企业竞争力评价的投影寻踪模型

建立了企业竞争能力评价的投影寻踪聚类模型,利用该模型可将企业竞争优势评价的多个指标转换为反映各指标综合信息的投影特征值,根据投影特征值的大小便可对企业竞争能力进行客观评价,整个过程无人为干扰。通过对5个煤炭企业竞争优势评价表明该方法操作简便,切实可行,为企业竞争能力综合评价的多因素影响问题提供了一条新途径。     

Projection Pursuit Indexes Based on Orthonormal Function Expansions

Abstract

Projection pursuit describes a procedure for searching high-dimensional data for “interesting” low-dimensional projections via the optimization of a criterion function called the projection pursuit index. By empirically examining the optimization process for several projection pursuit indexes, we observed differences in the types of structure that maximized each index. We were especially curious about differences between two indexes based on expansions in terms of orthogonal polynomials, the Legendre index, and the Hermite index. Being fast to compute, these indexes are ideally suited for dynamic graphics implementations.

Both Legendre and Hermite indexes are weighted L ² distances between the density of the projected data and a standard normal density. A general form for this type of index is introduced that encompasses both indexes. The form clarifies the effects of the weight function on the index's sensitivity to differences from normality, highlighting some conceptual problems with the Legendre and Hermite indexes. A new index, called the Natural Hermite index, which alleviates some of these problems, is introduced.

A polynomial expansion of the data density reduces the form of the index to a sum of squares of the coefficients used in the expansion. This drew our attention to examining these coefficients as indexes in their own right. We found that the first two coefficients, and the lowest-order indexes produced by them, are the most useful ones for practical data exploration because they respond to structure that can be analytically identified, and because they have “long-sighted” vision that enables them to “see” large structure from a distance. Complementing this low-order behavior, the higher-order indexes are “short-sighted.” They are able to see intricate structure, but only when they are close to it.

We also show some practical use of projection pursuit using the polynomial indexes, including a discovery of previously unseen structure in a set of telephone usage data, and two cautionary examples which illustrate that structure found is not always meaningful.     

基于投影寻踪法的坦克动力舱热工况综合评价

坦克动力舱的结构和布置方案,对于合理地设计主战坦克动力装置、传动装置、冷却系统和动力系统的总体结构具有重要意义.将投影寻踪法应用于某型主战坦克的动力舱不同结构布置方案热工况综合评价中,不但给出了各方案的综合评价排序,同时得到了各评价指标的权重,为找出最佳布置方案,进行正确决策提供科学依据.     

基于投影寻踪-随机森林的制造企业供应链稳定性评价

基于扎根理论提取制造企业供应链稳定性影响因素,鉴于因素的随机性和模糊性特征,引入云模型,将定性概念转化为定量数据,从众多影响因素中筛选出重要因素,构建制造企业供应链稳定性评价指标体系。采用加速遗传算法对建立的投影寻踪模型进行求解,确定指标权重与稳定性评价值。利用随机森林方法根据评价值划分供应链稳定性类型,检验评价方法科学性,并确定当前制造企业供应链稳定性的整体状态,据此提出优化制造企业供应链稳定性建议。     

基于模糊的投影寻踪算法在中医证候分类中的应用

本文提出一种新的聚类算法-基于模糊的投影寻踪算法,可以有效的处理医学中常常遇到的高维混合数据的模糊聚类问题.并将其应用在慢性肾衰的辩证分析问题中,为已有的慢性肾衰证候的分型标准提供科学支持.本文的研究方法为中医辩证的现代化研究开拓了新的思路,值得进一步深入探讨。     

基于投影寻踪和最优分割的企业信用评级模型

提出一种基于投影寻踪和最优分割的企业信用评级模型。该模型运用投影寻踪对样本企业进行信用综合评分,将信用综合得分由大到小排序,生成有序样品序列;利用最优分割法对有序样品进行聚类,得出明确的聚类结果;将最优分割点对应的信用综合得分作为划分信用等级的阈值,从而实现对样本企业的信用评级。应用实例证明了该模型的可行性和有效性。     

An approximation algorithm for multidimensional assignment problems minimizing the sum of squared errors

Given a complete k-partite graph G=(V₁,V₂,…,V_k;E) satisfying |V₁|=|V₂|=?=|V_k|=n and weights of all  k-cliques of G, the  k-dimensional assignment problem finds a partition of vertices of G into a set of (pairwise disjoint) n k-cliques that minimizes the sum total of weights of the chosen cliques. In this paper, we consider a case in which the weight of a clique is defined by the sum of given weights of edges induced by the clique. Additionally, we assume that vertices of G are embedded in the d-dimensional space Q^d and a weight of an edge is defined by the square of the Euclidean distance between its two endpoints. We describe that these problem instances arise from a multidimensional Gaussian model of a data-association problem.We propose a second-order cone programming relaxation of the problem and a polynomial time randomized rounding procedure. We show that the expected objective value obtained by our algorithm is bounded by (5/2−3/k) times the optimal value. Our result improves the previously known bound (4−6/k) of the approximation ratio.     

基于投影寻踪模型的企业绩效评价研究

针对现有企业绩效研究主要以静态评价为主的现状,本文采用投影寻踪模型对企业绩效进行时序动态评价.鉴于该模型求解属于复杂的非线性优化问题,传统方法难于直接处理,建立了基于免疫系统抗体浓度调节原理的免疫遗传算法进行全局寻优.通过对部分上市建筑企业2002～2007年的绩效状况进行评价,表明基于投影寻踪模型的企业绩效评价与实际一致,可以对企业绩效进行动态评价,并且动态评价是非常必要的.     

基于投影寻踪原理的建筑业综合实力评价分析

在分析影响建筑业综合实力因素的基础上,选择了规模效益水平、技术装备水平、效率水平三个方面共12个评判指标,建立了建筑业综合实力评价的投影寻踪分类模型(PPC),并利用基于实数编码的加速遗传算法(RAGA)求解最佳投影方向.根据投影值的大小对地区建筑业综合实力进行评价分析.PPC模型具有稳健性好、投影值准确度高、评价结果...     

一类新的共轭投影梯度算法

本文利用[5]引进的共轭投影的概念,结合堵丁柱［3］中的思想,提出一类新的共轭梯度投影算法．在一定的条件下,证明了该算法具有全局收敛性和超线性收敛速度．     

基于投影寻踪模型的装备保障性目标评估

应用投影寻踪法,对保障性目标评估标准进行分析,利用在每个级别范围内随机产生的样本,建立了投影寻踪模型,确定了保障性目标评估指标的权重系数,得到了投影特征值变化区域与分类级别的对应关系,对某型航空装备使用初期的保障性试验数据进行分析,得到了其使用初期的级别和评估等级.为实现装备保障性评估目标评估拓展了新的途径,提供了科学依据.     

投影寻踪回归在试验设计分析中的应用研究

本文对三个应用实例进行分析，研究结果表明：ＰＰＲ方法是试验设计回归分析行之有效的方法，它给技术工作者提供了一个处理试验数据的崭新统计方法。ＰＰＲ的应用，将会大幅度降低试验费用，提高试验研究工作效率。     

Bounds on the Size of the Likelihood Ratio Test of Independence in a Contingency Table

Bounds are obtained on the limiting size of the nominal level-α likelihood ratio test of independence in a r × c contingency table. The situations considered include sampling with both marginal totals random and with one margin fixed. Upper and lower bounds are obtained. The limiting size is greater than α when some marginal probabilities are small. As the degrees of freedom increase, the limiting size tends to 1 for all α-values.     

影响投影寻踪聚类建模的关键因素分析与实证研究

讨论了由于对Friedman等提出的投影寻踪聚类(PPC)建模基本思想的理解不同而提出的六种目标函数的特点和区别,分析了样本数据三种归一化预处理方法的区别与联系,阐述了四种取不同R值方案的本质和内涵。通过实证研究和理论分析发现,目标函数Q(a)=S_z*D_z不仅应用最广,且最能体现投影寻踪的基本思想,目标函数Q(a)=S_z+D_z存在大数吃小数的问题,目标函数Q(a)=1/S_z+μ*D_z~*仅适用于高相似度的大样本数据情况,但并没有取得更好的效果,目标函数Q(a)=S_z*C*E和Q(a)=S_z*D_z*E通过增加权重信息熵和样本投影值信息熵,但并没有取得更好的聚类效果,目标函数Q(a)=S_z不符合PPC基本建模思想。样本数据不同归一化预处理方法对建模结果有显著影响,极大值归一化方法更能体现样本数据的原始结构特性,极差归一化方法有利于弱化指标之间的权重差异,去均值归一化方法可以弱化异常值的影响。局部密度窗口半径R值对建模结果有显著影响,R取较小值(R≤0.1S_z)方案更有利于区分样本,但不利于聚类,最优化过程有时候无法求得真正的全局最优解。R取较大值(2m≥R≥r_(max))方案的前提、推导过程和结果都是错误的。R=(r_(i,j))_((k))取值方案只有在类内样本之间距离的最大值小于类间样本之间距离的最小值的特殊情况下才具有意义。R在r_(max)/5≤R≤r_(max)/3范围内取适度值的方案是合理的,也与Friedman等提出的选取R合理值的思想是一致的。     

非线性时间序列的投影寻踪学习网络逼近

本文研究非线性自回归模型投影寻踪学习网络逼近的收敛性,证明了在L^k(k为正整数）空间上,投影寻踪学习网络可以以任意精度逼近非线性自回归模型,给出基于投影寻踪学习网络的非线性时间序列模型建模和预报的计算方法和应用实例,对太阳黑子数据,山猫数据及西安数据进行了拟合和预报,将其结果与改进BP网和门限自回归模型相应的结果进行比较,结果表明基于投影寻踪学习网络的非线性时间序列的建模预报方法是一类行之有效的方法。     

A Projection Method for the Integer Quadratic Knapsack Problem

In this paper we present a new branch and bound algorithm for solving a class of integer quadratic knapsack problems. A previously published algorithm solves the continuous variable subproblems in the branch and bound tree by performing a binary search over the breakpoints of a piecewise linear equation resulting from the Kuhn-Tucker conditions. Here, we first present modifications to a projection method for solving the continuous subproblems. Then we implement the modified projection method in a branch and bound framework and report computational results indicating that the new branch and bound algorithm is superior to the earlier method.     

A Probe Method of Gradient Projection Type

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投影寻踪动态聚类模型在房地产投资环境评价中的应用

将投影寻踪动态聚类模型引入到房地产投资环境评价方法中.针对房地产投资环境评价所面临的多因素高维复杂性问题,该模型能够完全根据样本数据特性将高维数据通过投影向量投影到低维数据,同时实现对低维数据的排序和自动聚类分析,进而通过研究低维数据以实现对高维数据的研究.最后通过辽宁省工业地产投资环境评价实例验证了该模型在房地产投资环境评价中的适用性.     

多维非线性自回归模型的投影寻踪学习网络逼近

本文研究基于投影寻踪学习网络的多维非线性自回归模型逼近的收敛性，证明了在L^k(k为正整数）空间上，投影寻踪学习网络可以任意精度逼近多维非线性自回归模型，并给出应用实例。