同时测定铁钴铜的小波软阈值核心偏最小二乘法

提出了一种小波软阈值核心偏最小二乘法，同时测定铁、钴、铜；该法结合小波软阈值法和主组分分析改进除噪声质量，与其它软阈值法比较选用了HYBRID法；通过最佳化，小波函数和低频截止收缩水平（L）分别选用Symmlet6和2；设计了一个名为软阈值小波核心偏最小二乘法（STWKPLS）的程序进行全部计算，实验结果表明该法是成功的，并且优于核心偏最小二乘法。     

偏最小二乘光度法同时测定多种酚的研究有应用

利用Ｃｕ（Ⅱ）、吡啶能与酚形成稳定的三元配合物的特点，研究了Ｃｕ（Ⅱ）－吡啶－酚三元显色新体系，并以偏最小二乘法建立模型预测，同时测定了模拟水样和环境水样中的对苯二酚、间苯二酚、邻苯三酚和对硝基苯酚，取得满意效果。     

偏最小二乘法辅助分光光度法同时测定痕量锰、铁、铜和锌

痕量Mn（Ⅱ）、Fe（Ⅲ）、Cu（Ⅱ）和Zn（Ⅱ）与2－（5－溴－2－吡啶偶氮）－5－二乙氨基苯酚和聚乙二醇辛基本基醚在pH8．8发生高灵敏的显色反应，所形成的三元胶束络合物的吸收光谱严重重叠，用偏最小二乘法（PLS）辅助分光光度法成功地同时测定了模拟试样及铝合金和饲料添加剂中上述四种痕量组分。结果表明，PLS法是化学计量学法中一种可适用于基体较复杂的实际试样中痕量组分同时分光光度测定的优良的多元计算方法。     

偏最小二乘光度法同时测定铜和铁的研究及应用

７－（１－苯偶氮）－８－羟基喹啉－５－磺酸钠在ＰＨ＝４．７５ＨＡｃ－ＮａＡｃ缓冲溶液中能与Ｃｕ（Ⅱ）和ＦＥ（Ⅲ）形成稳定的络合物，本文研究了Ｃｕ（Ⅱ）－ＰＡＨＱＳ、Ｆｅ（Ⅲ）－ＰＡＨＱＳ体系的显色条件，以偏最小二乘法处理两者重叠吸收峰，建立了光度法同时测定铜和铁的方法。     

偏最小二乘吸光光度法同时测定钡和锶的研究

二溴对甲基偶氮甲磺（ＤＢＭ－ＭＳＡ）在磷酸介质中能与Ｂａ（Ⅱ）、Ｓｒ（Ⅱ）形成稳定的络合物。研究了该显色体系的反应条件以及应用偏最小二乘法（ＰＬＳ）处理两者叠吸收峰,建立了光度法同时测定Ｂａ（Ⅱ）和Ｓｒ（Ⅱ）的方法。方法用于合成试样和除氧剂试样中两元素含量的测定,结果满意。     

小波变换-偏最小二乘算法及其在复方甲硝唑注射液分析中的应用

提出了结合小波变换的偏最小二乘法（ＷＰＬＳ）,即先对光谱信号进行小波变换,去除噪声,再用偏最小二乘法对多组分同时测定。将该法用于模拟体系及复方甲硝唑注射液体系,结果表明,该法优于偏最小二乘法。     

偏最小二乘光度法同时测定多种酚的研究及应用

利用Ｃｕ（Ⅱ）吡啶能与酚形成稳定的三元配合物的特点，研究了Ｃｕ（Ⅱ）－吡啶－酚三元显色新体系，并以偏最小二乘法建立模型预测，同时测定了模拟水样和环境水样中的对苯二酚、间苯二酚、邻苯三酚和对硝基苯酚，取得满意效果。     

逆最小二乘法—导数谱同时测定锌,镉,汞和铅

本文研究了在碱性介质中，ＣＰＢ存在下，ｍｅｓｏ－四（４－三甲铵基苯）卟啉与Ｚｎ（Ⅱ），Ｃｄ（Ⅱ），Ｈｇ（Ⅱ）和Ｐｂ（Ⅱ）络合物的导数光谱，提出了应用逆最小二乘法（或称ＣＰＡ－矩阵法）原理对导数光谱进行解释，同时测定四组分的方法。应用本法对合成样品和水进行分析，结果满意。     

小波变换结合多维偏最小二乘方法用于近红外光谱定量分析

将小波变换和多维偏最小二乘法相结合用于近红外光谱定量校正模型的建立。首先将原始光谱进行小波变换分解，得到系列小波细节系数，通过选取一组受外界因素少、信息强的小波系数组成三维光谱阵，然后再采用多维偏最小二乘法建立校正模型。实验结果表明，该方法所建近红外校正模捌的预测能力更强，并更具稳健性。     

偏最小二乘分光光度法同时测定镍基合金中的铈和钇

以对乙酰基偶氮氯膦（ＣＰＡｐＡ）为显色剂，研究了同时测定Ｃｅ和Ｙ的最佳条件，由于二者吸收光谱严重重叠，本文运用偏最小二乘法实现了Ｃｅ和Ｙ的同时测定，结果满意。     

Robust partial least squares regression: Part I,algorithmic developments

The work summarized in this paper presents the first part of a three‐paper series on robust partial least squares (RPLS) regression. Motivated by recent research activities in this area, this part provides a detailed algorithmic analysis of associated techniques, showing that existing work (i) may not represent a true robust formulation of partial least squares (PLS), (ii) may lead to convergence problems or (iii) may be insensitive to a certain type of outlier. On the basis of this analysis, Part I introduces a new conceptual RPLS algorithm that overcomes the deficiencies of existing work. The second part of this work details this new RPLS technique, compares its peformance with existing RPLS methods and provides an analysis on the computational efficiency and sensitivity of these algorithms. Whilst the first two parts of this work discuss algorithmic developments of RPLS, the final part concentrates on practical issues of RPLS implementations. This third part is devoted to practitioners of chemistry and chemical engineering covering a wide range of applications involving a calibration experiment, the analysis of recorded data from an industrial debutanizer process and data from a number of Raman spectroscopy experiments. Copyright © 2007 John Wiley & Sons, Ltd.     

Stacked partial least squares regression analysis for spectral calibration and prediction

Two novel algorithms which employ the idea of stacked generalization or stacked regression, stacked partial least squares (SPLS) and stacked moving‐window partial least squares (SMWPLS) are reported in the present paper. The new algorithms establish parallel, conventional PLS models based on all intervals of a set of spectra to take advantage of the information from the whole spectrum by incorporating parallel models in a way to emphasize intervals highly related to the target property. It is theoretically and experimentally illustrated that the predictive ability of these two stacked methods combining all subsets or intervals of the whole spectrum is never poorer than that of a PLS model based only on the best interval. These two stacking algorithms generate more parsimonious regression models with better predictive power than conventional PLS, and perform best when the spectral information is neither isolated to a single, small region, nor spread uniformly over the response. A simulation data set is employed in this work not only to demonstrate this improvement, but also to demonstrate that stacked regressions have the potential capability of predicting property information from an outlier spectrum in the prediction set. Moisture, oil, protein and starch in Cargill corn samples have been successfully predicted by these new algorithms, as well as hydroxyl number for different instruments of terpolymer samples including and excluding an outlier spectrum. Copyright © 2009 John Wiley & Sons, Ltd.     

Principal component analysis with boundary constraints

Observed data often belong to some specific intervals of values (for instance in case of percentages or proportions) or are higher (lower) than pre‐specified values (for instance, chemical concentrations are higher than zero). The use of classical principal component analysis (PCA) may lead to extract components such that the reconstructed data take unfeasible values. In order to cope with this problem, a constrained generalization of PCA is proposed. The new technique, called bounded principal component analysis (B‐PCA), detects components such that the reconstructed data are constrained to belong to some pre‐specified bounds. This is done by implementing a row‐wise alternating least squares (ALS) algorithm, which exploits the potentialities of the least squares with inequality (LSI) algorithm. The results of a simulation study and two applications to bounded data are discussed for evaluating how the method and the algorithm for solving it work in practice. Copyright © 2007 John Wiley & Sons, Ltd.     

Rotational superposition and least squares: the SVD and quaternions approaches yield identical results. Reply to the preceding comment by G. Kneller

We clarify once again that Kabsch's method and the Quaternion method are mathematically equivalent methods, that is, that they contain identical information and, when properly understood and applied, lead to identical answers to any questions regarding least-squares rotational superposition, either by proper rotations or by rotation-reflections. We also provide the correct bounds for the eigenvalue spectrum.     

Averaged and weighted average partial least squares

Two alternative partial least squares (PLS) methods, averaged PLS and weighted average PLS, are proposed and compared with the classical PLS in terms of root mean square error of prediction (RMSEP) for three real data sets. These methods compute the (weighted) average of PLS models with different complexity. The prediction abilities of the alternative methods are comparable to that of the classical PLS but they do not require to determine how many components should be included in the model. They are also more robust in the sense that the quality of prediction depends less on a good choice of the number of components to be included. In addition, weighted average PLS is also compared with the weighted average part of LOCAL, a published method that also applies weighted average PLS, with however an entirely different weighting scheme.     

Algorithms for multi‐group PLS

Several approaches of investigation of the relationships between two datasets where the individuals are structured into groups are discussed. These strategies fit within the framework of partial least squares (PLS) regression. Each strategy of analysis is introduced on the basis of a maximization criterion, which involves the covariances between components associated with the groups of individuals in each dataset. Thereafter, algorithms are proposed to solve these maximization problems. The strategies of analysis can be considered as extensions of multi‐group principal components analysis to the context of PLS regression. Copyright © 2014 John Wiley & Sons, Ltd.     

Borrowing information from relevant microarray studies for sample classification using weighted partial least squares

With an increasing number of publicly available microarray datasets, it becomes attractive to borrow information from other relevant studies to have more reliable and powerful analysis of a given dataset. We do not assume that subjects in the current study and other relevant studies are drawn from the same population as assumed by meta-analysis. In particular, the set of parameters in the current study may be different from that of the other studies. We consider sample classification based on gene expression profiles in this context. We propose two new methods, a weighted partial least squares (WPLS) method and a weighted penalized partial least squares (WPPLS) method, to build a classifier by a combined use of multiple datasets. The methods can weight the individual datasets depending on their relevance to the current study. A more standard approach is first to build a classifier using each of the individual datasets, then to combine the outputs of the multiple classifiers using a weighted voting. Using two quite different datasets on human heart failure, we show first that WPLS/WPPLS, by borrowing information from the other dataset, can improve the performance of PLS/PPLS built on only a single dataset. Second, WPLS/WPPLS performs better than the standard approach of combining multiple classifiers. Third, WPPLS can improve over WPLS, just as PPLS does over PLS for a single dataset.     

Calibration transfer strategy to compensate for instrumental drift in portable quadrupole mass spectrometers

We report the use of a calibration transfer strategy to correct for drift in the quantitative sensitivity of a portable quadrupole mass spectrometer (QMS) aimed at process monitoring applications. Gas mixtures of CH₄/Ar/C₂H₆/CO₂ were studied with calibration phase measurements made of the pure gases for a univariate analysis and of 40 multi-component mixtures for a multivariate approach. To evaluate calibrations, test set spectra of a CH₄/Ar/C₂H₆/CO₂ gas mixture were recorded bi-weekly over a period of 12 months. As part of the strategy a standard of pure argon was measured during both calibration and test phases so that correction factors could be calculated for each measurement day. It was shown that in the absence of a calibration transfer strategy quantifications of test set spectra could be inaccurate by more than an order of magnitude over 12 months. Furthermore, due to the effects of drift in the sensitivity over the 6 days required to record the training set in the calibration phase it was found that the multivariate analysis quantified test spectra less accurately than the univariate analysis. However, by applying the calibration transfer strategy across all measurements (both calibration and test phases) it was shown that the errors in prediction using the multivariate analysis previously seen after 2 weeks were not observed until approximately 12 months later.