移的两个重要维度。隐性知识的流动和转移是一个不断反复、不断修正、不断完善的叠代过程，“专家咨询模式”存在N重互动关系。隐性知识的流动与转移是隐性知识价值化的必要路径，也是惟一途径。     

A New Dimension Reduction Method: Factor Discriminant K-means

Reduced K-means (RKM) and Factorial K-means (FKM) are two data reduction techniques incorporating principal component analysis and K-means into a unified methodology to obtain a reduced set of components for variables and an optimal partition for objects. RKM finds clusters in a reduced space by maximizing the between-clusters deviance without imposing any condition on the within-clusters deviance, so that clusters are isolated but they might be heterogeneous. On the other hand, FKM identifies clusters in a reduced space by minimizing the within-clusters deviance without imposing any condition on the between-clusters deviance. Thus, clusters are homogeneous, but they might not be isolated. The two techniques give different results because the total deviance in the reduced space for the two methodologies is not constant; hence the minimization of the within-clusters deviance is not equivalent to the maximization of the between-clusters deviance. In this paper a modification of the two techniques is introduced to avoid the afore mentioned weaknesses. It is shown that the two modified methods give the same results, thus merging RKM and FKM into a new methodology. It is called Factor Discriminant K-means (FDKM), because it combines Linear Discriminant Analysis and K-means. The paper examines several theoretical properties of FDKM and its performances with a simulation study. An application on real-world data is presented to show the features of FDKM.     

Reframing Architecture

I would like to thank Prof. Stephen Read (2011) and Prof. Andrew Benjamin (2011) for both giving inspiring and elaborate comments on my article “Dwelling in-between walls: the architectural surround”. As I will try to demonstrate below, their two different responses not only supplement my article very nicely, but also augment each other’s. In the beginning of Read’s comment, as he sets the stage for his observations, he unknowingly also points in the direction of Benjamin’s remarks: “I propose not to de-construct therefore, or add a point of view from an orthogonal position, but to try in the spirit of multidisciplinarity to talk in languages not well practiced—to begin to build what Bowker and Star call ‘boundary objects’ between different starting positions; points we can gather around to think further together” (Read 2011). Whereas Read facilitates a multidisciplinary dialogue, Benjamin focuses on how the absence of an initial distinction might threaten the endeavour of my paper. In my reply to Read and Benjamin, I will discuss their suggestions and arguments, while at the same time hopefully clarifying the postphenomenological approach to architecture.     

The Death and the Resurrection of (Psy)critique: The Case of Neuroeducation

A rapidly emerging hegemonic neuro-culture and a booming neural subjectivity signal the entry point for an inquiry into the status of the signifier neuro as a universal passe-partout. The wager of this paper is that the various (mis)appropriations of the neurosciences in the media and in academia itself point to something essential, if not structural, in connection with both the discipline of the neurosciences and the current socio-cultural and ideological climate. Starting from the case of neuroeducation (the application of neuroscience within education), the genealogy of the neurological turn is linked to the history of psychology and its inextricable bond with processes of psychologisation. If the neurological turn risks not merely neglecting the dimension of critique, but also obviating its possibility, then revivifying a psy-critique (understanding the academified modern subject as grounded in the scientific point of view from nowhere) might be necessary in order to understand today’s neural subjectivity and its place within current biopolitics.     

A mathematical programming approach to fitting general graphs

We present an algorithm for fitting general graphs to proximity data. The algorithm utilizes a mathematical programming procedure based on a penalty function approach to impose additivity constraints upon parameters. For a user-specified number of links, the algorithm seeks to provide the connected network that gives the least-squares approximation to the proximity data with the specified number of links, allowing for linear transformations of the data. The network distance is the minimum-path-length metric for connected graphs. As a limiting case, the algorithm provides a tree where each node corresponds to an object, if the number of links is set equal to the number of objects minus one. A Monte Carlo investigation indicates that the resulting networks tend to fall within one percentage point of the least-squares solution in terms of the variance accounted for, but do not always attain this global optimum. The network model is discussed in relation to ordinal network representations (Klauer 1989) and NETSCAL (Hutchinson 1989), and applied to several well-known data sets.     

华蘅芳《积较术》数学方法分析

在《积较术》中,基于独特的差分定义,华蘅芳构造了一个与Ｎｅｗｔｏｎ有限差分公式完全不同的差分体系,针对各种数表的使用,华蘅芳设计了一种”乘表相加“的计算方法。算理分析表明,这一算法与近代矩阵乘法一致。对《积较术》 中的数学思想与数学方法的分析,揭示了清末传统数学研究所的生长点及其在向近代数学转变过程的积极意义。