聚类问题的人工神经网络方法

在不同的实际问题中，往往视需要使用不同的准则对模式进行聚类。本文给出了一个聚类准则，并使用该准则用人工神经网络方法在计算机上进行了模拟。结果表明本文使用的聚类准则更适合于用人工神经网络实现，可以取得极好的聚类效果。     

一种随机聚类法(Ⅱ)

本文给出了一般情况下评价校验码算法的准则 .这个准则可以用于判定校验码算法的优劣并指导校验码算法的设计     

基于动态聚类-因子分析的社会发展评价指标构建模型

运用动态聚类与因子分析相结合的双重指标筛选法对社会发展评价指标进行定量筛选,最终建立了包含社会公平,社会公共利益保障两个准则层在内的共计9个指标的社会发展评价指标体系.主要特色一是利用动态聚类的方法分别对社会公平,社会公共利益保障两个准则层内的社会发展评价指标进行分类,使不同的聚类结果代表社会发展的不同层面,避免了各个社会发展评价指标之间反映的社会发展信息重叠;二是通过因子分析遴选出每一个社会发展评价指标类中信息贡献程度最大的社会发展评价指标,同时删除其他信息贡献率小的社会发展评价指标,保证了筛选出的社会发展评价指标能最大程度的反映整个海选社会发展评价指标的信息量;三是主成分-熵的信息贡献测算模型表明:最终构建的社会发展评价指标体系用29%的社会发展评价指标覆盖了社会发展海选指标体系中89%的原始信息量.     

上市公司经营业绩的分类与评价

首先运用R型聚类分析,从反映经营状况的9项指标中,筛选出5项典型指标作为分类指标,然后根据分类指标,运用Q型聚类中的系统聚类分析法将机械工业45家上市公司分成5类,并进一步按盈利性、成长性和财务安全性对每一类公司的业绩状况进行总体归纳评价.在此基础上,运用理想点法并考虑指标的重要性,对每一类各个公司的业绩进行评价和排序,通过分类与评价得出了一些有价值的结论.     

模糊C均值算法的改进

模糊聚类分析方法具有较强的实用性,但传统的模糊C均值算法对数据集进行分类时有均分的趋势,对于数据集中各类样本数目相差较大的情况,其聚类结果不是很理想.因此,本文对FCM算法进行了改进,使之不但能够达到更好的分类效果,同时也更加适用于样本分类不均衡的聚类问题.文中还结合具体算例进行了聚类分析,得到了理想的分类效果.     

基于Dirichlet分布有限混合模型的Bayes聚类

本文基于Dirichlet分布有限混合模型,提出了一种用于成分数据的Bayes聚类方法.采用EM算法获得模型参数的估计,用BIC准则确定类数,用类似于Bayes判别的方法对各观测分类.推导了计算公式,编写出程序.模拟研究结果表明,本文提出的方法有较好的聚类效果.     

模糊ISODATA中分类数C的确定

模糊ISODATA方法作为一种常用的聚类方法,在许多领域得到了广泛的应用.但作为一种聚类方法,它却没有显示出能自动聚类的效果,而只是对普通分类的一个扩展.在每次聚类前它仍要预先凭经验来给定一个分类数C因此,本文针对这个缺陷,提出了一个改进方案,使之能自动给出分类数C并在实例中得到了检验和应用.     

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。     

等混合聚类法的介绍

一、引言 聚类分析法是要解决在地质领域(或其它领域)中常碰到的分类问题.此方法在地质领域中的应用较为广泛.已用于地质上的地层对比、分类、石油地质上调整井油层水淹级划分及油气资源评价等方面,收到良好的地质效果. 目前我国常用的聚类方法,一般可分为系统聚类和动态聚类两种,但目前常用的聚类分析法,多变样本数量不能太大的限制.有的虽然能处理大数据量的资料,但往往花费的机时太长. 等混合聚类法是一种新的聚类法,这种方法不是一般的将一个样品和另外所有样品逐个加以比较,而是先将原始样品预分为若干组,然后根据一定原则,将各组分别…     

基于混合高斯模型的指标优化方法

借鉴混合高斯模型的方法,提出了基于混合高斯模型的非参数检验法用于评价指标体系的构建.首先运用混合高斯模型对现有指标体系进行聚类分析,然后运用非参数检验的秩相关系数对分类后的指标体系进行筛选,最终确定评价指标体系的构成,保证指标体系的全面性和代表性.实例结果表明,方法分类精度高、简便、实用,在指标优化中具有应用价值.     

从New ton定律到Kepler三定律

从 Newton运动学第二定律和 Newton万有引力定律出发 ,导出 Kepler行星绕日运动三定律     

Attractive force search algorithm for piecewise convex maximization problems

We consider mathematical programming problems with the so-called piecewise convex objective functions. A solution method for this interesting and important class of nonconvex problems is presented. This method is based on Newton??s law of universal gravitation, multicriteria optimization and Helly??s theorem on convex bodies. Numerical experiments using well known classes of test problems on piecewise convex maximization, convex maximization as well as the maximum clique problem show the efficiency of the approach.     

具有结构内阻尼磁性刚体航天器姿态动力学稳定性分析

在地球引力场和磁场中,在考虑了航天器结构内阻尼及气体阻力的影响条件下,研究磁性刚体航天器在绕地球圆轨道运行时可能出现的混沌问题.根据动量矩定理建立动力学模型,应用Melnikov方法证明了动力系统在一定条件下会发生混沌行为,并且给出了解析判据.最后利用数值仿真分析了系统的动力学行为,理论结果与数值仿真结果相一致.     

牛顿是如何站在巨人肩膀上的?

将以现今的微积分学符号,对开普勒(Kepler)行星运行定律进行三步简单的数理分析,推出著名的牛顿(Newton)万有引力定律,以此显示微积分学的巨大威力.在微积分学的教学中,不仅可以让学生知道微积分有用,而且可以让学生知道如何应用.对现代数学建模的教学与学习也具有一定的启发意义.     

Superstrings,Cantorian-fractal Spacetime and Quantum-like Chaos in Atmospheric Flows

Atmospheric flows exhibit long-range spatiotemporal correlations manifested as the fractal geometry to the global cloud cover pattern concomitant with the inverse power law form for spectra of temporal fluctuations. Such non-local connections are ubiquitous to dynamical systems in nature and are identified as signatures of self-organized criticality. A recently developed cell dynamical system model for atmospheric flows predicts the observed self-organized criticality as a natural consequence of quantum-like mechanics governing flow dynamics. The model is based on the concept that spatial integration of enclosed small scale fluctuations results in the formation of large eddy circulations. The model predicts the following: (a) The flow structure consists of an overall logarithmic spiral trajectory with the quasiperiodic Penrose tiling pattern for the internal structure. (b) Conventional power spectrum analysis will resolve such spiral trajectories as a continuum of eddies with progressive increase in phase. (c) Increments in phase are concomitant with increases in period length and also represent the variance, a characteristic of quantum systems identified as Berrys phase. (d) The universal algorithm for self-organized criticality is expressed in terms of the universal Feigenbaum constants, a and d, as 2a²=πd, where the fractional volume intermittency of occurrence πd contributes to the total variance 2a² of fractal structures. (e) The Feigenbaum constants are expressed as functions of the golden mean. ( f) The quantum mechanical constants fine structure constant and ratio of proton mass to electron mass, which are pure numbers and are obtained by experimental observations only, are now derived in terms of the Feigenbaum constant, a. (g) Atmospheric flow structure follows Keplers third law of planetary motion. Therefore, Newtons inverse square law for gravitation also applies to eddy masses. The centripetal acceleration representing the inertial masses (of eddies) are equivalent to gravitational masses. The fractal-Cantorian structure of spacetime can also be visualized as a nested continuum of vortex (eddy) circulations, whose inertial masses obey Newtons inverse square law of gravitation. The model concept resembles a superstring model for subatomic dynamics which incorporates gravitational forces.     

Cartesian Product of the Universal Covering Property

The paper (Boxer, J. Math. Imaging Vis. 25:159–171, 2006) introduces the important tool of the universal (2,k)-covering property for classifying digital covering spaces. Even though the study of its Cartesian product property is important in expanding the property, it still remains open. In this paper, investigating various properties of a universal (2,k)-covering, we study a Cartesian product of the universal covering property, which plays an important role in classifying Cartesian products of digital coverings.     

On the universe's missing mass

In local radial gravitational force fields there is no viable flow of the force itself, and if divergence of a vector is constructed within the field, then it actually requires time-based radial gravitational potentials rather than the usual distance-based radial potentials. When cast in structural relationships of multispatial hyperspace, the new multispatial representation of the usual, Newtonian radial gravity term suggests thus that the allegedly missing mass-energy of the known universe may be the result of inappropriate accounting methods rather than cosmic mass deficiency, as some used to believe. More detailed analysis of local radial gravitational field reveals that the allegedly universal gravitational constant hides fairly compound functional of locally constant value and therefore the radial force depends on more variables than are explicitly displayed in the Newton's inverse square law of gravitation.     

Friction law for turbulent boundary layers on a flat plate with suction

A universal friction law for turbulent boundary layers on a flat plate with suction is established. Experimental skin-friction distributions obtained for various suction factors and Reynolds numbers are described in similarity variables by a single universal curve. The law is valid for the entire range of suction velocities from zero one till the limiting values corresponding to asymptotic-suction boundary layers. The analysis is not based on any particular turbulence model. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

De Morgan classifying toposes

We present a general method for deciding whether a Grothendieck topos satisfies De Morgan's law (resp. the law of excluded middle) or not; applications to the theory of classifying toposes follow. Specifically, we obtain a syntactic characterization of the class of geometric theories whose classifying toposes satisfy De Morgan's law (resp. are Boolean), as well as model-theoretic criteria for theories whose classifying toposes arise as localizations of a given presheaf topos.     

New algebraic invariants for definable subsets in universal algebra

We consider problems of comparing universal algebras in respect of their conditional algebraic geometries. Such comparisons admit of a quite natural algebraic interpretation. Geometric scales for varieties of algebras constructed based on these relations are a natural tool for classifying the varieties of algebras, discriminator varieties in particular.