关于聚类有效性函数熵公式HP（u,c）

对文[1]提出的聚类有效性函数HP(u,c）作了一定的理论分析,并就文[1]使用的数据及其他数据进行了计算机模拟。模拟结果显示：HP（u,c) 作为FCM算法的聚类有效性函数是不合适的。     

基于样本最大分类信息的聚类有效性函数

根据每一样本的最大分类信息,对Bezdek定义的划分系数进行修改,提出了一个新的聚类有效性函数,讨论了该函数的若干性质。实验结果表明在某些情形该函数的判决效果优于划分系数。     

A mathematical programming approach to key-based election analysis

This article describes a fast, easily implemented MILP algorithm which selects optimal boolean factors (called keys) for predicting the outcomes of Presidential elections in the United States. Results derived from the method support the validity and parsimony of the key-based election model offered by Lichtman and Keilis-Borok.     

Cluster validity for fuzzy clustering algorithms

The proportion exponent is introduced as a measure of the validity of the clustering obtained for a data set using a fuzzy clustering algorithm. It is assumed that the output of an algorithm includes a fuzzy nembership function for each data point. We show how to compute the proportion of possible memberships whose maximum entry exceeds the maximum entry of a given membership function, and use these proportions to define the proportion exponent. Its use as a validity functional is illustrated with four numerical examples and its effectiveness compared to other validity functionals, namely, classification entropy and partition coefficient.     

Economic disequilibrium by mathematical programming

This paper outlines the general principles of constructing mathematical programming models of the market formation for one or several goods in the presence of rigid prices. For the purpose of exposition, it is assumed that each good may be traded internationally and that the domestic price of the good is bounded from above by its import price and from below by its export price. In principle, however, any other institutional factor causing prices to be rigid can be dealt with in a similar manner.The Lagrange multiplier of the market balance of the good can be interpreted as its market price. From a mathematical point of view, one is confronted with a class of mathematical programming problems wherea priori upper and lower bounds have been imposed upon the Lagrange multipliers.     

聚类分析在无回答现象中的应用

对于抽样调查中的无回答现象,本文应用聚类分析方法对辅助变量的数据进行分层,更好地利用了分层后的信息,改进了对无回答变量的估计。将聚类分析与抽样调查结合起来,是一个比较新的尝试,能够更好地解决实际问题中多变量数据的分层问题,进而对提高抽样调查的精度有重要意义。     

聚类分析在股票市场板块分析中的应用

本文将聚类分析应用于股票市场的研究,研究实例表明,聚类分析方法是股市板块分析中的一种有效、实用的方法     

The Hierarchical compromise programming

This paper presents a multicriteria decision making method, the Hierarchical Compromise Programming (HCP), which combines a hierarchical structure for the modelization of a problem with the minimization of the distance to an ideal point as a resolution procedure. The proposed method allows the application of a model based on the minimization of a distance function, with tangible and intangible aspects. This research has been partially supported by the project SISDEMA: UN SISTEMA DECISIONAL AMBIENTAL (ref.: PMA-2196 CONSID-DGA)     

Lipschitz properties of solutions in mathematical programming

This paper deals with the dependence of the solutions and the associated multipliers of a nonlinear programming problem when the data of the problem are subjected to small perturbations. Sufficient conditions are given which imply that the solutions and the multipliers of a perturbed nonlinear programming problem are Lipschitzian with respect to the perturbations.The authors wish to thank J. Drèze and J. P. Vial for many helpful discussions and J. B. Hiriart-Urruty for comments on a previous version of the paper.     

Integer programming methods for normalisation and variable selection in mathematical programming discriminant analysis models

Mathematical programming discriminant analysis models must be normalised to prevent the generation of discriminant functions in which the variable coefficients and the constant term are zero. This normalisation requirement can cause difficulties, and unlike statistical discriminant analysis, variables cannot be selected in a computationally efficient way with mathematical programming discriminant analysis models. Two new integer programming normalisations are proposed in this paper. In the first, binary variables are used to represent the constant term, but with this normalisation functions with a zero constant term cannot be generated and the variable coefficients are not invariant under origin shifts. These limitations are overcome by using integer programming methods to constrain the sum of the absolute values of the variable coefficients to a constant. These new normalisations are extended to allow variable selection with mathematical programming discriminant analysis models. The use of these new applications of integer programming is illustrated using published data.     

运用聚类分析法对我国企业信贷风险的评估与预测

本文通过对企业财务指标的分析与选取,运用聚类分析法对我国企业的信用风险贷款质量进行了评估与预测。根据企业信用风险程度,将商业银行对企业的贷款质量分为正常、关注、次级、可疑、损失五类形态。以此对上市公司的运行状况作出评价,为商业银行是否对其贷款提供依据。     

帐号的聚类分析

本文应用聚类分析的方法分析了银行帐号，对于银行系统选择类似帐号校验码的算法这类问题有参考价值。     

Nondifferentiable mathematical programming and convex-concave functions

For a convex-concave functionL(x, y), we define the functionf(x) which is obtained by maximizingL with respect toy over a specified set. The minimization problem with objective functionf is considered. We derive necessary conditions of optimality for this problem. Based upon these necessary conditions, we define its dual problem. Furthermore, a duality theorem and a converse duality theorem are obtained. It is made clear that these results are extensions of those derived in studies on a class of nondifferentiable mathematical programming problems.This work was supported by the Japan Society for the Promotion of Sciences.     

Heuristics for feature selection in mathematical programming discriminant analysis models

In developing a classification model for assigning observations of unknown class to one of a number of specified classes using the values of a set of features associated with each observation, it is often desirable to base the classifier on a limited number of features. Mathematical programming discriminant analysis methods for developing classification models can be extended for feature selection. Classification accuracy can be used as the feature selection criterion by using a mixed integer programming (MIP) model in which a binary variable is associated with each training sample observation, but the binary variable requirements limit the size of problems to which this approach can be applied. Heuristic feature selection methods for problems with large numbers of observations are developed in this paper. These heuristic procedures, which are based on the MIP model for maximizing classification accuracy, are then applied to three credit scoring data sets.     

Potential-reduction methods in mathematical programming

We provide a survey of interior-point methods for linear programming and its extensions that are based on reducing a suitable potential function at each iteration. We give a fairly complete overview of potential-reduction methods for linear programming, focusing on the possibility of taking long steps and the properties of the barrier function that are necessary for the analysis. We then describe briefly how the methods and results can be extended to certain convex programming problems, following the approach of Nesterov and Todd. We conclude with some open problems. Research supported in part by NSF, AFOSR and ONR through NSF Grant DMS-8920550. Some of this work was done while the author was on a sabbatical leave from Cornell University visiting the Department of Mathematics at the University of Washington.     

Error bounds in mathematical programming

Originated from the practical implementation and numerical considerations of iterative methods for solving mathematical programs, the study of error bounds has grown and proliferated in many interesting areas within mathematical programming. This paper gives a comprehensive, state-of-the-art survey of the extensive theory and rich applications of error bounds for inequality and optimization systems and solution sets of equilibrium problems. This work is based on research supported by the U.S. National Science Foundation under grant CCR-9624018.     

Constraint classification in mathematical programming

Consider a set of algebraic inequality constraints defining either an empty or a nonempty feasible region. It is known that each constraint can be classified as either absolutely strongly redundant, relatively strongly redundant, absolutely weakly redundant, relatively weakly redundant, or necessary. We show that is is worth making a distinction between weakly necessary constraints and strongly necessary constraints. We also present afeasible set cover method which can detect both weakly and strongly necessary constraints.The main interest in constraint classification is due to the advantages gained by the removal of redundant constraints. Since classification errors are likely to occur, we examine how the removal of a single constraint can affect the classification of the remaining constraints.