主成分回归的建模策略研究

分析了国际上通用的主成分回归的工作原理和失效原因.在此基础上,提出一种新的主成分回归建模策略:①提取所有主成分建立模型;②删除模型中t检验不显著的成分;③用t检验显著的成分建立最终需要的模型.由于任一主成分的回归系数和t检验值以及与其余主成分无关.因此,当采用向后删除变量法时,如果有多个成分t检验不显著,则可以将它们同时删除,而无须逐个删除.采用仿真案例对所提出的方法的合理性进行验证.这种新的建模策略可以有效地提取对因变量有较强解释作用的成分,实现在自变量多重相关条件下的回归建模,并且允许在模型中包含所有的原始变量.此外,该方法的成分筛选过程简便,累计计算误差小于偏最小二乘回归等迭代算法.      

连续谱数据的函数型主成分回归

对连续谱数据不做离散化处理,而是将光滑后的连续谱作为连续曲线,进行函数型主成分回归分析,以期获得既可降维又能减少信息损失的回归方程.在此建模过程中,还引入连续谱的导数曲线作为协变量,并给出函数型主成分回归系数的bootstrap置信区间.作为实证研究,对玻璃样品的X射线谱和样品中硅元素含量进行回归分析.研究结果表明,基于函数型主成分的回归分析对响应变量具有较强解释能力,同时其回归系数更加符合数据本身的特点,显示出新方法所具有的优越性与实用价值.      

基于核主成分分析的多输出模型确认方法

目前对于不确定性环境下多个相关的复杂计算模型进行确认的方法存在计算困难及稳定性较差的问题。针对这类复杂计算模型,提出了一种新的基于核主成分分析(KPCA)的多输出模型确认方法。该方法将核主成分分析与面积法的思想相结合,构造了一个新的易于计算且稳定性高的模型确认指标。所提方法通过核主成分分析将相关的输出变量转化为不相关的核主成分,再对每一核主成分进行模型与实验的对比,从而避免了传统多输出模型确认方法中需要求解多个输出的联合累积分布函数的困难。由于核主成分分析(PCA)方法能够有效提取分析对象的非线性成分,因此基于核主成分分析的多输出模型确认方法较基于主成分分析的模型确认方法更为稳定,这表现在相同的实验样本数据下核主成分分析的方法具有更低的出错率。另外核主成分分析通过核主成分提取,可以实现多输出模型的降维,从而降低多输出模型确认的复杂度。所提方法既可以用于一般的多输出模型的确认,也可以用于多确认点的输出模型的确认。最后通过数值算例和工程算例证明了该方法的正确性与有效性。     

Gram-Schmidt回归及在刀具磨损预报中的应用

多元线性回归是一种应用广泛的统计分析方法.在实际应用中,当自变量集合存在严重多重相关性时,普通最小二乘方法就会失效.为解决这一问题,利用Gram-Schmidt 正交变换,提出一种新的多元线性回归建模方法——Gram-Schmidt回归.该方法可实现多元线性回归中的变量筛选,同时也解决了自变量多重相关条件下的有效建模问题.将该方法应用于机械加工过程中刀具磨损的预报分析,有效地进行了变量筛选,并得到了解释性强同时拟合优度也很高的模型结果.      

两种成分提取回归方法的比较分析

对两种采用成分提取进行回归建模的方法进行比较分析.指出采用主成分分析提取的主成分,虽然能很好地概括自变量系统中的信息,却往往对因变量缺乏解释能力.而采用PLS回归所提取的成分,则能在很好地概括自变量系统信息的同时,最好地解释因变量,排除无意义的信息干扰作用.     

一种修正的马氏距离判别法

马氏距离判别法是一种基于马氏距离的多元统计分析方法,其引入了协方差矩阵的逆矩阵,以排除属性变量的量纲及变量之间的相关性对距离度量的干扰。然而,在属性变量存在严重的多重共线性时,样本协方差矩阵的奇异性会影响其逆矩阵估计的稳定性,从而降低马氏距离判别法的有效性。为此,提出了一种修正的马氏距离判别法,采用了一般交叉验证(GCV)方法,在属性变量间存在高度相关性的情况下,选择预测效果最好的变量维度,同时可以对协方差矩阵的逆矩阵进行稳定的估计。修正的马氏距离判别法可以得到可靠的协方差矩阵的估计,提高模型的判别准确率;也可以抵抗样本外的扰动,提高模型的泛化能力。仿真实验结果验证了在属性变量存在严重的多重共线性情形下,修正的马氏距离判别法的判别效果较经典的马氏距离判别法有明显的提升。      

基于中心-对数半长的区间数据主成分分析

为研究多变量区间数据的降维和可视化,采用包含中心点和半长对数值的二维数组表征区间数据,建立了区间数据的代数运算法则,并在此基础上提出了一种新的区间数据主成分分析(PCA)方法。对区间半长取对数的处理保证了最终得到的区间主成分半长非负的合理性,计算过程简单、复杂度较低,并且使得降维前后样本集合中点点之间相对位置的改变尽可能小。通过对高维空间进行变量降维,从而多种经典的统计分析方法能够得到运用,同时能够在低维空间中描绘原始高维空间中的样本点,使得多变量区间数据的可视化成为可能。仿真实验结果表明了所提方法的有效性。      

基于变量贡献率的MSPC异常识别方法

异常识别是多元统计过程控制(MSPC, Multivariate Statistical Process Control)方法有效应用的关键.针对现有研究对历史异常信息利用的不足,综合考虑了主成分变量贡献率与重构误差变量贡献率对异常识别的影响,将两种变量贡献率进行归一化处理并求和得到综合变量贡献率;提出了一种基于综合变量贡献率的MSPC异常识别方法,并基于matlab计算平台实现了该算法.通过田纳西过程故障模式仿真及异常识别,对该方法的应用及算法有效性进行了实例验证.     

一类混合动态系统的稳定性

混合动态系统是一类同时含有连续时间变量和离散事件变量的系统，在这类系统中，两类变量耦合在一起，具有复杂的动力学特性和时钟关系。本文在一般度量空间上刻画了混合动态系统，并给出了混合动态系统在Ｌｙａｐｕｎｏｖ意义下稳定和渐近稳定的定义及其充分必要条件，同时研究了一类混合动态系统稳定与其连续和离散事件子系统的稳定性之间的关系。     

The nighttime anomalies using Global IGS VTEC Maps

In this paper we show the VTEC variations at night, considering their geomagnetic, seasonal and solar activity dependences. The variations are analyzed in two time periods 10 p.m. (pre-midnight) and 2 a.m. (post-midnight); and for two different solar conditions; one during high solar activity (2000) and the other during low solar activity (2008). Spatial and temporal ionosphere variability is investigated from Global IGS VTEC maps applying Principal Component Analysis (PCA).     

Comparison of Landsat OLI,ASTER, and Sentinel 2A data in lithological mapping : A Case study of Rich area (Central High Atlas,Morocco)

The eastern part of the Rich area consists of the massive Paleozoic and Meso-Cenozoic cover formations that present the geodynamic development of the study area, where is characterized by various carbonate facies of Jurassic age. The geographical characteristic of the study area leaves the zone difficult to map by conventional methods. The objective of this work focuses on the mapping of the constituent lithological units of the study area using multispectral data of Landsat OLI, ASTER, and Sentinel 2A MSI. The processing of these data is based on a precise methodology that distinguishs and highlights the limits of the different lithological units that have an approximate similarity of spectral signature. Three techniques were used to enhance the image including Principal Component Analysis (PCA), Minimum Noise Fraction (MNF), and Independent Component Analysis (ICA). Lithological mapping was performed using two types of supervised classification : Maximum likelihood classifier (MLC) and Support Vector Machine (SVM).The results of processing data show the effectiveness of Sentinel 2A data in mapping of lithological units than the ASTER and Landsat OLI data. The classification evaluation of two methods of the Sentinel 2A MSI image showed that the SVM method give a better classification with an overall accuracy of 93,93% and a Kappa coefficient of 0.93, while the MLC method present an overall accuracy of 82,86% and a Kappa coefficient of 0.80. The results of mapping obtained show a good correlation with the geological map of the study area as well as the efficiency of remote sensing in identification of different lithological units in the Central High Atlas.     

基于多约束因子图优化的无人车定位与建图方法

针对目前在特定场景下应用的低速无人车定位系统极度依赖全球导航卫星系统（GNSS）,存在定位精度不高、漂移误差大、受环境影响严重等问题,提出一种低成本、高精度的无人车定位与建图方法。该方法基于三维激光定位与建图（SLAM）技术。首先,使用点云主成分分析（PCA）实现基于特征匹配的激光里程计;其次,将GNSS位置信息、点云分割聚类得到的地平面和点云聚类特征作为位姿约束分别加入图优化框架,消除激光里程计的累积误差;最后,得到最优位姿和大规模场景的点云地图,以实现无人车的自主定位导航。利用包含大型户外城市街道环境的KITTI数据集对所提出的SLAM算法进行了评估,结果表明:系统在3km运动距离情况下定位偏差可控制在1.5 m以下,在局部精度和全局一致性方面均优于其他里程计系统,为无人车的定位提供了新思路。      

基于PCA方法对太阳活动区主要参量的分析

太阳耀斑与太阳质子事件的发生通常与太阳活动区存在非常密切的关系, 对这种关系的深入分析有助于太阳耀斑和太阳质子事件预报模型的建立. 本文利用主成分分析(Principal Component Analysis, PCA)方法对1997-2010年太阳质子事件所在活动区的主要参量进行分析, 选取的参量包括黑子磁分类、 McIntosh分类、太阳黑子群面积、10.7 cm射电流量、耀斑指数、质子耀斑位置和软X射线耀斑强度. 结果得到81个太阳活动主成分得分值排序(得分值代表每个事件的强弱), 与太阳质子事件峰值流量、太阳黑子年均值以及10.7 cm射电流量年均值的对比显示相似度非常高, 表明主成分得分值一定程度上可以反映太阳活动的强弱规律.      

一种基于PCA的面向对象多尺度分割优化算法

多尺度分割是图像面向对象分类的基础,针对不同区域特征最优分割尺度确定的主观性以及采用聚类算法时聚类中心确定的随机性,提出了一种联合降维与聚类算法的面向对象多尺度分割优化算法。该算法首先利用主成分分析法（PCA）降维排序后的结果产生初始聚类中心;然后采用K-means聚类和度量每一个像素点合并的概率,从而得到适应不同研究区域内不同尺度地物的分割结果。采用多个影像数据库,通过引入聚类评价指标（内部评价指标和外部评价指标）、分割评价指标（分割精度、过分割率和欠分割率）并结合现有的图像分割方法及原始的K-means算法、与PCA降维后的K-means聚类对比分析。研究结果表明:经过降维处理后进行的聚类算法稳定性更高;与传统的聚类算法相比,结合PCA降维更能自动识别最优分割尺度;降维技术和聚类算法联合之中,目视和定量评价指标表明经过降维预处理后的聚类能得到更高质量的分割结果。      

青海省柴达木盆地大气电场随高度的变化特征

大气电场强度是大气电学的重要参数.大气电场的准确测量及其时空特性对研究空间天气活动、气象活动以及大型地质活动具有重要意义.2019年8月26日和28日,中国科学院鸿鹄专项团队在青海省海西蒙古自治州大柴旦镇地区放飞搭载模式电场仪的探空气球,测量了不同高度的大气电场强度.利用互相关函数法和主成分分析法研究了此次气球实验得到的电场数据.结果表明,尽管通常情况下决定大气垂直电场大小的主要因素是高度,但是该地区风场对大气电场强度的影响也比较显著.晴天大气条件下,有无薄云的存在对大气电场测量存在一定影响,有云条件下,风速会通过影响云的形成间接影响到大气电场.此外,柴达木盆地存在一个易受下垫面影响的大气电场边界层,分析表明这个边界层厚度在3km以上.对边界层大气电场变化以及晴天无云时3600m以上的大气电场分布进行了分析和拟合.      

Mapping hydrothermal alteration zones and lineaments associated with orogenic gold mineralization using ASTER data: A case study from the Sanandaj-Sirjan Zone,Iran

The Sanandaj-Sirjan Zone (SSZ) is considered as an important region for gold exploration in the western sector of Iran. Its mountainous topography and unpaved routes make its study challenging for researchers and raise the costs for mining companies strating new exploration plans. Gold mineralization mainly occurs as irregular to lenticular sulfide-bearing quartz veins along shear zones in deformed mafic to intermediate metavolcanic and metasedimentary rocks. In this investigation, ASTER data are used for mapping hydrothermal alteration minerals and to better discriminate geological structural features associated with orogenic gold occurrences in the area. Image transformation techniques such as specialized band ratioing and Principal Component Analysis are used to delineate lithological units and alteration minerals. Supervised classification techniques, namely Spectral Angle Mapper (SAM) and Spectral Information Divergence (SID) are applied to detect subtle differences between indicator alteration minerals associated with ground-truth gold locations in the area. The directional filtering technique is applied to help in tracing along the strike the different linear structures. Results demonstrate that the integration of image transformation techniques and supervised classification of ASTER data with fieldwork and geochemical exploration studies has a great efficiency in targeting new prospects of gold mineralization in the SSZ. The approach used in this research provides a fast, cost-efficient means to start a comprehensive geological and geochemical exploration programs in the study area and elsewhere in similar regions.     

Integrating aeromagnetic data and Landsat-8 imagery for detection of post-accretionary shear zones controlling hydrothermal alterations: The Allaqi-Heiani Suture zone,South Eastern Desert,Egypt

The Arabian-Nubian Shield (ANS) underwent a regional carbonation event with CO₂ fluxes derived from the mantle and circulated along post-accretionary shear zones, thus affecting the redistribution of gold mineralization. Formerly, the analyses of remotely-sensed data have suggested regions of gold mineralization linked to the post-accretionary structured framework, but the results were insufficient for detailed prospecting in the ANS. In this research, aeromagnetic data and Landsat-8 imagery were integrated for delineating new high potential zones of gold mineralization in the Allaqi-Heiani Suture (AHS) zone, the ANS, South Eastern Desert (SED) of Egypt. Aeromagnetic data were enhanced using the Center for exploration targeting (CET) grid enhancement technique to detect the main structures that control hydrothermal alterations in the study area. Principal Component Analysis (PCA) technique and ratios of spectral bands were applied to Landsat-8 data for mapping zones of hydrothermal alteration associated with gold mineralization. The traced structural elements from RTP, CET and Landsat-8 maps were statistically plotted and interpreted using rose diagrams. These diagrams indicated that the NW and NE trends are the most dominant in the RTP map and that the intersection zones obtained from the CET analysis are aligned along the NW-oriented trend. While the NNW, WNW and NE trends were the most dominant ones in Landsat maps. The integration of the results indicates several new high potential zones of gold and Cu/Ni mineralization types, which are mostly concentrated at the western part of the AHS zone. The hydrothermal alteration zones and associated gold mineralization are strongly linked to NW, NE, E-W and WNW trending lineaments. The approach used in this study can be applied to other parts of the ANS and other regions with similar geological conditions around the world.     

Principal components in the PG-X-ray QSO sample

We have performed a spectral principal component analysis for a complete sample of 22 low redshift QSOs with spectra from Ly to H, and found three significant principal components, which account for 78% of the spectrum-to-spectrum variance. We present strong arguments that the first principal component represents the Baldwin effect, relating equivalent widths to the luminosity (i.e. accretion rate). The second component represents continuum variations, probably dominated by intrinsic reddening. The third principal component is directly related to broad emission-line width and X-ray spectral index, and therefore probably driven by Eddington accretion ratio, L/L_Edd. The third set of relationships tie directly to the optical Principal Component 1 found by Boroson and Green [Boroson, T., Green, R.F., Astrophys. J. Suppl. 80, 109, 1992 (BG92)], and are the primary cause of scatter in the Baldwin relationships.