A Procedure for Estimating the Number of Clusters in Logistic Regression Clustering

This paper studies the problem of estimating the number of clusters in the context of logistic regression clustering. The classification likelihood approach is employed to tackle this problem. A model-selection based criterion for selecting the number of logistic curves is proposed and its asymptotic property is also considered. The small sample performance of the proposed criterion is studied by Monto Carlo simulation. In addition, a real data example is presented. The authors would like to thank the editor, Prof. Willem J. Heiser, and the anonymous referees for the valuable comments and suggestions, which have led to the improvement of this paper.     

OCLUS: An Analytic Method for Generating Clusters with Known Overlap

The primary method for validating cluster analysis techniques is throughMonte Carlo simulations that rely on generating data with known cluster structure (e.g., Milligan 1996). This paper defines two kinds of data generation mechanisms with cluster overlap, marginal and joint; current cluster generation methods are framed within these definitions. An algorithm generating overlapping clusters based on shared densities from several different multivariate distributions is proposed and shown to lead to an easily understandable notion of cluster overlap. Besides outlining the advantages of generating clusters within this framework, a discussion is given of how the proposed data generation technique can be used to augment research into current classification techniques such as finite mixture modeling, classification algorithm robustness, and latent profile analysis.     

Intelligent Choice of the Number of Clusters in K-Means Clustering: An Experimental Study with Different Cluster Spreads

The issue of determining “the right number of clusters” in K-Means has attracted considerable interest, especially in the recent years. Cluster intermix appears to be a factor most affecting the clustering results. This paper proposes an experimental setting for comparison of different approaches at data generated from Gaussian clusters with the controlled parameters of between- and within-cluster spread to model cluster intermix. The setting allows for evaluating the centroid recovery on par with conventional evaluation of the cluster recovery. The subjects of our interest are two versions of the “intelligent” K-Means method, ik-Means, that find the “right” number of clusters by extracting “anomalous patterns” from the data one-by-one. We compare them with seven other methods, including Hartigan’s rule, averaged Silhouette width and Gap statistic, under different between- and within-cluster spread-shape conditions. There are several consistent patterns in the results of our experiments, such as that the right K is reproduced best by Hartigan’s rule – but not clusters or their centroids. This leads us to propose an adjusted version of iK-Means, which performs well in the current experiment setting.     

A Combinatorial Approach to Assess the Separability of Clusters

Separability of clusters is an issue that arises in many different areas, and is often used in a rather vague and subjective manner. We introduce a combinatorial notion of interiority to derive a global view on separability of a set of entities. We develop this approach further to evaluate the overall separability of a partition in the context of cluster analysis. Our approach captures combinatorial and geometrical aspects of data and provides, in addition to numerical evaluations, graphical representations particularly useful when data are not easily visualized. We illustrate the methodology on some real and simulated datasets.     

Fixed Point Clusters for Linear Regression: Computation and Comparison

In this paper an algorithm is developed, which aims to find all FPCs of a dataset corresponding to well separated linear regression subpopulations. Its ability to find such subpopulations under the occurence of outliers is compared to methods based on ML-estimation of mixture models by means of a simulation study. Furthermore, FPC analysis is applied to a real dataset.     

大规模成矿作用与大型矿集区预测研究

《大规模成矿作用与大型矿集区预测》是国家重点基础研究发展计划 (973计划 )实施以来第一个以固体矿产资源为目标的研究项目。通过 5年 (1 999年 1 0月— 2 0 0 4年 9月 )研究 ,在多项基础地质和矿产资源成矿理论研究方面取得了重要进展 :初步提出了中国中新生代大陆成矿理论体系 ,为预测大矿和大型矿集区奠定了理论基础 ;研制和发展了 4项找矿新技术方法 ,以及提出了两种找矿新思路 ;并在实验阶段圈定了 5个矿集区尺度的找矿靶区 ,发现了一批矿化异常区。此外 ,在研究过程中还形成了 3个国家级优秀科研群体和 3个部门级优秀科研群体 ,培养出 9名优秀中青年人才以及大批博士后工作人员、博士研究生和硕士研究生 ,其中有不少中青年科学家已在国际学术组织任职。研究期间共发表科学论文 772篇 ,其中SCI检索论文2 2 7篇 (国外论文 1 2 5篇 )     

A Nonlinear Method for Measuring the Effects of Environmental Variations

Ever wonder if it is possible to construct a numeric scale for environmental variables, like one does for the temperature? This paper is an attempt to construct one. There are two main parts: section “Statistical Analysis of Variations” presents a general statistical strategy for environmental factor selection. Section “Nonlinear Analytical Geometric Model of Variations” develops an analytical geometric representation of system variations in response to environmental changes. The model is used to quantify the effects of environmental interactions. The paper treats only one-dimensional case, however, the derivation of the case of multiple independent factors follows immediately. The general method developed in this paper may prove applicable to many different fields, such as extensions beyond classical physics, economics, and other sciences. Section “Conclusion” provides an illustration of applications, examples and implications of the results.     

探寻公众感知的本质与迭代逻辑

德国著名科技哲学的先驱汉斯·赖辛巴赫认为,科学的哲学是人类思想一切形式的逻辑分析,并提出包括情感主义理论学在内的分析哲学,有助于促进科学研究、决策等;而哲学本身是由概念探究组成的,科学技术的进步可以提高人们的认知能力,社会舆情的进步则使人们渴望探寻公众感知的本质。本文在情感、行为、认知的基础上分析了公众感知本质的源、功能、层级效应,并通过情感的递进关系分析了公众感知各组成要素的关系结构及多元迭代关系逻辑,由此,公众感知的本质与迭代逻辑研究开启了新的路径。     

伦理矩阵:一种技术评价工具

现代技术的应用导致了众多的伦理争议,如何解决这类争议已成为学界日益重视的问题。伦理矩阵作为一种兼顾个人和团体的多元综合评价方法,在转基因技术的伦理评价中已较传统技术评价方法显示出更多的合理性。充分认识这一方法的思想内涵,掌握系统操作程序,有助于我们对技术做出合理评价,对科学决策有积极的帮助。     

数与力:牛顿科学纲领的基本内核探微

牛顿科学劳作背后的形上理念及其方法论架构乃科学史中的元问题之一,也是以往学界乏有论及的盲区。本文注重一种回到事情本身的理路,从牛顿的具体文本出发,撷取出微分定律的工具理性、力之概念的别样意蕴和运动机制的自然本态等三大理论质点,以图彰显牛顿科学纲领的别样意蕴,并澄清以往学界对牛顿的某些误解与误读之处。     

A Rational Belief: The Method of Discovery in the Complex Variable

The importance of mathematics in the context of the scientific and technological development of humanity is determined by the possibility of creating mathematical models of the objects studied under the different branches of Science and Technology. The arithmetisation process that took place during the nineteenth century consisted of the quest to discover a new mathematical reality in which the validity of logic would stand as something essential and central. Nevertheless, in contrast to this process, the development of mathematical analysis within a framework that largely involves intuition and geometry is a fact that cannot go unnoticed amongst the mathematics community, as we shall show in this paper through the research made by Bernhard Riemann on complex variables.     

数的观念与治道传统--兼论"李约瑟难题"

中国古代数的观念与治道传统关系极为紧密。受传统治道思想的影响，数的观念在起源与发展过程中，“理性”受到“神性”的抑制；在理论形成阶段，人们注重对“公约”的遵守而采走上“公理化”的道路；而在对数的运用与研究过程中，则过于强调实用、功利，始终采能超越封建政治文化制度，仅以求得特定的方法、技巧为满足，从而陷入“数术”的框架，采能像近代西方那样创设独立的“数学”理论体系。     

Detecting Clusters in the Data from Variance Decompositions of Its Projections

A new projection-pursuit index is used to identify clusters and other structures in multivariate data. It is obtained from the variance decompositions of the data’s one-dimensional projections, without assuming a model for the data or that the number of clusters is known. The index is affine invariant and successful with real and simulated data. A general result is obtained indicating that clusters’ separation increases with the data’s dimension. In simulations it is thus confirmed, as expected, that the performance of the index either improves or does not deteriorate when the data’s dimension increases, making it especially useful for “large dimension-small sample size” data. The efficiency of this index will increase with the continuously improved computer technology. Several applications are presented.     

Beyond Physics? On the Prospects of Finding a Meaningful Oracle

Certain enterprises at the fringes of science, such as intelligent design creationism, claim to identify phenomena that go beyond not just our present physics but any possible physical explanation. Asking what it would take for such a claim to succeed, we introduce a version of physicalism that formulates the proposition that all available data sets are best explained by combinations of “chance and necessity”—algorithmic rules and randomness. Physicalism would then be violated by the existence of oracles that produce certain kinds of noncomputable functions. Examining how a candidate for such an oracle would be evaluated leads to questions that do not admit an easy resolution. Since we lack any plausible candidate for any such oracle, however, chance-and-necessity physicalism appears very likely to be correct.     

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.     

A Generalized Rand-Index Method for Consensus Clustering of Separate Partitions of the Same Data Base

T clusters, based on J distinct, contributory partitions (or, equivalently, J polytomous attributes). We describe a new model/algorithm for implementing this objective. The method's objective function incorporates a modified Rand measure, both in initial cluster selection and in subsequent refinement of the starting partition. The method is applied to both synthetic and real data. The performance of the proposed model is compared to latent class analysis of the same data set.     

内证：中国人文主义心理学之独特研究方法

中国人文主义心理学研究方法中最具独特价值,且蕴藏着无可替代强大生命力的唯有内证法。本从儒、道、佛三家求道的方法论实践出发,描述了其在精神领域、心灵层面实现内在实证的基本过程。三家虽在求道的终极追求上各不相同,但其“静观”、“存想”和“禅定”的内证表现出如下特征：统合主客、摒弃言语、超越经验等。内证作为中国人文主义心理学研究中觉知自我意识的极有效方法,也极大地扩展了西方心理学研究方法的内容和视野。     

对心灵因果性的辩护——论过决定的区分

金在权的排斥论证为非还原的物理主义带来严重的危机,该论证通过说明非还原物理主义所接受的五个前提之间的不自洽,从理论层面否定了不可还原的心灵因果性。面对金在权的质疑,很多学者尝试从前提之一——非过决定论入手,试图解决危机。然而,笔者认为他们的尝试没有从根本上解决过决定状况所带来的困难。在本文中,笔者试图对过决定状况的定义做出进一步的澄清,从而对过决定定义中的关键概念进行区分。以此说明非过决定论这一前提的合理性有待考量,金在权的排斥论证的有效性也有待商榷。     

A Property of the CHAID Partitioning Method for Dichotomous Randomized Response Data and Categorical Predictors

In this paper, we present empirical and theoretical results on classification trees for randomized response data. We considered a dichotomous sensitive response variable with the true status intentionally misclassified by the respondents using rules prescribed by a randomized response method. We assumed that classification trees are grown using the Pearson chi-square test as a splitting criterion, and that the randomized response data are analyzed using classification trees as if they were not perturbed. We proved that classification trees analyzing observed randomized response data and estimated true data have a one-to-one correspondence in terms of ranking the splitting variables. This is illustrated using two real data sets.     

论数字的哲学特性对法律发展的影响

由于理性能力的基础和核心就是计算,因此现代法律的形式合理性立基于数字、数学和逻辑思维体系之上,数字的哲学特性深刻影响着近现代法律的发展。主要体现在四个方面,其一,对数字科学性的认识是法律科学化的起点;其二,数字的确定性对实现法律的确定性作用巨大;其三,数字的简单性对法哲学基本范畴的影响;其四,数字的客观性影响法学思维方式的转变。