Globally Optimal Clusterwise Regression By Column Generation Enhanced with Heuristics,Sequencing and Ending Subset Optimization

A column generation based approach is proposed for solving the cluster-wise regression problem. The proposed strategy relies firstly on several efficient heuristic strategies to insert columns into the restricted master problem. If these heuristics fail to identify an improving column, an exhaustive search is performed starting with incrementally larger ending subsets, all the while iteratively performing heuristic optimization to ensure a proper balance of exact and heuristic optimization. Additionally, observations are sequenced by their dual variables and by their inclusion in joint pair branching rules. The proposed strategy is shown to outperform the best known alternative (BBHSE) when the number of clusters is greater than three. Additionally, the current work further demonstrates and expands the successful use of the new paradigm of using incrementally larger ending subsets to strengthen the lower bounds of a branch and bound search as pioneered by Brusco's Repetitive Branch and Bound Algorithm (RBBA).     

s-Consensus index method: An additional axiom

A consensus index method is an ordered pair consisting of a consensus method and a consensus index Day and McMorris (1985) have specified two minimal axioms, one which should be satisfied by the consensus method and the other by the consensus index The axiom for consensus indices is not satisfied by the s-consensus index In this paper, an additional axiom, which states that a consensus index equal to one implies profile unanimity, is proposed The s-consensus method together with a modification of the s-consensus index (i e, normalized by the number of distinct nontrivial clusters in the profile) is shown to satisfy the two axioms proposed by Day and McMorris and the new axiom     

A Permutation-Translation Simulated Annealing Algorithm for L1 and L2 Unidimensional Scaling

Given a set of objects and a symmetric matrix of dissimilarities between them, Unidimensional Scaling is the problem of finding a representation by locating points on a continuum. Approximating dissimilarities by the absolute value of the difference between coordinates on a line constitutes a serious computational problem. This paper presents an algorithm that implements Simulated Annealing in a new way, via a strategy based on a weighted alternating process that uses permutations and point-wise translations to locate the optimal configuration. Explicit implementation details are given for least squares loss functions and for least absolute deviations. The weighted, alternating process is shown to outperform earlier implementations of Simulated Annealing and other optimization strategies for Unidimensional Scaling in run time efficiency, in solution quality, or in both.     

Technology and the Body: the (Im)Possibilities of Re-embodiment

This article argues for a more rigorous distinction between body extensions on the one hand and incorporation of non-bodily objects into the body on the other hand. Real re-embodiment would be a matter of taking things (most often technologies) into the body, i.e. of incorporation of non-bodily items into the body. This, however, is a difficult process often limited by a number of conditions of possibility that are absent in the case of ??mere?? body extensions. Three categories are discussed: limb extensions/prostheses, perceptual extensions/prostheses and cognitive extensions/prostheses. For each category, a distinction between extensions and incorporations is proposed, and the conditions of possibility for real incorporation are discussed. These conditions of possibility differ in each category, but in general they ask for radical or fundamental alterations not only in the motor and/or sensory or cognitive constitution of a human subject, but also in his or her subjective experience.     

Evolution of Cognition: Towards the Theory of Origin of Human Logic

The main problem discussed in this paper is: “Why and how did animal cognition abilities arise?” It is argued that investigations of the evolution of animal cognition abilities are very important from an epistemological point of view. A new direction for interdisciplinary researches – the creation and development of the theory of human logic origin – is proposed. The approaches to the origination of such a theory (mathematical models of ``intelligent invention'' of biological evolution, the cybernetic schemes of evolutionary progress and purposeful adaptive behavior) as well as potential interdisciplinary links of the theory are described and analyzed.     

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。     

MCS: A Method for Finding the Number of Clusters

This paper proposes a maximum clustering similarity (MCS) method for determining the number of clusters in a data set by studying the behavior of similarity indices comparing two (of several) clustering methods. The similarity between the two clusterings is calculated at the same number of clusters, using the indices of Rand (R), Fowlkes and Mallows (FM), and Kulczynski (K) each corrected for chance agreement. The number of clusters at which the index attains its maximum is a candidate for the optimal number of clusters. The proposed method is applied to simulated bivariate normal data, and further extended for use in circular data. Its performance is compared to the criteria discussed in Tibshirani, Walther, and Hastie (2001). The proposed method is not based on any distributional or data assumption which makes it widely applicable to any type of data that can be clustered using at least two clustering algorithms.     

关于信息技术创新项目的决策分析

在信息技术创新项目生命周期的各个阶段上，包含有多种形式的实物期权。从不同形式实物期权的角度，探讨信息技术创新项目决策分析的内容和目标及其过程和准则。对于促进信息技术的发展具有突出的理论意义和实际价值。     

Percept Variance,Subadditivity and the Metric Classification of Similarity,and Dissimilarity Data

Percept variance is shown to change the additive property of city-block distances and make city-block distances more subadditive than Euclidean distances. Failure to account for percept variance will result in the misclassification of city-block data as Euclidean. A maximum likelihood estimation procedure is proposed for the multidimensional scaling of similarity data characterized by percept variance. Monte Carlo and empirical experiments are used to evaluate the proposed approach.     

A Nonlinear Programming Approach to Metric Unidimensional Scaling

Classical unidimensional scaling provides a difficult combinatorial task. A procedure formulated as a nonlinear programming (NLP) model is proposed to solve this problem. The new method can be implemented with standard mathematical programming software. Unlike the traditional procedures that minimize either the sum of squared error (L ₂ norm) or the sum pf absolute error (L ₁ norm), the proposed method can minimize the error based on any L _p norm for 1 ≤p < ∞. Extensions of the NLP formulation to address a multidimensional scaling problem under the city-block model are also discussed.     

Two classes of element-wise transformations preserving the psd nature of coefficient matrices

Two classes of element-wise transformations are proved to preserve the positive semi-definite nature of coefficient matrices. The correctness of a conjecture by Gower and Legendre on the positive semidefinite nature of a certain coefficient matrix is proved. It is shown that the matrix of monotonicity coefficients proposed by Bentler is positive semidefinite for data without ties.     

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.     

先秦云梯形制辨

该文主要从先秦文献中所载之楼车及云梯形制，说明二者实有相同之功能，即用以窥伺敌军。从汉儒服《左传》时引用《兵法》一书，即提供了一项较少为右来学界注意的材料。后人由于二者名称各不相同，乃以二者并不相涉；文中则典籍所载，提出所谓“飞楼”者，当为设于云梯上用来观察敌情之塔楼，以证二者理应极有关系。     

"Every Man in His Notions" or Alchemists' Discussion on Artificial Intelligence

A survey of the main approaches in a mind study -oriented part of Artificial Intelligence is made focusing on controversial issues and extreme hypotheses. Various meanings of terms: "intelligence" and "artificial intelligence" are discussed. Limitations for constructing intelligent systems resulting from the lack of formalized models of cognitive activity are shown. The approaches surveyed are then recapitulated in the light of these limitations.     

Between-group analysis with heterogeneous covariance matrices: The common principal component model

Analysis of between-group differences using canonical variates assumes equality of population covariance matrices. Sometimes these matrices are sufficiently different for the null hypothesis of equality to be rejected, but there exist some common features which should be exploited in any analysis. The common principal component model is often suitable in such circumstances, and this model is shown to be appropriate in a practical example. Two methods for between-group analysis are proposed when this model replaces the equal dispersion matrix assumption. One method is by extension of the two-stage approach to canonical variate analysis using sequential principal component analyses as described by Campbell and Atchley (1981). The second method is by definition of a distance function between populations satisfying the common principal component model, followed by metric scaling of the resulting between-populations distance matrix. The two methods are compared with each other and with ordinary canonical variate analysis on the previously introduced data set.     

Resistant orthogonal procrustes analysis

In this paper two alternative loss criteria for the least squares Procrustes problem are studied. These alternative criteria are based on the Huber function and on the more radical biweight function, which are designed to be resistant to outliers. Using iterative majorization it is shown how a convergent reweighted least squares algorithm can be developed. In asimulation study it turns out that the proposed methods perform well over a specific range of contamination. When a uniform dilation factor is included, mixed results are obtained. The methods also yield a set of weights that can be used for diagnostic purposes.     

Cluster Differences Unfolding for Two-Way Two-Mode Preference Rating Data

Classification and spatial methods can be used in conjunction to represent the individual information of similar preferences by means of groups. In the context of latent class models and using Simulated Annealing, the cluster-unfolding model for two-way two-mode preference rating data has been shown to be superior to a two-step approach of first deriving the clusters and then unfolding the classes. However, the high computational cost makes the procedure only suitable for small or medium-sized data sets, and the hypothesis of independent and normally distributed preference data may also be too restrictive in many practical situations. Therefore, an alternating least squares procedure is proposed, in which the individuals and the objects are partitioned into clusters, while at the same time the cluster centers are represented by unfolding. An enhanced Simulated Annealing algorithm in the least squares framework is also proposed in order to address the local optimum problem. Real and artificial data sets are analyzed to illustrate the performance of the model.     

产业遗产、产业考古学与技术史研究

本文通过对产业遗产及其利用和保护的历史回顾,对产业考古学的一般概念以及相关术语之间的区别和联系进行了探讨,指出产业考古学研究的现实意义,并提出若干建议。     

Utilization of singularity exponent in nearest neighbor based classifier

Classifiers serve as tools for classifying data into classes. They directly or indirectly take a distribution of data points around a given query point into account. To express the distribution of points from the viewpoint of distances from a given point, a probability distribution mapping function is introduced here. The approximation of this function in a form of a suitable power of the distance is presented. How to state this power—the distribution mapping exponent—is described. This exponent is used for probability density estimation in high-dimensional spaces and for classification. A close relation of the exponent to a singularity exponent is discussed. It is also shown that this classifier exhibits better behavior (classification accuracy) than other kinds of classifiers for some tasks.