基于GPU计算的并行PLS算法研究与实现

偏最小二乘算法(PLS)是与红外、近红外光谱分析结合使用最为广泛的化学计量学算法,然而当前PLS算法通常采用单线程方式实现,当校正模型数量多或样本数量大、波长点数和主成分数较多,模型需对光谱预处理和波长选择方法反复优化时,计算十分缓慢。为大幅提高建模速度,该文提出了一种基于图形处理器(GPU)的并行计算策略,利用具有大规模并行计算特性的GPU作为计算设备,结合CUBLAS库函数实现了基于GPU并行的PLS建模算法(CUPLS)。利用近红外光谱数据集进行性能对比实验,结果表明CUPLS建模算法较传统单线程实现的PLS算法,加速比可达近42倍,极大地提升了化学计量学算法的建模效率。该方法亦可用于其它化学计量学算法的加速。     

激光诱导击穿光谱(LIBS)结合机器学习算法快速测定石油焦中微量元素

石油焦中微量元素对其作为预焙阳极的性能起着决定性的作用。首先，通过基于LIBS光谱构建用于石油焦中铁(Fe)和铜(Cu)定量分析的PLS校正模型。然后，考察了不同光谱预处理(归一化、多元散射校正、标准正态变换、一阶导数和二阶导数)以及变量选择算法(粒子群优化算法和变量重要性投影)对PLS校正模型预测性能的影响。建立了一种基于激光诱导击穿光谱(Laser-induced breakdown spectroscopy, LIBS)结合偏最小二乘(Partial least squares, PLS)的石油焦中微量元素定量分析方法。结果显示，与其他PLS校正模型相比，基于二阶导数和变量重要性投影的PLS模型对Fe的预测性能最优，最优的交叉验证相关系数(R-squared cross validation,R²cv)为0.966 7,均方根误差(Root mean squared error cross validation, RMSEcv)为10.282 1 mg/kg,预测集的相关系数(R-squared prediction,R²p)为0.86...     

化学计量学-荧光分析法同时测定萘、1-萘酚和2-萘酚

根据正交信号校正(OSC)、小波包变换(WPT)及偏最小二乘法(PLS)的算法原理,编制了名为POSC-WPTPLS的程序,结合荧光分析法快速、灵敏、选择性较好的优点,将该程序用于同时测定荧光光谱严重重叠的萘、1-萘酚和2-萘酚多组分体系,并将3种化学计量学方法(OSC-WPT-PLS、WPT-PLS和PLS)进行比较...     

复杂化学模式群的非线性映射及其应用

提出新的非线性映射算法，并分别采用传统非线性映射算法和新的非线性映射算法，将8维橄榄油样本映射于平面。其中新的非线性映射算法获得更好保留样本模式拓扑结构的映射平面，映射平面清晰地反映模式的类别关系，即同类模式都清晰地聚集在一起，实现聚类。     

主成分回归残差神经网络校正算法用于近红外光谱快速测定汽油辛烷值

根据汽油辛值预测体系本身的非线性特点,提出主成分回归残差神经网络校正算法（principal component regression residual artificial neural network,PCRRANN)用于近红外测定汽油辛烷值的预测模型校正,该方法给合了主成分回归算法（PC）,与经典的线性校正算法（PLS（Partial Least Square),PCR, 以及非线性PLS（NPLS,Non-linear PLS)等相比,预测明显的改善,文中还讨论了PCR主成分数及训练参数对预则模可能的影响。     

径向基函数网络在近红外人体无创伤血糖浓度检测基础研究中的应用

在近红外无创伤血糖浓度检测的基础研究中，对于多组分的混合物的分析，常因光谱与样品浓度之间呈现非线性响应，使得基于线性模型的校正方法失效。本文讨论了非线性校正方法径向基函数神经网络( RBFN )的有效性，并与线性校正方法中的主成分分析和偏最小二乘法作了对比研究。验证实验所用样品为①葡萄糖水溶液②包含牛血红蛋白和白蛋白的葡萄糖水溶液，结果表明：在①实验中PLS模型和RBFN预测标准偏差分别为8．2、8．9；在②实验中分别为15．6、8．8。可见在样品组分增多时，RBFN算法较线性PLS方法建立的模型预测能力强。     

小波变换用于钨和钼的同时光度测定

钨、钼与水杨基荧光酮（SAF）形成三元络合物,以SAF作为显色剂,溴化十六烷基三甲铵（CTMAB）作为稳定剂,室温下,在500-540nm波长范围内测定其吸光值,将测定结果分别用偏最小二乘法（PLS）处理和经小波变换后用偏最小二乘法处理。结果表明,经小波变换后处理结果误差明显减小。     

激光诱导击穿光谱对U元素的定量分析

铀矿是核领域最重要的矿产资源之一，快速、有效勘探铀矿资源能促进核领域平稳、健康发展。激光诱导击穿光谱(LIBS)技术具备多目标元素现场快速检测的优点，能实现铀矿资源准确、快速的现场分析。本工作基于LIBS技术对铀矿中U元素进行了定量分析，对比了偏最小二乘(PLS)和随机森林(RF)两种机器学习算法的定量效果。结果显示，RF模型的定量线性相关系数为0.996，对三个验证集的相对误差分别是22.33%、12.79%和12.04%；PLS模型的定量线性相关系数为0.997，对三个验证集的相对误差分别是4.33%、6.63%和6.85%。对比结果表明，本研究中的PLS模型定量准确度更高，同RF算法相比，PLS算法更适用于铀矿中U的LIBS定量分析。     

基于LASSO算法的光谱变量选择方法研究

光谱分析技术由于具有简单、快速、无损等优势,在复杂体系的定性和定量分析中得到了广泛应用。然而光谱中往往包含成百上千的波长点,有些波长点与研究的目标性质并不相关,加大了计算量并降低了模型的预测准确度。因此,在建立模型前需要进行变量选择。最小绝对收缩与选择算子（LASSO）可将回归系数收缩为0,进而达到变量选择的目的。该研究将LASSO用于三元调和油样品近红外光谱和生物样品拉曼光谱的变量选择,基于偏最小二乘（PLS）和多元线性回归（MLR）模型,分别对香油和肌氨酸的含量进行定量分析,并与无信息变量消除－PLS（UVE－PLS）、蒙特卡罗结合UVE－PLS（MCUVE－PLS）和随机检验－PLS（RT－PLS）3种变量选择方法进行比较。结果表明,基于LASSO的变量选择方法保留的变量数最少,运算速度最快。对三元调和油样品,LASSO－PLS预测的准确度最高;对生物样品,LASSO－MLR预测的准确度最高。因此,基于LASSO的变量选择算法有望在光谱分析领域中得到良好应用。     

自适应模糊偏最小二乘方法在药物构效关系建模中的应用

作为一种局部逼近方法,自适应神经模糊推理系统(ANFIS)适于为药物定量构效关系(QSAR)建模。描述药物分子结构的参数较多,常存在耦合关系,会增加建模难度,并影响模型的预报性能。为此,将ANFIS和偏最小二乘(PLS)相结合,先由PLS从样本数据中提取成分,再由ANFIS实现每对成分间的非线性映射,并基于输出误差进一步修正所提取的成分,使之对因变量具有最优的解释能力,由此构建为EB-AFPLS方法。该法已成功地应用于HIV-1蛋白酶抑制剂的QSAR建模,效果良好,显示出很强的学习能力,所建模型的预报性能也优于其它方法。     

Comparison of different partial least-squares methods in quantitative structure-activity relationships

In this paper, the partial least-squares (PLS) is discussed. A new hybrid method combining PLS with GAGP, in which selection of variables, selection of functions and optimization of parameters were carried at the same time without any foreknowledge, was studied. A number of PLS algorithms (linear PLS, QPLS, SPL-PLS, NPLSNGA) that have appeared were compared from a theoretical viewpoint. Eight practical results with all the compared methods indicated that nonlinear models are better than linear model. In nonlinear methods, GAGP-PLS is significant.     

Non-linear calibration models for near infrared spectroscopy

Different calibration techniques are available for spectroscopic applications that show nonlinear behavior. This comprehensive comparative study presents a comparison of different nonlinear calibration techniques: kernel PLS (KPLS), support vector machines (SVM), least-squares SVM (LS-SVM), relevance vector machines (RVM), Gaussian process regression (GPR), artificial neural network (ANN), and Bayesian ANN (BANN). In this comparison, partial least squares (PLS) regression is used as a linear benchmark, while the relationship of the methods is considered in terms of traditional calibration by ridge regression (RR). The performance of the different methods is demonstrated by their practical applications using three real-life near infrared (NIR) data sets. Different aspects of the various approaches including computational time, model interpretability, potential over-fitting using the non-linear models on linear problems, robustness to small or medium sample sets, and robustness to pre-processing, are discussed. The results suggest that GPR and BANN are powerful and promising methods for handling linear as well as nonlinear systems, even when the data sets are moderately small. The LS-SVM is also attractive due to its good predictive performance for both linear and nonlinear calibrations.     

Towards a complete identification of orthogonal variation in multiple regression from a PLS1 modeling point of view: including OPLS by a change of orthogonal basis

It is well known that the predictions of the single response orthogonal projections to latent structures (OPLS) and the single response partial least squares regression (PLS1) regression are identical in the single‐response case. The present paper presents an approach to identification of the complete y ‐orthogonal structure by starting from the viewpoint of standard PLS1 regression. Three alternative non‐deflating OPLS algorithms and a modified principal component analysis (PCA)‐driven method (including MATLAB code) is presented. The first algorithm implements a postprocessing routine of the standard PLS1 solution where QR factorization applied to a shifted version of the non‐orthogonal scores is the key to express the OPLS solution. The second algorithm finds the OPLS model directly by an iterative procedure. By a rigorous mathematical argument, we explain that orthogonal filtering is a ‘built‐in’ property of the traditional PLS1 regression coefficients. Consequently, the capabilities of OPLS with respect to improving the predictions (also for new samples) compared with PLS1 are non‐existing. The PCA‐driven method is based on the fact that truncating off one dimension from the row subspace of X results in a matrix X _orth with y ‐orthogonal columns and a rank of one less than the rank of X . The desired truncation corresponds exactly to the first X deflation step of Martens non‐orthogonal PLS algorithm. The significant y ‐orthogonal structure of X found by PCA of X _orth is split into two fundamental parts: one part that is significantly contributing to correct the first PLS score toward y and one part that is not. The third and final OPLS algorithm presented is a modification of Martens non‐orthogonal algorithm into an efficient dual PLS1–OPLS algorithm. Copyright © 2014 John Wiley & Sons, Ltd.     

Simultaneous spectrophotometric determination of paracetamol, ibuprofen and caffeine in pharmaceuticals by chemometric methods

In this study, the simultaneous determination of paracetamol, ibuprofen and caffeine in pharmaceuticals by chemometric approaches using UV spectrophotometry has been reported as a simple alternative to using separate models for each component. Spectra of paracetamol, ibuprofen and caffeine were recorded at several concentrations within their linear ranges and were used to compute the calibration mixture between wavelengths 200 and 400 nm at an interval of 1 nm in methanol:0.1 HCl (3:1). Partial least squares regression (PLS), genetic algorithm coupled with PLS (GA-PLS), and principal component-artificial neural network (PC-ANN) were used for chemometric analysis of data and the parameters of the chemometric procedures were optimized. The analytical performances of these chemometric methods were characterized by relative prediction errors and recoveries (%) and were compared with each other. The GA-PLS shows superiority over other applied multivariate methods due to the wavelength selection in PLS calibration using a genetic algorithm without loss of prediction capacity. Although the components show an important degree of spectral overlap, they have been determined simultaneously and rapidly requiring no separation step. These three methods were successfully applied to pharmaceutical formulation, capsule, with no interference from excipients as indicated by the recovery study results. The proposed methods are simple and rapid and can be easily used in the quality control of drugs as alternative analysis tools.     

Comparison of Artificial Neural Networks with Partial Least Squares Regression for Simultaneous Determinations by ICP-AES

Simultaneous determination of several elements （U, Ta, Mn, Zr and W） with inductively coupled plasma atomic emission spectrometry （ICP-AES） in the presence of spectral interference was performed using chemometrics methods. True comparison between artificial neural network （ANN） and partial least squares regression （PLS） for simultaneous determination in different degrees of overlap was investigated. The emission spectra were recorded at uranium analytical line （263.553 nm） with a 0.06 nm spectral window by ICP-AES. Principal component analysis was applied to data and scores on 5 dominant principal components were subjected to ANN. A 5-5-5 （input, hidden and output neurons） network was used with linear transfer function after both hidden and output layers. The PI,S model was trained with five latent variables and 20 samples in calibration set. The relative errors of predictions （REP） in test set were 3.75% and 3.56% for ANN and PLS respectively.     

Different approaches to multivariate calibration of nonlinear sensor data

In this study, different approaches to the multivariate calibration of the vapors of two refrigerants are reported. As the relationships between the time-resolved sensor signals and the concentrations of the analytes are nonlinear, the widely used partial least-squares regression (PLS) fails. Therefore, different methods are used, which are known to be able to deal with nonlinearities present in data. First, the Box–Cox transformation, which transforms the dependent variables nonlinearly, was applied. The second approach, the implicit nonlinear PLS regression, tries to account for nonlinearities by introducing squared terms of the independent variables to the original independent variables. The third approach, quadratic PLS (QPLS), uses a nonlinear quadratic inner relationship for the model instead of a linear relationship such as PLS. Tree algorithms are also used, which split a nonlinear problem into smaller subproblems, which are modeled using linear methods or discrete values. Finally, neural networks are applied, which are able to model any relationship. Different special implementations, like genetic algorithms with neural networks and growing neural networks, are also used to prevent an overfitting. Among the fast and simpler algorithms, QPLS shows good results. Different implementations of neural networks show excellent results. Among the different implementations, the most sophisticated and computing-intensive algorithms (growing neural networks) show the best results. Thus, the optimal method for the data set presented is a compromise between quality of calibration and complexity of the algorithm.Electronic Supplementary Material Supplementary material is available for this article at     

The geometry of PLS1 explained properly: 10 key notes on mathematical properties of and some alternative algorithmic approaches to PLS1 modelling

The insight from, and conclusions of this paper motivate efficient and numerically robust ‘new’ variants of algorithms for solving the single response partial least squares regression (PLS1) problem. Prototype MATLAB code for these variants are included in the Appendix. The analysis of and conclusions regarding PLS1 modelling are based on a rich and nontrivial application of numerous key concepts from elementary linear algebra. The investigation starts with a simple analysis of the nonlinear iterative partial least squares (NIPALS) PLS1 algorithm variant computing orthonormal scores and weights. A rigorous interpretation of the squared P ‐loadings as the variable‐wise explained sum of squares is presented. We show that the orthonormal row‐subspace basis of W ‐weights can be found from a recurrence equation. Consequently, the NIPALS deflation steps of the centered predictor matrix can be replaced by a corresponding sequence of Gram–Schmidt steps that compute the orthonormal column‐subspace basis of T ‐scores from the associated non‐orthogonal scores. The transitions between the non‐orthogonal and orthonormal scores and weights (illustrated by an easy‐to‐grasp commutative diagram), respectively, are both given by QR factorizations of the non‐orthogonal matrices. The properties of singular value decomposition combined with the mappings between the alternative representations of the PLS1 ‘truncated’ X data (including P ^t W ) are taken to justify an invariance principle to distinguish between the PLS1 truncation alternatives. The fundamental orthogonal truncation of PLS1 is illustrated by a Lanczos bidiagonalization type of algorithm where the predictor matrix deflation is required to be different from the standard NIPALS deflation. A mathematical argument concluding the PLS1 inconsistency debate (published in 2009 in this journal) is also presented. Copyright © 2014 John Wiley & Sons, Ltd.     

一种改进BP网络结构用于化学中的非线性校正

针对化学领域中的非线性关系特点,在常规BP网络基础上,提出了一种“杂交”型BP网络,包含两个隐层,并有输入层到输出层的直连接。它可很好地解释数据中同时存在的线性及非线性关系,效果优于多元回归法及普通BP算法。