基于聚类分析的增强型蚁群算法

针对蚁群算法存在的早熟收敛、搜索时间长等不足,提出一种增强型蚁群算法.该算法构建了一优解池,保存到当前迭代为止获得的若干优解,并提出一种基于邻域的聚类算法,通过对优解池中的元素聚类,捕获不同的优解分布区域.该算法交替使用不同簇中的优解更新信息素,兼顾考虑了搜索的强化性和分散性.针对典型的旅行商问题进行仿真实验,结果表明该算法获得的解质量高于已有的蚁群算法.     

对称Toeplitz线性方程组的基于余弦变换的最佳预优矩阵

利用第四类离散余弦变换矩阵构造出求解对称Toeplitz线性方程组的最佳预优矩阵,构造该预优矩阵所需的运算量为O(n).理论和数值实验显示,利用本文中所构造的预优矩阵求解对称Toeplitz线性方程组所需的迭代次数与现有的其它类型预优矩阵差不多,但预优矩阵的构造要更简单.     

基于类中心与边界自寻优的聚类算法

随着互联网应用的普及和深入,涌现了许多新的应用场景和数据类型,导致许多经典的聚类算法不能有效地适应新的发展形势,成为数据挖掘中的棘手问题和研究热点,为此提出一种新颖的基于类中心与边界自寻优的数据聚类算法.该算法引入数据点“距离半径”分布矩阵R及其“距离半径累计”分布矩阵ΣR概念表征数据聚合度,并依据广度优先原则自寻优R与ΣR中皆为最小的数据点作为类中心;同时,提出“距离半径偏导”分布矩阵R’,描述簇类之间的松散度,并采用广度优先原则自寻优矩阵R’中的突变跃迁增长点,作为簇类之间的分界.通过经典的Aggregation聚类数据集的仿真实验测试,表明该算法能够有效地对多种形状、大小和不同密度分布的数据集进行聚类分析,能较好地识别出孤立点和噪声,具有较高的鲁棒性和分析精度.     

一种基于关联规则的多类标分类算法

提出了一种基于关联规则的多类标算法(MLAC).利用多类标FP-tree来分解组合生成多类标规则.并通过组合多重关联规则分类器进行分类预测,降低了由高维属性带来的高计算复杂度,有效地提高了算法的性能和效率.针对多类标数据集的实验结果表明,MLAC算法在性能和效率等方面均优干ML-KNN等多类标分类算法.     

基于白化权函数聚类法的航电系统效能评估

航空电子综合系统是作战飞机的神经中枢,准确评估航电系统的效能对我国航空电子技术的发展具有重要意义。为了用灰色白化权函数聚类法对基于1553B总线的航电系统进行效能评估。首先将1553B总线负载、延迟时间、总线使用效率三项指标分为优、良、中、差四个灰类,综合各指标的白化权函数和其隶属于不同灰类的权重得到航电系统聚类系数向量,然后由该向量中的最大聚类系数所属灰类来确定该航电系统的灰类等级。灰色白化权函数聚类方法为航电系统的设计和效能评估提供了重要方法和理论依据。     

一种偏置场环境下的模糊聚类分割算法

针对偏置环境下图像分割问题,提出了一种基于偏置场估计的模糊聚类算法。通过建立依赖于偏置场的模糊聚类目标函数,提出了模糊聚类隶属函数和偏置场估计的迭代算法。该方法较好地处理了传统模糊聚类在偏置场存在的情况下图像分割精度下降问题。实验结果表明,该算法能有效分割具有偏置噪声的图像,其分割精度优于传统模糊聚类法。     

改进的均值聚类算法对织物图像颜色类别的判定

利用图像测量织物颜色的首要工作是识别出适合测色的区域,针对均值聚类算法(k-means)在聚类中心和类别数选取中存在的缺点,提出了改进的聚类算法。将RGB色泽分布中局部极大点位置作为聚类中心、以分类优度为标准确定最优分类,通过颜色聚类中心和类别数的判定,实现了不同物理形态织物图像的颜色聚类。实验表明,用改进的k-means算法处理后的颜色更均匀,更相似于理想图像,因此更适合测色。     

基于两阶段搜索的密度聚类算法

为克服当前密度聚类算法存在的随机性、主观性和连带错误等问题,提出一种基于两阶段搜索的密度聚类算法。给出密度阈值和簇最近邻定义及计算方法。采用密度排序、簇最近邻分配和自适应搜索策略构建算法的两阶段聚类机制,设计邻域递归搜索和簇最近邻搜索两个阶段的聚类算法,实现不同密度数据点的准确聚类。8个数据集聚类实验结果表明,该密度聚类算法聚类稳定,无噪声,且自动确定类簇数,聚类精度优于比较的密度聚类算法。     

一种基于模糊聚类的离散化方法

由于粗糙集只能对离散属性进行处理,因而连续属性的离散化也就成了粗糙集的主要问题之一。提出了一种从模糊聚类出发的离散化方法,并给出了一个判别函数,由该函数从聚类结果中选择最优的一个解,因而是一种自寻优的求解过程,避免了人为划分类数的主观影响。最后进行了实验比较,证实了该方法的有效性和合理性。     

一种基于模糊聚类的离散化方法

由于粗糙集只能对离散属性进行处理,因而连续属性的离散化也就成了粗糙集的主要问题之一.提出了一种从模糊聚类出发的离散化方法,并给出了一个判别函数,由该函数从聚类结果中选择最优的一个解,因而是一种自寻优的求解过程,避免了人为划分类数的主观影响.最后进行了实验比较,证实了该方法的有效性和合理性.     

Estimating the probability of misclassification and variate selection

This paper considers the problem of estimating the probability of misclassifying normal variates using the usual discriminant function when the parameters are unknown. The probability of misclassification is estimated, by Monte Carlo simulation, as a function of n₁ and n₂ (sample sizes), p (number of variates) and α (measure of separation between the two populations). The probability of misclassification is used to determine, for a given situation, the best number and subset of variates for various sample sizes. An example using real data is given.     

DALASS: Variable selection in discriminant analysis via the LASSO

The objective of DALASS is to simplify the interpretation of Fisher's discriminant function coefficients. The DALASS problem—discriminant analysis (DA) modified so that the canonical variates satisfy the LASSO constraint—is formulated as a dynamical system on the unit sphere. Both standard and orthogonal canonical variates are considered. The globally convergent continuous-time algorithms are illustrated numerically and applied to some well-known data sets.     

Sparse CCA using a Lasso with positivity constraints

Canonical correlation analysis (CCA) describes the relationship between two sets of variables by finding linear combinations of the variables with maximal correlation. A sparse version of CCA is proposed that reduces the chance of including unimportant variables in the canonical variates and thus improves their interpretation. A version of the Lasso algorithm incorporating positivity constraints is implemented in tandem with alternating least squares (ALS), to obtain sparse canonical variates. The proposed method is demonstrated on simulation studies and a data set from market basket analysis.     

随机系统仿真中方差衰减技术的应用

本文对随机系统仿真中的主要方差衰减技术作一个综合评述。内容涉及到公共随机数法、对偶变量法、控制变量法、重要抽样法、分层方法、条件期望法和其它相关内容。     

Canonical correlation analysis of coniferous forest spectral and biotic relations

Canonical correlation analysis was used to examine the relations between the six reflective Thematic Mapper bands and six forest structural variables for 70 lodgepole pine forest stands in Yellowstone National Park, U.S.A. Two significant canonical variate pairs were extracted, accounting for 96·4 per cent of the total information in the overall canonical correlation analysis. Results of the canonical redundancy analysis indicate that 78 per cent of the overall unstandardized variance in spectral data is explained by the first two spectral canonical variates, while the first and second biotic canonical variates explain 59 per cent and 5·9 per cent of the raw variance in the spectral data. The first two biotic canonical variates collectively explain 59 per cent of the raw variance in the biotic data, and the first and second spectral canonical variates explain 41 per cent and 6 per cent of the raw variance in the biotic data, respectively. Height, live basal area, leaf area index (LAI), and size diversity are highly intercorrelated and act in combination to affect the overall reflectance, or brightness, of a forest stand. Overstory live density and understory total living cover relate strongly to stand greenness, particularly TM band 4.     

A method for discrete stochastic MADM problems based on the ideal and nadir solutions

Many real life decision making problems can be modeled as discrete stochastic multi-attribute decision making (MADM) problems. A novel method for discrete stochastic MADM problems is developed based on the ideal and nadir solutions as in the classical TOPSIS method. In a stochastic MADM problem, the evaluations of the alternatives with respect to the different attributes are represented by discrete stochastic variables. According to stochastic dominance rules, the probability distributions of the ideal and nadir variates, both are discrete stochastic variables, are defined and determined for a set of discrete stochastic variables. A metric is proposed to measure the distance between two discrete stochastic variables. The ideal solution is a vector of ideal variates and the nadir solution is a vector of nadir variates for the multiple attributes. As in the classical TOPSIS method, the relative closeness of an alternative is determined by its distances from the ideal and nadir solutions. The rankings of the alternatives are determined using the relative closeness. Examples are presented to illustrate the effectiveness of the proposed method. Through the examples, several significant advantages of the proposed method over some existing methods are discussed.     

Simple and interpretable discrimination

A number of approaches have been proposed for constructing alternatives to principal components that are more easily interpretable, while still explaining considerable part of the data variability. One such approach is employed in order to produce interpretable canonical variates and explore their discrimination behavior, which is more complicated as orthogonality with respect to the within-groups sums-of-squares matrix is involved. The proposed simple and interpretable canonical variates are an optimal choice between good and sparse approximation to the original ones, rather than identifying the variables that dominate the discrimination. The numerical algorithms require low computational cost, and are illustrated on the Fisher’s iris data and on moderately large real data.     

Output Autocorrelation Functions of Smooth and Hard Limiters†

For a stationary Gaussian input, the output autocorrelation functions of the full-wave smooth and hard limiters are derived by applying Blaehman's (1964) technique. A new method is used, in conjunction with Plackett's (1954) reduction formula for the case of four Gaussian variates, to evaluate the probability that these variates are positive, when their covariance matrix is of a specific form. On combining this method with Blaehman's technique, the autocorrelation functions of the half-wave smooth and hard limiters are derived in terms of the dilogarithm function and its real part, both of which have been studied and tabulated.     

Construction of bivariate S-distributions with copulas

S-distributions are univariate statistical distributions with four parameters. They have a simple mathematical structure yet provide excellent approximations for many traditional distributions and also contain a multitude of distributional shapes without a traditional analog. S-distributions furthermore have a number of beneficial features, for instance, in terms of data classification and scaling properties. They provide an appealing compromise between generality in data representation and logistic simplicity and have been applied in a variety of fields from applied biostatistics to survival analysis and risk assessment. Given their advantages in the single- variable case, it is desirable to extend S-distributions to several variates. This article proposes such an extension. It focuses on bivariate distributions whose marginals are S-distributions, but it is clear how more than two variates are to be addressed. The construction of bivariate S- distributions utilizes copulas, which have been developed quite rapidly in recent years. It is demonstrated here how one may generate such copulas and employ them to construct and analyze bivariate—and, by extension, multivariate—S-distributions. Particular emphasis is placed on Archimedean copulas, because they are easy to implement, yet quite flexible in fitting a variety of distributional shapes. It is illustrated that the bivariate S-distributions thus constructed have considerable flexibility. They cover a variety of marginals and a wide range of dependences between the variates and facilitate the formulation of relationships between measures of dependence and model parameters. Several examples of marginals and copulas illustrate the flexibility of bivariate S-distributions.     

Generation of random variates using asymptotic expansions

Monte-Carlo methods are widely used numerical tools in various fields of application, like rarefied gas dynamics, vacuum technology, stellar dynamics or nuclear physics. A central part is the generation of random variates according to a given probability law. Fundamental techniques are the inversion principle or the acceptance-rejection method—both may be quite time-consuming if the given probability law has a complicated structure. In this paper probability laws depending on a small parameter are considered and the use of asymptotic expansions to generate random variates is investigated. The results given in the paper are restricted to first order expansions. Error estimates for the discrepancy as well as for the bounded Lipschitz distance of the asymptotic expansion are derived. Furthermore the integration error for some special classes of functions is given. The efficiency of the method is proved by a numerical example from rarefied gas flows.