Covariance Matrix Learning Differential Evolution Algorithm Based on Correlation

Differential evolution algorithm based on the covariance matrix learning can adjust the coordinate system according to the characteristics of the population, which makes the search move in a more favorable direction. In order to obtain more accurate information about the function shape, this paper proposes covariance matrix learning differential evolution algorithm based on correlation (denoted as RCLDE) to improve the search efficiency of the algorithm. First, a hybrid mutation strategy is designed to balance the diversity and convergence of the population;secondly, the covariance learning matrix is constructed by selecting the individual with the less correlation;then, a comprehensive learning mechanism is comprehensively designed by two covariance matrix learning mechanisms based on the principle of probability. Finally, the algorithm is tested on the CEC2005, and the experimental results are compared with other effective differential evolution algorithms. The experimental results show that the algorithm proposed in this paper is an effective algorithm.

On the Covariance of Regression Coefficients

In many applications, such as in multivariate meta-analysis or in the construction of multivariate models from summary statistics, the covariance of regression coefficients needs to be calculated without having access to individual patients’ data. In this work, we derive an alternative analytic expression for the covariance matrix of the regression coefficients in a multiple linear regression model. In contrast to the well-known expressions which make use of the cross-product matrix and hence require access to individual data, we express the covariance matrix of the regression coefficients directly in terms of covariance matrix of the explanatory variables. In particular, we show that the covariance matrix of the regression coefficients can be calculated using the matrix of the partial correlation coefficients of the explanatory variables, which in turn can be calculated easily from the correlation matrix of the explanatory variables. This is very important since the covariance matrix of the explanatory variables can be easily obtained or imputed using data from the literature, without requiring access to individual data. Two important applications of the method are discussed, namely the multivariate meta-analysis of regression coefficients and the so-called synthesis analysis, and the aim of which is to combine in a single predictive model, information from different variables. The estimator proposed in this work can increase the usefulness of these methods providing better results, as seen by application in a publicly available dataset. Source code is provided in the Appendix and in http://www.compgen.org/tools/regression.

Decomposition Method of Genetic Correlation Coefficient Based on NC Ⅱ Mating Design

There are different degrees of correlation between crop traits. The phenotypic correlation is decomposed into genetic and environmental correlation in quantitative genetics. In this paper,according to stochastic model of variance and covariance analysis,we calculate different genetic components,bring up a decomposition method of genetic correlation coefficient based on NC II mating design,and use examples to show analytic steps and interpret results.

New correlated MIMO radar covariance matrix design with low side lobe levels and much lower complexity

In this paper,a new correlated covariance matrix for Multi-Input Multi-Output(MIMO)radar is proposed,which has lower Side Lobe Levels(SLLs)compared to the new covariance matrix designs and the well-known multi-antenna radar designs including phased-array,MIMO radar and phased-MIMO radar schemes.It is shown that Binary Phased-Shift Keying(BPSK)waveforms that have constant envelope can be used in a closed-form to realize the proposed covariance matrix.Therefore,there is no need to deploy different types of radio amplifiers in the transmitter which will reduce the cost,considerably.The proposed design allows the same transmit power from each antenna in contrast to the phased-MIMO radar.Moreover,the proposed covariance matrix is full-rank and has the same capability as MIMO radar to identify more targets,simultaneously.Performance of the proposed transmit covariance matrix including receive beampattern and output Signal-to-Interference plus Noise Ratio(SINR)is simulated,which validates analytical results.

The canonical correlation coefficients and canonical variables of groups of random variables

1 Correlation of groups of random variables Suppose we have k groups of random variables: The covariance matrix of Y exists and is denoted by ∑:

Centrality Measures Based on Matrix Functions

Network is considered naturally as a wide range of different contexts, such as biological systems, social relationships as well as various technological scenarios. Investigation of the dynamic phenomena taking place in the network, determination of the structure of the network and community and description of the interactions between various elements of the network are the key issues in network analysis. One of the huge network structure challenges is the identification of the node(s) with an outstanding structural position within the network. The popular method for doing this is to calculate a measure of centrality. We examine node centrality measures such as degree, closeness, eigenvector, Katz and subgraph centrality for undirected networks. We show how the Katz centrality can be turned into degree and eigenvector centrality by considering limiting cases. Some existing centrality measures are linked to matrix functions. We extend this idea and examine the centrality measures based on general matrix functions and in particular, the logarithmic, cosine, sine, and hyperbolic functions. We also explore the concept of generalised Katz centrality. Various experiments are conducted for different networks generated by using random graph models. The results show that the logarithmic function in particular has potential as a centrality measure. Similar results were obtained for real-world networks.

Local canonical correlation coefficients and canonical variables of groups of random variables

The concepts of local correlation coefficient, local canonical correlation coefficients and local canonical variables of groups of random variables are defined, which generalize the classical concepts in two groups of random variables.These concepts together with total corresponding concepts clarify the correlativity among groups of random variables.

多工况输气管道泄漏声波信号自适应去噪

为实现极低信噪比下管道泄漏声波信号去噪,基于多通道信号的相关性,提出使用相关系数矩阵筛选变分模态分解所得模态分量。针对不同工况的泄漏信号,提出不依赖真值的去噪质量评价指标,将其作为多目标灰狼优化算法目标函数,基于Pareto前沿获取变分模态分解的最佳模态数K和惩罚因子η,实现多工况自适应去噪。搭建了输气管道泄漏多工况实验平台,在不同工况、不同输入信号信噪比(-8~4 dB)下验证所提方法的去噪效果。结果表明,该方法能有效抑制噪声,-8 dB时去噪信号信噪比提升2.84 dB以上。对比基于单目标优化的去噪方法,-8 dB下新方法的信噪比和相关系数分别提高了3.65 dB和31.26%。

电子传递链对阿尔兹海默病的影响分析

阿尔兹海默病(Alzheimer’s disease,AD)是一种神经退行性疾病.临床上以记忆障碍、视空间技能损害、执行功能障碍以及人格行为改变等全面性痴呆表现为特征.AD致病源现今不明确,其中有毒物质损害使得脑内区域性能量代谢减退是AD发生的病因特征之一,而电子传递链(ETC)在能量代谢中扮演着重要角色.通过差异分析(LIMMA)及加权基因共表达网络(WGCNA)构建获得聚类基因,并对聚类后基因进行生理分析(GO)、通路分析(KEGG)后锁定ETC,以及对其进行表达量分析及相关系数矩阵的构建,并结合临床指标(MMSE)解释说明,最终验证了ETC的异常对阿尔兹海默病存在影响的事实.

基于非负矩阵分解和改进相关分析的低压台区拓扑辨识方法

针对低压配电台区拓扑更新不及时,量测质量低、拓扑信息不够精确的问题,提出一种基于非负矩阵分解改进Pearson相关系数的低压配电台区拓扑辨识方法。首先,利用非负矩阵分解对电压时间序列进行降维。然后,在Pearson相关系数的基础上,加入距离度量来修正相似性矩阵。最后,对综合相似度矩阵进行系统聚类,实现低压配电台区户-变识别和台区内用户相邻关系识别。通过实际低压配电台区算例验证了所提方法的有效性和准确性。

干湿循环作用下岩桥破裂演化及前兆异常定量识别研究

为探究干湿循环作用下锁固段型岩质边坡内部岩桥的破裂演化及前兆异常,对岩桥试件开展不同干湿循环次数下的单轴压缩试验。基于数字图像相关(DIC)技术,实现加载过程中试件全场变形的实时测量,通过求解位移矢量识别裂纹扩展类型。引入协方差矩阵,定量描述应变场多元分量的离散程度,提出一种识别岩桥应变场前兆异常的方法,并分析干湿循环作用的影响规律。研究结果表明:随着干湿循环次数的增加,岩桥的起裂应力和抗压强度均逐渐劣化。岩桥中裂纹发展时,周围岩石的位移矢量会发生明显的差异,共识别出两种基本裂纹,即张拉裂纹和剪切裂纹。裂纹起裂和贯通所需的轴向应力随着干湿循环次数的增加而逐渐减小。应变场有效方差的演化过程可划分为初始分异、稳定分异和加速分异3个阶段;当剪切裂纹起裂时,干燥状态下的试件有效方差突增,而干湿循环作用后的试件有效方差出现加速增长的态势,均可识别为前兆点。经过干湿循环作用的试件前兆应力水平和时间水平均小于干燥状态下的试件,这是因为干湿循环作用对岩样产生了软化作用。

谱系群分析法在洮河大夏河流域水资源区划分中的分析应用

洮河大夏河流域位于黄河流域第一阶梯东部边缘一隅,属第一阶梯向第二阶梯的过渡地带。水资源时空分布在一定范围内的相似性就是变化与联系相互制约的结果。在洮河大夏河区域内选择15个降水量代表站,各站组合计算相关系数,然后采用逐次形成法依次进行连接合群,相关系数在一定置信水平下的临界值作为水资源区划群的划分参照。经区域站点相关性分析计算和流域对照,相关站点降水量呈现较好的相关性,计算的分区能较好的反映区域内各分区的降水量特点,与当地的降水特性,地形地貌及成雨条件吻合度较高,对水资源分区与计算提供了可行可操作的分析方法。

关于两随机变量不相关概念的思考

通过两随机变量的相关系数为零来定义两随机变量的不相关是一种通行的做法.当其中一个随机变量的方差为零时,它们的相关性将无法依据此定义进行判断.此外,在上述定义下,得出的“两随机变量独立一定不相关”的结论并不严谨.因此,有必要重新深入剖析不相关的概念,并给出相关教学建议.

相关系数矩阵—非线性可逆网络模型在氧化镥价格预测上的应用

以氧化镥价格作为预测对象,选取2013年6月-2023年3月的月度数据,构建相关系数矩阵—非线性可逆网络模型(CM-INN模型),对氧化镥价格进行预测.预测结果表明,CM-INN模型能够解决异常值和离群点敏感、参数选择困难的问题,可有效处理复杂建模关系,提升特征值计算和模型训练效率.CM-INN仿真能力强、误差低、收敛精度高、计算效率高,对重稀土氧化镥价格走势有一定的预测意义.

Spatio-Temporal Correlation Analysis of Global Temperature Based on the Correlation Matrix Theory

Based on the NCEP/NCAR reanalysis daily mean temperature data from 1948 to 2005 and random time series of the same size,temperature correlation matrixes（TCMs） and random correlation matrixes（RCMs） are constructed and compared.The results show that there are meaningful true correlations as well as correlation＂noises＂in the TCMs.The true correlations contain short range correlations（SRCs） among temperature series of neighboring grid points as well as long range correlations（LRCs） among temperature series of different regions,such as the El Nino area and the warm pool areas of the Pacific,the Indian Ocean,the Atlantic,etc.At different time scales,these two kinds of correlations show different features：at 1-10-day scale,SRCs are more important than LRCs;while at 15-day-or-more scale,the importance of SRCs and LRCs decreases and increases respectively,compared with the case of 1-10-day scale.It is found from the analyses of eigenvalues and eigenvectors of TCMs and corresponding RCMs that most correlation information is contained in several eigenvectors of TCMs with relatively larger eigenvalues,and the projections of global temperature series onto these eigenvectors are able to reflect the overall characteristics of global temperature changes to some extent.Besides,the correlation coefficients（CCs） of grid point temperature series show significant temporal and spatial variations.The average CCs over 1950-1956,1972-1977,and 1996-2000 are significantly higher than average while that over the periods 1978-1982 and 1991-1996 are opposite,suggesting a distinctive oscillation of quasi-10-20 yr.Spatially,the CCs at 1-and 15-day scales both show band-like zonal distributions;the zonally averaged CCs at 1-day scale display a better latitudinal symmetry,while they are relatively worse at 15-day scale because of sea-land contrast of the Northern and Southern Hemisphere.However,the meridionally averaged CCs at 15-day scale display a longitudinal quasi-symmetry.

Truncated Estimator of Asymptotic Covariance Matrix in Partially Linear Models with Heteroscedastic Errors

A partially linear regression model with heteroscedastic and/or serially correlated errors is studied here. It is well known that in order to apply the semiparametric least squares estimation （SLSE） to make statistical inference a consistent estimator of the asymptotic covariance matrix is needed. The traditional residual-based estimator of the asymptotic covariance matrix is not consistent when the errors are heteroscedastic and/or serially correlated. In this paper we propose a new estimator by truncating, which is an extension of the procedure in White. This estimator is shown to be consistent when the truncating parameter converges to infinity with some rate.

On Two-stage Estimate Based on Independent Estimate of Covariance Matrix

When an independent estimate of covariance matrix is available, we often prefer two-stage estimate （TSE）. Expressions of exact covarianee matrix of the TSE obtained by using all and some covariables in eovariance adjustment approach are given, and a necessary and sufficient condition for the TSE to be superior to the least square estimate and related large sample test is also established. Furthermore the TSE, by using some covariables, is expressed as weighted least square estimate. Basing on this fact, a necessary and sufficient condition for the TSE by using some covariables to be superior to the TSE by using all eovariables is obtained. These results give us some insight into the selection of covariables in the TSE and its application.

低压配电系统的拓扑与阻抗识别方法研究

电力系统中的低压配电网面临电压波动、电能质量不合格和拓扑结构不明确等挑战。基于此,提出一种基于智能电表测量的低压配电网拓扑和阻抗辨识方法。首先,通过构建电压相关系数矩阵并引入Kruskal最小生成树算法,实现配电网拓扑结构的识别。其次,开发一种利用智能电能表数据进行低压配电网拓扑和阻抗识别的新方法,构建配电变压器到用户电表箱的物理拓扑模型及阻抗分析模型。这些模型可用于计算线路损耗和节点处的功率流。再次,结合配电变压器端数据和智能表计数据的分析,实现一套低压电网拓扑识别和阻抗估计的算法,其能够准确映射出配电网中的支路结构和阻抗特性。最后,通过实证研究验证方法的有效性。

基于量测数据相关性的电力系统不良数据检测和辨识新方法

电力系统量测数据的质量是影响电力系统状态估计效率和结果的重要因素,而量测数据中客观地存在少量不良数据,检测和辨识这些不良数据是电力系统状态估计的重要组成部分。文章分析了量测数据协方差矩阵中的元素值在量测数据中含有白噪声、突变量和不良数据时的变化规律,提出了通过量测数据协方差矩阵中元素的变化规律检测和辨识不良数据的新方法,在IEEE14节点系统上的仿真试验验证了该方法的正确性。

基于统计升尺度方法的区域风电场群功率预测

对区域性风电场群输出功率进行预测是增加风电接入容量,提高大规模风电接入条件下电力系统运行安全性和经济性的有效手段。文中对区域预测建模技术进行研究,利用输出功率相关系数矩阵和预测精度指数进行代表风电场选取和权重系数计算,采用基于少数代表风电场的统计升尺度方法,并利用华北电网2011年1月至6月风电场实际数据进行统计升尺度建模和方法验证。验证结果表明,相比于传统的累加法,统计升尺度方法可改进所实现的区域风电功率预测模型的区域预测精度,同时减少区域预测模型对单个风电场数据完备性的依赖。