FAST RECURSIVE LEAST SQUARES LEARNING ALGORITHM FOR PRINCIPAL COMPONENT ANALYSIS

Based on the least-square minimization a computationally efficient learning algorithm for the Principal Component Analysis(PCA) is derived. The dual learning rate parameters are adaptively introduced to make the proposed algorithm providing the capability of the fast convergence and high accuracy for extracting all the principal components. It is shown that all the information needed for PCA can be completely represented by the unnormalized weight vector which is updated based only on the corresponding neuron input-output product. The convergence performance of the proposed algorithm is briefly analyzed.The relation between Oja’s rule and the least squares learning rule is also established. Finally, a simulation example is given to illustrate the effectiveness of this algorithm for PCA.

Comparison of dimension reduction-based logistic regression models for case-control genome-wide association study:principal components analysis vs.partial least squares

With recent advances in biotechnology, genome-wide association study （GWAS） has been widely used to identify genetic variants that underlie human complex diseases and traits. In case-control GWAS, typical statistical strategy is traditional logistical regression （LR） based on single-locus analysis. However, such a single-locus analysis leads to the well-known multiplicity problem, with a risk of inflating type I error and reducing power. Dimension reduction-based techniques, such as principal component-based logistic regression （PC-LR）, partial least squares-based logistic regression （PLS-LR）, have recently gained much attention in the analysis of high dimensional genomic data. However, the perfor- mance of these methods is still not clear, especially in GWAS. We conducted simulations and real data application to compare the type I error and power of PC-LR, PLS-LR and LR applicable to GWAS within a defined single nucleotide polymorphism （SNP） set region. We found that PC-LR and PLS can reasonably control type I error under null hypothesis. On contrast, LR, which is corrected by Bonferroni method, was more conserved in all simulation settings. In particular, we found that PC-LR and PLS-LR had comparable power and they both outperformed LR, especially when the causal SNP was in high linkage disequilibrium with genotyped ones and with a small effective size in simulation. Based on SNP set analysis, we applied all three methods to analyze non-small cell lung cancer GWAS data.

Calculation of stratum surface principal curvature based on a moving least square method

With the east section of the Changji sag Zhunger Basin as a case study, both a principal curvature method and a moving least square method are elaborated. The moving least square method is introduced, for the first time, to fit a stratum surface. The results show that, using the same-degree base function, compared with a traditional least square method, the moving least square method can produce lower fitting errors, the fitting surface can describe the morphological characteristics of stratum surfaces more accurately and the principal curvature values vary within a wide range and may be more suitable for the prediction of the distribution of structural fractures. The moving least square method could be useful in curved surface fitting and stratum curvature analysis.

Characterizing and estimating rice brown spot disease severity using stepwise regression,principal component regression and partial least-square regression

Detecting plant health conditions plays a key role in farm pest management and crop protection. In this study, measurement of hyperspectral leaf reflectance in rice crop (Oryzasativa L.) was conducted on groups of healthy and infected leaves by the fungus Bipolaris oryzae (Helminthosporium oryzae Breda. de Hann) through the wavelength range from 350 to 2 500 nm. The percentage of leaf surface lesions was estimated and defined as the disease severity. Statistical methods like multiple stepwise regression, principal component analysis and partial least-square regression were utilized to calculate and estimate the disease severity of rice brown spot at the leaf level. Our results revealed that multiple stepwise linear regressions could efficiently estimate disease severity with three wavebands in seven steps. The root mean square errors (RMSEs) for training (n=210) and testing (n=53) dataset were 6.5% and 5.8%, respectively. Principal component analysis showed that the first principal component could explain approximately 80% of the variance of the original hyperspectral reflectance. The regression model with the first two principal components predicted a disease severity with RMSEs of 16.3% and 13.9% for the training and testing dataset, respec-tively. Partial least-square regression with seven extracted factors could most effectively predict disease severity compared with other statistical methods with RMSEs of 4.1% and 2.0% for the training and testing dataset, respectively. Our research demon-strates that it is feasible to estimate the disease severity of rice brown spot using hyperspectral reflectance data at the leaf level.

Near-Infrared Spectroscopy Combined with Partial Least Squares Discriminant Analysis Applied to Identification of Liquor Brands

The identification of liquor brands is very important for food safety. Most of the fake liquors are usually made into the products with the same flavor and alcohol content as regular brand, so the identification for the liquor brands with the same flavor and the same alcohol content is essential. However, it is also difficult because the components of such liquor samples are very similar. Near-infrared (NIR) spectroscopy combined with partial least squares discriminant analysis (PLS-DA) was applied to identification of liquor brands with the same flavor and alcohol content. A total of 160 samples of Luzhou Laojiao liquor and 200 samples of non-Luzhou Laojiao liquor with the same flavor and alcohol content were used for identification. Samples of each type were randomly divided into the modeling and validation sets. The modeling samples were further divided into calibration and prediction sets using the Kennard-Stone algorithm to achieve uniformity and representativeness. In the modeling and validation processes based on PLS-DA method, the recognition rates of samples achieved 99.1% and 98.7%, respectively. The results show high prediction performance for the identification of liquor brands, and were obviously better than those obtained from the principal component linear discriminant analysis method. NIR spectroscopy combined with the PLS-DA method provides a quick and effective means of the discriminant analysis of liquor brands, and is also a promising tool for large-scale inspection of liquor food safety.

Continuous Iteratively Reweighted Least Squares Algorithm for Solving Linear Models by Convex Relaxation

In this paper, we present continuous iteratively reweighted least squares algorithm (CIRLS) for solving the linear models problem by convex relaxation, and prove the convergence of this algorithm. Under some conditions, we give an error bound for the algorithm. In addition, the numerical result shows the efficiency of the algorithm.

Application of Principal Component Regression with Dummy Variable in Statistical Downscaling to Forecast Rainfall

Statistical downscaling (SD) analyzes relationship between local-scale response and global-scale predictors. The SD model can be used to forecast rainfall (local-scale) using global-scale precipitation from global circulation model output (GCM). The objectives of this research were to determine the time lag of GCM data and build SD model using PCR method with time lag of the GCM precipitation data. The observations of rainfall data in Indramayu were taken from 1979 to 2007 showing similar patterns with GCM data on 1st grid to 64th grid after time shift (time lag). The time lag was determined using the cross-correlation function. However, GCM data of 64 grids showed multicollinearity problem. This problem was solved by principal component regression (PCR), but the PCR model resulted heterogeneous errors. PCR model was modified to overcome the errors with adding dummy variables to the model. Dummy variables were determined based on partial least squares regression (PLSR). The PCR model with dummy variables improved the rainfall prediction. The SD model with lag-GCM predictors was also better than SD model without lag-GCM.

Application of nonlinear partial least square in catalyst modeling

The neural network partial least square (NNPLS) method was used to establish a robust reaction model for a multi-component catalyst of methane oxidative coupling. The details, including the learning algorithm, the number of hidden units of the inner network, activation function, initialization of the network weights and the principal components, are discussed. The results show that the structural organizations of inner neural network are 1-10-5-1, 1-8-4-1, 1-8-5-1, 1-7-4-1, 1-8-4-1, 1-8-6-1, respectively. The Levenberg-Marquardt method was used in the learning algorithm, and the central sigmoidal function is the activation function. Calculation results show that four principal components are convenient in the use of the multi-component catalyst modeling of methane oxidative coupling. Therefore a robust reaction model expressed by NNPLS succeeds in correlating the relations between elements in catalyst and catalytic reaction results. Compared with the direct network modeling, NNPLS model can be adjusted by experimental data and the calculation of the model is simpler and faster than that of the direct network model.

Multivariate Cluster and Principle Component Analyses of Selected Yield Traits in Uzbek Bread Wheat Cultivars

Investigation of genetic diversity of geographically distant wheat genotypes is a useful approach in wheat breeding providing efficient crop varieties. This article presents multivariate cluster and principal component analyses (PCA) of some yield traits of wheat, such as thousand-kernel weight (TKW), grain number, grain yield and plant height. Based on the results, an evaluation of economically valuable attributes by eigenvalues made it possible to determine the components that significantly contribute to the yield of common wheat genotypes. Twenty-five genotypes were grouped into four clusters on the basis of average linkage. The PCA showed four principal components (PC) with eigenvalues > 1, explaining approximately 90.8% of the total variability. According to PC analysis, the variance in the eigenvalues was the greatest (4.33) for PC-1, PC-2 (1.86) and PC-3 (1.01). The cluster analysis revealed the classification of 25 accessions into four diverse groups. Averages, standard deviations and variances for clusters based on morpho-physiological traits showed that the maximum average values for grain yield (742.2), biomass (1756.7), grains square meter (18,373.7), and grains per spike (45.3) were higher in cluster C compared to other clusters. Cluster D exhibited the maximum thousand-kernel weight (TKW) (46.6).

An Upper Bound for the Number of Normalized Latin Square

In this note, the author find an upper bound formula for the number of the p × p normalized Latin Square,the first row and column of which are both standard order 1, 2,…p.

基于HHT的绝缘子泄漏电流分析及放电状态分类识别

泄漏电流是污秽绝缘子在线监测参数,能动态地反映绝缘子表面的放电状态。文中开展了瓷绝缘子人工污秽放电试验,利用Hilbert-Huang变换分析了不同污闪阶段的泄漏电流固有模态函数分量、Hilbert边际谱与时频熵,从时频域及波形细节提取了15个特征量,使用主成分分析法与最小二乘支持向量机分类器对污秽放电状态进行识别。结果表明:起始放电阶段与闪络阶段的泄漏电流固有模态函数分量较多;泄漏电流的Hilbert边际谱上频率主要分布在0~150 Hz、200~250 Hz范围内;闪络前泄漏电流的时频熵值总是大于闪络后的;当训练样本数为测试样本数5倍及以上时,分类器的综合评判准确率可达99%,准确实现了污秽放电状态的分类识别。文中研究结果可为建立绝缘子污闪预警系统提供依据。

红芪搓条前后主要次级代谢产物变化规律研究

目的 考察红芪搓条前后主要次级代谢产物的变化规律。方法 UPLC-MS/MS法测定芒柄花素、芒柄花苷、毛蕊异黄酮、毛蕊异黄酮苷、美迪紫檀素、染料木素、木犀草素、甘草素、异甘草素、香草酸、阿魏酸、γ-氨基丁酸、腺苷、甜菜碱的含量,聚类分析、主成分分析、正交偏最小二乘判别分析进行化学模式识别以寻找差异性成分。结果 搓条后,芒柄花素、毛蕊异黄酮、甘草素、γ-氨基丁酸含量升高,芒柄花苷、毛蕊异黄酮苷、香草酸含量降低。搓条、未搓条药材聚为2类,毛蕊异黄酮苷、芒柄花素、γ-氨基丁酸、香草酸、毛蕊异黄酮、芒柄花苷为差异性成分。结论 本实验阐明红芪搓条前后化学成分差异,可为其他药材搓条机制研究提供参考。

基于化学计量学和指纹图谱的辽宁道地药材北五味子质量评价研究

目的 采用指纹图谱与化学计量学相结合的方法,评价辽宁岫岩产北五味子的质量。方法 采用HPLC法,柱温30℃,流速1 mL/min,流动相采用水-乙腈梯度洗脱,检测波长220 nm,对10批辽宁岫岩五味子基地生产的北五味子建立指纹图谱,运用聚类分析(hierarchical cluster analysis, HCA)、主成分分析(principal component analysis, PCA)及正交偏最小二乘法-判别分析(orthogonal partial least squares-discriminant analysis, OPLS-DA)进行化学模式识别分析。结果 建立了岫岩产北五味子的指纹图谱,相似度为0.970^0.999,共标定了29个共有峰,指认了14个成分;HCA分析10批北五味子可分为2类;PCA共得到6个主要成分,其累计方差贡献率为95.5%;OPLS-DA表明五味子甲素、戈米辛G、五味子丙素、五味子醇乙等11个成分可能是影响北五味子质量的差异性标志物。结论 研究所建立的指纹图谱结合化学模式识别分析,方法准确、稳定、可靠,可用于北五味子药材的质量控制研究。

早期高血压弦脉脉象特点及其瞬时波强技术参数特征分析

目的:应用瞬时波强(WI)技术探测早期高血压弦脉患者颈总动脉各参数,分析早期高血压弦脉的脉象特点;提取弦脉脉象判别的特征参数,探讨早期高血压弦脉患者颈总动脉WI参数的特点,以期为弦脉的精准分型及信息解读提供客观依据。方法:选择52例早期原发性高血压弦脉、50例生理性弦脉、50例平脉受试者,分析其颈总动脉的WI参数,总结早期高血压弦脉的脉象特点,并运用SIMCA14.1统计软件提取脉象分型的主参数。结果:早期高血压弦脉组与平脉组及生理性弦脉组比较,瞬时加速度波强(W1)、负向波面积(NA)值增高,W1-W2间期降低(均P<0.01);而平脉组与生理性弦脉组W1、NA、W1-W2间期比较,差异均无统计学意义(均P>0.05)。平脉组、生理性弦脉组、早期高血压弦脉组的血管压力应变弹性模量(EP)、脉搏波传导速度(PWV)、血管硬化参数(β)数值均逐渐增高(均P<0.01)。平脉组血管顺应性(AC)高于其他2组(均P<0.01),生理性弦脉组AC高于早期高血压弦脉组(P<0.05)。3组R-W1间期比较差异无统计学意义(P>0.05)。基于主成分分析(PCA)和正交偏最小二乘法判别分析(OPLS-DA),生理性弦脉组与平脉组样本区分明显,表明2组WI各参数比较差异均有统计学意义(均P<0.05),特征性的WI参数[投影重要性(VIP值)>1]为EP、PWV、β、AC,其中贡献率为EP>PWV>β>AC。基于PCA和OPLS-DA,生理性弦脉组与早期高血压弦脉组样本区分明显,表明2组WI各参数差异均有统计学意义(均P<0.05),特征性的WI参数(VIP值>1)为EP、PWV、NA、W1、β,其中贡献率为EP>PWV>NA>W1>β。结论:区分早期高血压弦脉组与生理性弦脉组的WI特征性参数为EP、PWV、β、NA、W1。区分平脉组与生理性弦脉组特征性参数为EP、PWV、β、AC。WI技术可为脉象的精准分型和信息解读提供客观依据,值得进一步推广应用。

经典名方旋覆代赭汤乙酸乙酯部位指纹图谱及化学模式识别研究

目的:建立旋覆代赭汤乙酸乙酯部位UPLC指纹图谱,结合化学模式识别分析不同产地饮片对旋覆代赭汤质量的影响。方法:采用Waters UPLC BEH C_(18)(2.1 mm×150 mm,1.7μm)色谱柱,流动相为乙腈-甲醇-0.4%甲酸水溶液,体积流量0.1 mL·min^(-1),梯度洗脱,检测波长350 nm;建立13批不同产地饮片提取的旋覆代赭汤样品指纹图谱,进行相似度评价,并结合聚类分析(CA)、主成分分析(PCA)和正交偏最小二乘法-判别分析(OPLS-DA),对旋覆代赭汤指纹图谱数据进行分析。结果:13批旋覆代赭汤指纹图谱确定22个共有特征峰,指认出12个多酚类成分,其中11个多酚类成分来自于旋覆花,其相似度均在0.9以上;通过CA发现,13批样品可按旋覆花产地分为三类;PCA与CA结果基本一致,并提取出4个主成分;OPLS-DA筛选出影响分类的差异性质量标志物,其中已指认出的成分有异绿原酸、异槲皮苷、异鼠李素-3-O-葡萄糖苷、异绿原酸B、1,5-二咖啡酰奎宁酸、绿原酸、槲皮万寿菊苷、槲皮素。结论:通过指纹图谱结合化学模式识别技术的分析策略,可快速有效地筛选不同批次旋覆代赭汤中多酚类成分中的差异质量标志物,为后续旋覆代赭汤的药效物质基础研究和质量评价提供参考。

基于PCA-LM的空战目标威胁评估

空战过程中态势瞬息万变,获取敌目标的威胁是我方取得攻击占位优势和采取战术规避的前提条件。提出主成分分析法和阻尼最小二乘法相结合的回归模型对目标的威胁进行评估。利用主成分分析法,分析指标之间的相关性,转化成相互独立的分量,确定主成分分量,重构目标威胁评估体系;对目标威胁与主成分分量进行回归分析,利用阻尼最小二乘法对回归模型参数进行估计,得到主成分分量与目标威胁之间的统计关系;利用目标威胁估计值与实际值之间的误差大小,验证了回归模型的有效性。消除了指标之间的相关性对评估结果的影响,提高了评估结果的客观性,解决了传统评估方法忽略指标之间耦合性的问题。

基于UPLC-Q-TOF-MS分析江西特色炮制技术对中药升麻化学成分的影响

目的比较江西特色炮制技术对升麻化学成分的影响,筛选优质饮片品种。方法采用超高效液相色谱-四极杆-飞行时间串联质谱(ultra performance liquid chromatography-quadrupole-time of flight tandem mass spectrometry,UPLC-Q-TOF-MS)技术,在正、负离子模式下分析升麻不同炮制品的化学成分,通过对照品、相对分子质量、质谱裂解规律和文献信息进行鉴定。利用SIMCA-P13.0软件建立升麻各炮制品主成分分析(principal component analysis,PCA)和偏最小二乘法-判别分析(partial least squares discriminant analysis,PLS-DA)模型,获取PCA得分图、PLA-DA得分图和变量重要性投影(variable importance plot,VIP)值,筛选造成升麻炮制前后主要差异的物质基础。利用MetaboAnatyst网页绘图工具,制作得到热图,可更直观地观察升麻化学成分经炮制后的变化趋势。结果鉴定出71个化学成分,PCA显示经不同方法炮制后升麻组间差异性大,PLS-DA筛选出VIP值>1的33个化学成分作为炮制前后差异性的主要化学标记物。其中生品和蜜炙升麻中三萜类含量较高,蜜麸、蜜糠炒升麻中酚酸类物质含量较高,蜜麸升麻中阿魏酸含量较高。结论酚酸类和三萜皂苷类是区分升麻不同炮制品最重要的化合物类别,为江西特色升麻饮片的药效物质基础及优势品种研究提供了依据。

偏最小二乘法在激光诱导击穿光谱定量分析中的应用研究

介绍了激光诱导击穿光谱(laser induced breakdown spectroscopy,LIBS)技术、主元分析(principal component an alysis,PCA)法和偏最小二乘(partial least squares,PLS)法的基本原理。对Pb元素特征谱线附近的36个维度进行主成分信息提取,对36维波长数据压缩到2维后,采用每个样品的20个脉冲的主元分数进行偏最小二乘拟合,对数据进行平均处理后,拟合结果质量较高,拟合系数平方的值从0.49810提高到0.97000;残差平方和从0.72529下降到1.36366*10^(-4)。PCA法可以有效的缩减具有一定相关性的样本数据空间,对于数据维度较大的数据处理能显著提升效率,再结合PLS法拟合压缩后的主元,实验结论得出PLS适合用于LIBS定量分析。

气相色谱-离子迁移谱结合化学计量学分析对新会陈皮的鉴别

采用气相色谱-离子迁移谱(gas chromatography-ion mobility spectrometry,GC-IMS)技术对包括新会陈皮在内的10个产地陈皮的风味成分进行测定,运用主成分分析和偏最小二乘判别分析(partial least squares discriminant analysis,PLS-DA)方法对GC-IMS检出的75种风味成分进行分析,以建立新会陈皮的鉴别方法。结果表明,该方法可将新会陈皮与其他陈皮区分开,实现对新会陈皮的有效鉴别。同时,分析变量投影重要性可进一步筛选出20种对有效区分新会陈皮和其他产地陈皮发挥关键作用的特征标志物。本研究通过引入GC-IMS技术和PLSDA方法实现了新会陈皮与其他产地陈皮的准确鉴别,可为新会陈皮的国家地理标志产品保护和产地溯源提供新的技术参考。

基于主成分分析和随机森林回归的冬小麦冠层叶绿素含量估算

为提高冬小麦冠层光谱对叶绿素含量的估算精度,以陕西省乾县冬小麦为研究对象,利用SVC-1024i光谱仪和SPAD-502型叶绿素仪实测了冬小麦冠层反射率和叶绿素含量,分析了一阶导数光谱、10种特征参数和9种植被指数与叶绿素含量的相关性,并利用主成分分析(PCA)对叶绿素敏感的可见光波段(390~780 nm)一阶导数光谱进行降维,将特征值大于1的主分量结合特征参数和植被指数形成不同的输入变量,用偏最小二乘回归和随机森林回归构建冬小麦冠层叶绿素估算模型,并利用独立样本对模型进行验证。结果表明,小麦冠层叶绿素含量与一阶导数光谱在751 nm处的相关性最高(r=0.71),特征参数中红边蓝边归一化(SDr-SDb)/(SDr+SDb)与叶绿素含量的相关性最高(r=0.66),植被指数(VI)中修正归一化差异指数(mND705)相关性最高(r=0.74)。在输入变量相同的情况下,基于随机森林(RF)回归的预测模型均优于偏最小二乘回归(PLSR)模型,其中PCA-VI-RF模型的各精度指标均达到最优(r^(2)=0.94,RMSE=1.05,RPD=3.70),是冬小麦冠层叶绿素含量估算的最优模型。