PARTIAL LEAST-SQUARES(PLS)REGRESSION AND SPECTROPHOTOMETRY AS APPLIED TO THE ANALYSIS OF MULTICOMPONENT MIXTURES

The UV absorption spectra of o-naphthol,α-naphthylamine,2,7-dihydroxy naphthalene,2,4-dimethoxy ben- zaldehyde and methyl salicylate,overlap severely;therefore it is impossible to determine them in mixtures by traditional spectrophotometric methods.In this paper,the partial least-squares(PLS)regression is applied to the simultaneous determination of these compounds in mixtures by UV spectrophtometry without any pretreatment of the samples.Ten synthetic mixture samples are analyzed by the proposed method.The mean recoveries are 99.4%,996%,100.2%,99.3% and 99.1%,and the relative standard deviations(RSD) are 1.87%,1.98%,1.94%,0.960% and 0.672%,respectively.

Application of partial least squares regression in data analysis of mining subsidence

Based on the surveying data of strata-moving angle and the ordinary least squares regression, this paper is to construct, a regression model is constructed which is strata-moving parameter β concerning the coal bed obliquity, coal thickness, mining depth, etc. But the regression is unsuccessful. The result is that none of the parameters is suited, this is not up to objective reality. This paper presents a novel method, partial least squares regression (PLS regression), to construct the statistic model of strata-moving parameter β. The experiment shows that the forecasting model is reasonable.

Quantum partial least squares regression algorithm for multiple correlation problem

Partial least squares(PLS) regression is an important linear regression method that efficiently addresses the multiple correlation problem by combining principal component analysis and multiple regression. In this paper, we present a quantum partial least squares(QPLS) regression algorithm. To solve the high time complexity of the PLS regression, we design a quantum eigenvector search method to speed up principal components and regression parameters construction. Meanwhile, we give a density matrix product method to avoid multiple access to quantum random access memory(QRAM)during building residual matrices. The time and space complexities of the QPLS regression are logarithmic in the independent variable dimension n, the dependent variable dimension w, and the number of variables m. This algorithm achieves exponential speed-ups over the PLS regression on n, m, and w. In addition, the QPLS regression inspires us to explore more potential quantum machine learning applications in future works.

基于PLSR和LSSVM模型的土壤水分高光谱反演

为对地下采矿扰动区表层土壤水分进行反演,以大柳塔煤矿52501工作面为例,利用无人机搭载成像光谱仪获取高光谱影像,对获取的光谱数据进行对数、倒数对数、一阶和包络线去除变换,结合地面采集的128个土壤水分数据,基于偏最小二乘回归(PLSR)和最小二乘支持向量机(LSSVM)构建土壤水分预测模型并验证其预测精度。结果表明,基于一阶变换的PLSR模型和LSSVM模型预测精度相对较好,一阶变换的PLSR模型建模集R^(2)_(c)和预测集R^(2)_(p)分别为0.7021和0.6405,均方根误差RMSE_(c)和RMSE_(p)分别为1.6384%和1.1034%,相对分析误差RPD_(p)为1.7263;一阶变换的LSSVM模型建模集R^(2)_(c)和预测集R^(2)_(p)分别为0.8125和0.5979,均方根误差RMSE_(c)和RMSE_(p)分别为1.2755%和1.3459%,相对分析误差RPD_(P)为1.6323。最终基于PLSR和LSSVM模型完成了土壤水分的制图,实现了土壤水分的空间预测,为该研究区植被引导修复中土壤水分精准提升提供了空间数据支持。

Discrimination of Transgenic Rice Based on Near Infrared Reflectance Spectroscopy and Partial Least Squares Regression Discriminant Analysis

Near infrared reflectance spectroscopy （NIRS）, a non-destructive measurement technique, was combined with partial least squares regression discrimiant analysis （PLS-DA） to discriminate the transgenic （TCTP and mi166） and wild type （Zhonghua 11） rice. Furthermore, rice lines transformed with protein gene （OsTCTP） and regulation gene （Osmi166） were also discriminated by the NIRS method. The performances of PLS-DA in spectral ranges of 4 000-8 000 cm-1 and 4 000-10 000 cm-1 were compared to obtain the optimal spectral range. As a result, the transgenic and wild type rice were distinguished from each other in the range of 4 000-10 000 cm-1, and the correct classification rate was 100.0% in the validation test. The transgenic rice TCTP and mi166 were also distinguished from each other in the range of 4 000-10 000 cm-1, and the correct classification rate was also 100.0%. In conclusion, NIRS combined with PLS-DA can be used for the discrimination of transgenic rice.

Estimating Wheat Grain Protein Content Using Multi-Temporal Remote Sensing Data Based on Partial Least Squares Regression

Estimating wheat grain protein content by remote sensing is important for assessing wheat quality at maturity and making grains harvest and purchase policies. However, spatial variability of soil condition, temperature, and precipitation will affect grain protein contents and these factors usually cannot be monitored accurately by remote sensing data from single image. In this research, the relationships between wheat protein content at maturity and wheat agronomic parameters at different growing stages were analyzed and multi-temporal images of Landsat TM were used to estimate grain protein content by partial least squares regression. Experiment data were acquired in the suburb of Beijing during a 2-yr experiment in the period from 2003 to 2004. Determination coefficient, average deviation of self-modeling, and deviation of cross- validation were employed to assess the estimation accuracy of wheat grain protein content. Their values were 0.88, 1.30%, 3.81% and 0.72, 5.22%, 12.36% for 2003 and 2004, respectively. The research laid an agronomic foundation for GPC （grain protein content） estimation by multi-temporal remote sensing. The results showed that it is feasible to estimate GPC of wheat from multi-temporal remote sensing data in large area.

Simultaneous Spectrophotometric Determination of Three Components Including Deoxyschizandrin by Partial Least Squares Regression

The computer auxiliary partial least squares is introduced to simultaneously determine the contents of Deoxyschizandin, Schisandrin, r-Schisandrin in the extracted solution of wuweizi. Regression analysis of the experimental results shows that the average recovery of each component is all in the range from 98.9% to 110.3% , which means the partial least squares regression spectrophotometry can circumvent the overlappirtg of absorption spectrums of mlulti-components, so that sctisfactory results can be obtained without any scrapple pre-separation.

Partial Least Squares Regression Model to Predict Water Quality in Urban Water Distribution Systems

The water distribution system of one residential district in Tianjin is taken as an example to analyze the changes of water quality.Partial least squares(PLS) regression model,in which the turbidity and Fe are regarded as control objectives,is used to establish the statistical model.The experimental results indicate that the PLS regression model has good predicted results of water quality compared with the monitored data.The percentages of absolute relative error(below 15%,20%,30%) are 44.4%,66.7%,100%(turbidity) and 33.3%,44.4%,77.8%(Fe) on the 4th sampling point;77.8%,88.9%,88.9%(turbidity) and 44.4%,55.6%,66.7%(Fe) on the 5th sampling point.

优化光谱指数结合PLSR的多金属矿区土壤As含量高光谱反演

砷(As)是我国多金属矿区的主要污染物之一,对环境、农业和人类健康构成严重威胁。近地高光谱技术具有快速、动态、无损、光谱分辨率高等优势,对于多金属矿区土壤As污染监测与综合治理具有巨大应用潜力。然而,由于受污染区域、土壤背景以及高光谱质量、光谱输入量等因素影响,高光谱反演模型的适用性和精度差异较大。本研究针对湘南某多金属矿区,基于Pearson相关性分析并结合变量投影重要性(VIP)准则,提取18种变换光谱形式下的单变量特征波段及4种光谱指数算法下的优化光谱指数作为光谱输入量,建立偏最小二乘回归(PLSR)模型,实现了矿区土壤As含量反演。结果表明:倒数(RT)、对数(L)、平方根(Sqrt)、标准正态变量变换二阶导(SNV_SD)等变换后的光谱数据与As含量具有较高的相关性;优化光谱指数能从二维光谱空间揭示As的光谱响应,相较于单变量特征波段,以优化光谱指数为自变量构建的模型性能更优;比值指数(RI)模型的R_(c)^(2)、RMSE_(c)、R_(p)^(2)、RMSE_(p)、RPD分别为0.908、50.8 mg/kg、0.949、35.6 mg/kg、4.45,是研究区土壤As含量反演的最优模型。单变量特征波段结合优化光谱指数预测土壤As含量具有较好的可行性,可为多金属矿区土壤As污染高光谱快速监测提供科学依据。

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.

A partial least-squares regression approach to land use studies in the Suzhou-Wuxi-Changzhou region

In several LUCC studies, statistical methods are being used to analyze land use data. A problem using conventional statistical methods in land use analysis is that these methods assume the data to be statistically independent. But in fact, they have the tendency to be dependent, a phenomenon known as multicollinearity, especially in the cases of few observations. In this paper, a Partial Least-Squares （PLS） regression approach is developed to study relationships between land use and its influencing factors through a case study of the Suzhou-Wuxi-Changzhou region in China. Multicollinearity exists in the dataset and the number of variables is high compared to the number of observations. Four PLS factors are selected through a preliminary analysis. The correlation analyses between land use and influencing factors demonstrate the land use character of rural industrialization and urbanization in the Suzhou-Wuxi-Changzhou region, meanwhile illustrate that the first PLS factor has enough ability to best describe land use patterns quantitatively, and most of the statistical relations derived from it accord with the fact. By the decreasing capacity of the PLS factors, the reliability of model outcome decreases correspondingly.

Factors Affecting Box Office during Broad Spring Festival Based on Partial Least Squares Regression

The box office during the later Spring Festival shows an attractive prospect.This paper studied the factors affecting total box office during the broad Spring Festival which is from the Spring Festival to the Lantern Festival.Data of films released during the broad Spring Festival from the years 2016 to 2019 in China were gathered,and the impact of eight explanatory variables on the box office during the broad Spring Festival was empirically analyzed by partial least squares(PLS)regression with software SIMCA.The results suggest that word-of-mouth has the most positive effect on the box office during the broad Spring Festival.Later propaganda has a positive effect,while early promotion has a negative effect on the box office.Director’s influence has a positive effect,while actor’s influence does not contribute much to the box office.Length of the trailer has a negative effect.The film format of 2D or 3D doesn’t contribute much to the box office.

Based on Partial Least-squares Regression to Build up and Analyze the Model of Rice Evapotranspiration

During the course of calculating the rice evapotranspiration using weather factors,we often find that some independent variables have multiple correlation.The phenomena can lead to the traditional multivariate regression model which based on least square method distortion.And the stability of the model will be lost.The model will be built based on partial least square regression in the paper,through applying the idea of main component analyze and typical correlation analyze,the writer picks up some component from original material.Thus,the writer builds up the model of rice evapotranspiration to solve the multiple correlation among the independent variables (some weather factors).At last,the writer analyses the model in some parts,and gains the satisfied result.

A Novel Extension of Kernel Partial Least Squares Regression

Based on continuum power regression(CPR) method, a novel derivation of kernel partial least squares(named CPR-KPLS) regression is proposed for approximating arbitrary nonlinear functions.Kernel function is used to map the input variables(input space) into a Reproducing Kernel Hilbert Space(so called feature space),where a linear CPR-PLS is constructed based on the projection of explanatory variables to latent variables(components). The linear CPR-PLS in the high-dimensional feature space corresponds to a nonlinear CPR-KPLS in the original input space. This method offers a novel extension for kernel partial least squares regression(KPLS),and some numerical simulation results are presented to illustrate the feasibility of the proposed method.

基于PCA-HCA联合PLS回归模型的蚯蚓粪肥品质等级划分

蚯蚓粪肥理化特性涉及指标多,如何从众多易检测的指标中筛选出能够反映蚯蚓粪肥特点的关键指标,进而用于构建评价模型,高效、快速地评价蚯蚓粪肥的品质等级,是蚯蚓粪肥应用前亟需解决的重要问题与难点。研究针对不同原料类型、不同蚯蚓堆肥时间获得的蚯蚓粪肥,采用统计学与化学计量学对蚯蚓粪肥23个主要指标开展描述统计与相关分析,筛选出了13个蚯蚓粪肥特异性指标。以13个关键指标为基础,首先,结合主成分分析(PCA)与分层聚类分析(HCA)对不同蚯蚓粪肥样品开展品质初级划分;其次,采用偏最小二乘回归(PLS)-判别分析(DA)对分级结果进行效果判定;最后,整体构建基于PLS模型的蚯蚓粪肥等级评价方法并开展验证分析。结果表明:PCA与HCA分析法可将蚯蚓粪肥划分为3个品质等级,通过PLS-DA判别该划分结果合理有效,形成了基于PLS蚯蚓粪肥等级评价模型:蚯蚓粪肥品质等级(Y)=3.0796+0.0026×TOC-0.1381×HS-0.1446×HA-0.1378×TN-0.1355×TP-0.1494×AK-0.1324×AN-0.1402×AP+0.0004×EOC+0.03985×ROC+0.07685×C/N-0.0049×Kos-0.1481×HI(TOC、HS、HA、TN、TP、AK、AN、AP、EOC、ROC、C/N、Kos、HI分别代表总有机碳、腐殖质碳、胡敏酸、总氮、总磷、速效钾、碱解氮、有效磷、易氧化有机碳、难氧化有机碳、碳氮比、氧化稳定系数、腐殖化指数),分级标准为:若Y在0.45~1.56之间,品质等级为一等品;Y在1.63~2.20之间,为二等品;Y在2.28~3.72之间,为三等品。变量权重值表明影响蚯蚓粪肥品质前5的关键指标顺序为HI>TN>HS>HA>AN。研究成功建立了一套“PCA+HCA+PLS”的蚯蚓粪肥品质评价方法,对蚯蚓粪肥分级应用与规范蚯蚓产业市场具有重要意义。

黄金矿山岩体质量分级知识库与PLS简化预测模型

针对黄金矿山工程岩体特征,分析了岩石单轴抗压强度、RQD值、节理结构面状态、节理结构面间距、地下水状态、节理结构面方向对工程影响和地应力值这7个主要因素对岩体稳定性的影响,对7个指标进行修正,建立了地下矿山M-RMR岩体质量评价指标体系。采用M-RMR岩体质量评价指标体系划分了焦家金矿直属矿区、寺庄矿区和望儿山矿区工程岩体质量等级,建立了焦家金矿地下矿山岩体质量与其影响因素的神经网络知识库模型,达到了焦家金矿工程岩体质量智能分级的目的。为简化M-RMR指标体系中指标数量,更利于实际应用,采用变量投影重要性指标VIP对7个指标所携带信息量的大小进行排序,并逐个删除不重要的指标,利用单因变量的偏最小二乘回归方法(PLS1)建立了精简指标的简化预测模型。简化预测模型可使用较少的评价指标对岩体质量给出准确的分级,具有实际使用价值。

基于MW-MKEPLS的多重时变间歇生产过程质量预测

间歇生产过程的多重时变特性和非线性使得质量预测问题变得复杂。为了提高间歇过程质量预测精度,提出了滑动窗多向核熵偏最小二乘(moving window multiway kernel entropy partial least squares,MW-MKEPLS)方法。首先采用滑动窗进行数据的动态更新获取,构建了滑动窗多重时变模型;然后在滑动窗多重时变模型下通过核函数将数据映射到高维特征空间,采用Renyi熵贡献度进行数据特征提取,更好地获取数据的信息熵和非线性;最后在KECA处理后的高维特征空间进行质量预测。通过青霉素生产发酵过程进行了实验验证,并与MKPLS和MKEPLS进行对比分析,结果表明所提方法的质量预测精度更高。

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.

Boosting the partial least square algorithm for regression modelling

Boosting algorithms are a class of general methods used to improve the general periormance of regression analysis. The main idea is to maintain a distribution over the train set. In order to use the given distribution directly, a modified PLS algorithm is proposed and used as the base learner to deal with the nonlinear multivariate regression problems. Experiments on gasoline octane number prediction demonstrate that boosting the modified PLS algorithm has better general performance over the PLS algorithm.