偏最小二乘回归用于近红外光谱分析的稳健策略

偏最小二乘法（PLS）在近红外光谱（NIR）定量分析中占有重要地位,但预测结果往往容易受到样本分组和奇异样本等因素的影响,稳健性不强。多模型PLS (EPLS）方法在模型稳健性上得到提高,然而它无法识别样本中存在的奇异样本。为了同时提高模型的预测准确性和稳健性,本文提出了一种根据取样概率重新取样的多模型PLS方法,称为稳健共识PLS（RE-PLS）方法。该方法通过迭代赋权偏最小二乘法(IRPLS)计算样本回归残差得到每个校正集样本的取样概率,然后根据样本的取样概率来选择训练子集建立多个PLS模型,最后将所有PLS模型的预测结果平均作为最终预测结果。该方法用于两种不同植物样品的近红外光谱建模,并与传统的PLS及EPLS方法进行比较。结果表明该方法可以有效的避免校正集中奇异样本对模型的影响,同时可以提高预测精确度和稳健性。对于含有较多奇异样本的,复杂近红外光谱烟草实际样本,利用简单PLS或者EPLS方法建模预测效果不是很理想,而RE-PLS凭借其独特优势则有望在这种复杂光谱定量分析中得到广泛的应用。     

Development and validation of a near infrared method for the analytical control of a pharmaceutical preparation in three steps of the manufacturing process

A near infrared diffuse reflectance spectroscopy (NIRS) procedure for the quantitative control analysis of the active compound (otilonium bromide) in a pharmaceutical preparation in three steps of the production process (blended product, cores and coated tablets) and a methodology for its validation are proposed. The analytical procedure is composed by two consecutive steps. First, the sample is identified by comparing its spectrum with a second derivative spectral library. If the sample is positively identified, the active compound is quantified by using a previously established partial least squares (PLS) calibration model. The procedure was validated by studying repeatability, intermediate precision, accuracy and linearity. To this end, an adaptation of ICH (International Conference on Harmonisation) validation methodology to an NIR multivariate calibration procedure is proposed. The relative standard error of prediction (RSEP) was < or = 1% and the suitability of the procedure for control analysis was confirmed by the results obtained analysing new production samples produced over a three-month period.     

Development and validation of a near infrared method for the analytical control of a pharmaceutical preparation in three steps of the manufacturing process

A near infrared diffuse reflectance spectroscopy (NIRS) procedure for the quantitative control analysis of the active compound (otilonium bromide) in a pharmaceutical preparation in three steps of the production process (blended product, cores and coated tablets) and a methodology for its validation are proposed. The analytical procedure is composed by two consecutive steps. First, the sample is identified by comparing its spectrum with a second derivative spectral library. If the sample is positively identified, the active compound is quantified by using a previously established partial least squares (PLS) calibration model. The procedure was validated by studying repeatability, intermediate precision, accuracy and linearity. To this end, an adaptation of ICH (International Conference on Harmonisation) validation methodology to an NIR multivariate calibration procedure is proposed. The relative standard error of prediction (RSEP) was ≤ 1% and the suitability of the procedure for control analysis was confirmed by the results obtained analysing new production samples produced over a three-month period.     

A method for calibration and validation subset partitioning

This paper proposes a new method to divide a pool of samples into calibration and validation subsets for multivariate modelling. The proposed method is of value for analytical applications involving complex matrices, in which the composition variability of real samples cannot be easily reproduced by optimized experimental designs. A stepwise procedure is employed to select samples according to their differences in both x (instrumental responses) and y (predicted parameter) spaces. The proposed technique is illustrated in a case study involving the prediction of three quality parameters (specific mass and distillation temperatures at which 10 and 90% of the sample has evaporated) of diesel by NIR spectrometry and PLS modelling. For comparison, PLS models are also constructed by full cross-validation, as well as by using the Kennard-Stone and random sampling methods for calibration and validation subset partitioning. The obtained models are compared in terms of prediction performance by employing an independent set of samples not used for calibration or validation. The results of F-tests at 95% confidence level reveal that the proposed technique may be an advantageous alternative to the other three strategies.     

Efficient use of pure component and interferent spectra in multivariate calibration

Partial Least Squares (PLS) is by far the most popular regression method for building multivariate calibration models for spectroscopic data. However, the success of the conventional PLS approach depends on the availability of a ‘representative data set’ as the model needs to be trained for all expected variation at the prediction stage. When the concentration of the known interferents and their correlation with the analyte of interest change in a fashion which is not covered in the calibration set, the predictive performance of inverse calibration approaches such as conventional PLS can deteriorate. This underscores the need for calibration methods that are capable of building multivariate calibration models which can be robustified against the unexpected variation in the concentrations and the correlations of the known interferents in the test set. Several methods incorporating ‘a priori’ information such as pure component spectra of the analyte of interest and/or the known interferents have been proposed to build more robust calibration models. In the present study, four such calibration techniques have been benchmarked on two data sets with respect to their predictive ability and robustness: Net Analyte Preprocessing (NAP), Improved Direct Calibration (IDC), Science Based Calibration (SBC) and Augmented Classical Least Squares (ACLS) Calibration. For both data sets, the alternative calibration techniques were found to give good prediction performance even when the interferent structure in the test set was different from the one in the calibration set. The best results were obtained by the ACLS model incorporating both the pure component spectra of the analyte of interest and the interferents, resulting in a reduction of the RMSEP by a factor 3 compared to conventional PLS for the situation when the test set had a different interferent structure than the one in the calibration set.     

Experimental design and multivariate calibration in the development, set-up and validation of a differential pulse polarographic and UV spectrophotometric method for the simultaneous plasmatic determination of the therapeutic metronidazole-pefloxacin combination

Partial least squares regression (PLS1 and PLS2) and GOLPE variable selection procedures were used for the treatment of differential pulse polarographic and UV spectrophotometric data obtained from the analysis of the therapeutic combination of metronidazole and pefloxacin. The analytical method used for the determination was set up using experimental design strategies (Doehlert's design, full factorial design, fractional face center cube design, etc.) and by involving the simultaneous optimization of several responses (desirability function). Method validation was also performed, determining accuracy, precision, linearity and range, detection and quantification limits and robustness. The quantitative prediction abilities in determining metronidazole and pefloxacin plasma levels of the PLS1 and PLS2 models were tested on spiked plasma samples and good results were obtained (metronidazole, 97.5%, RSD = 4.8%, n = 3; pefloxacin, 100.6%, RSD = 3.6%, n = 3). The use of multivariate calibration was particularly useful for spectrophotometric quantification because of the highly overlapping spectra of the binary mixture.     

Optimized sample-weighted partial least squares

In ordinary multivariate calibration methods, when the calibration set is determined to build the model describing the relationship between the dependent variables and the predictor variables, each sample in the calibration set makes the same contribution to the model, where the difference of representativeness between the samples is ignored. In this paper, by introducing the concept of weighted sampling into partial least squares (PLS), a new multivariate regression method, optimized sample-weighted PLS (OSWPLS) is proposed. OSWPLS differs from PLS in that it builds a new calibration set, where each sample in the original calibration set is weighted differently to account for its representativeness to improve the prediction ability of the algorithm. A recently suggested global optimization algorithm, particle swarm optimization (PSO) algorithm is used to search for the best sample weights to optimize the calibration of the original training set and the prediction of an independent validation set. The proposed method is applied to two real data sets and compared with the results of PLS, the most significant improvement is obtained for the meat data, where the root mean squared error of prediction (RMSEP) is reduced from 3.03 to 2.35. For the fuel data, OSWPLS can also perform slightly better or no worse than PLS for the prediction of the four analytes. The stability and efficiency of OSWPLS is also studied, the results demonstrate that the proposed method can obtain desirable results within moderate PSO cycles.     

Ensemble Multivariate Calibration Based on Mutual Information for Food Analysis Using Near-Infrared Spectroscopy

An ensemble multivariate calibration algorithm, termed as MISEPLS, is proposed. In MISEPLS, when constructing a member model, the variables that have mutual information (MI) with the response less than a threshold are eliminated; thus, the modeling can be performed in a subset of original variables and some problems arising from multi-collinearity can be avoided. Through experiments on three near-infrared (NIR) spectroscopic datasets from the food industry, MISEPLS proves to be superior to the single-model full-spectrum PLS and MIPLS (PLS combined with MI-induced variable selection). MISEPLS can improve the accuracy and robustness of a calibration model, without increasing its complexity.     

Multivariate versus univariate calibration for nonlinear chemiluminescence data: Application to chromium determination by luminol-hydrogen peroxide reaction

Multivariate calibration is tested as an alternative to model chromium(III) concentration versus chemiluminescence registers obtained from luminol-hydrogen peroxide reaction. The multivariate calibration approaches included have been: conventional linear methods (principal component regression (PCR) and partial least squares (PLS)), nonlinear methods (nonlinear variants and variants of locally weighted regression) and linear methods combined with variable selection performed in the original or in the transformed data (stepwise multiple linear regression procedure). Both the direct and inverse univariate approaches have been also tested.

The use of a double logarithmic transformation previous to the linear regression has been also evaluated. A new double logarithmic transformation previous to the linear regression is proposed in order to avoid the effect of the noise in the calibration model. Pre-processing, optimization and prediction ability of the multivariate calibration models has been studied at nine different experimental conditions including batch and FIA measurements. Box-plots, PCA and cluster analysis have been employed to test the prediction ability of the different models tested. Nonlinear PCR and nonlinear PLS provide the best results. Real samples have been analyzed and compared with the reference method. The results confirm the successful use of the proposed methodology.     

A novel algorithm for linear multivariate calibration based on the mixed model of samples

We present a novel algorithm for linear multivariate calibration that can generate good prediction results. This is accomplished by the idea of that testing samples are mixed by the calibration samples in proper proportion. The algorithm is based on the mixed model of samples and is therefore called MMS algorithm. With both theoretical support and analysis of two data sets, it is demonstrated that MMS algorithm produces lower prediction errors than partial least squares (PLS2) model, has similar prediction performance to PLS1. In the anti-interference test of background, MMS algorithm performs better than PLS2. At the condition of the lack of some component information, MMS algorithm shows better robustness than PLS2.     

Systematic prediction error correction: a novel strategy for maintaining the predictive abilities of multivariate calibration models

The development of reliable multivariate calibration models for spectroscopic instruments in on-line/in-line monitoring of chemical and bio-chemical processes is generally difficult, time-consuming and costly. Therefore, it is preferable if calibration models can be used for an extended period, without the need to replace them. However, in many process applications, changes in the instrumental response (e.g. owing to a change of spectrometer) or variations in the measurement conditions (e.g. a change in temperature) can cause a multivariate calibration model to become invalid. In this contribution, a new method, systematic prediction error correction (SPEC), has been developed to maintain the predictive abilities of multivariate calibration models when e.g. the spectrometer or measurement conditions are altered. The performance of the method has been tested on two NIR data sets (one with changes in instrumental responses, the other with variations in experimental conditions) and the outcomes compared with those of some popular methods, i.e. global PLS, univariate slope and bias correction (SBC) and piecewise direct standardization (PDS). The results show that SPEC achieves satisfactory analyte predictions with significantly lower RMSEP values than global PLS and SBC for both data sets, even when only a few standardization samples are used. Furthermore, SPEC is simple to implement and requires less information than PDS, which offers advantages for applications with limited data.     

Kinetic spectrophotometric determination of trace amounts of palladium by whole kinetic curve and a fixed time method using resazurine sulfide reaction

The univariate and multivariate calibration methods were applied for the determination of trace amounts of palladium based on the catalytic effect on the reaction between resazurine and sulfide. The decrease in absorbance of resazurine at 602 nm over a fixed time is proportional to the concentration of palladium over the range of 10.0-160.0 ng mL(-1). The calibration matrix for partial least squares (PLS) regression was designed with 14 samples. Orthogonal signal correction (OSC) is a preprocessing technique used for removing the information unrelated to the target variables based on constrained principal component analysis. OSC is a suitable preprocessing method for PLS calibration without loss of prediction ability using spectrophotometric method. The root mean square error of prediction (RMSEP) for palladium determination with fixed-time, PLS and OSC-PLS were 3.71, 2.84 and 0.68, respectively. This procedure allows the determination of palladium in synthetic and real samples with good reliability of the determination.     

Spectrophotometric determination of ternary mixtures of thiamin, riboflavin and pyridoxal in pharmaceutical and human plasma by least-squares support vector machines.

Ternary mixtures of thiamin, riboflavin and pyridoxal have been simultaneously determined in synthetic and real samples by applications of spectrophotometric and least-squares support vector machines. The calibration graphs were linear in the ranges of 1.0 - 20.0, 1.0 - 10.0 and 1.0 - 20.0 microg ml(-1) with detection limits of 0.6, 0.5 and 0.7 microg ml(-1) for thiamin, riboflavin and pyridoxal, respectively. The experimental calibration matrix was designed with 21 mixtures of these chemicals. The concentrations were varied between calibration graph concentrations of vitamins. The simultaneous determination of these vitamin mixtures by using spectrophotometric methods is a difficult problem, due to spectral interferences. The partial least squares (PLS) modeling and least-squares support vector machines were used for the multivariate calibration of the spectrophotometric data. An excellent model was built using LS-SVM, with low prediction errors and superior performance in relation to PLS. The root mean square errors of prediction (RMSEP) for thiamin, riboflavin and pyridoxal with PLS and LS-SVM were 0.6926, 0.3755, 0.4322 and 0.0421, 0.0318, 0.0457, respectively. The proposed method was satisfactorily applied to the rapid simultaneous determination of thiamin, riboflavin and pyridoxal in commercial pharmaceutical preparations and human plasma samples.     

Simultaneous Differential Pulse Adsorptive Stripping Determination of Imipramine and Its Metabolite Desipramine by the PLS‐1 Multivariate Method

A method, using stripping differential pulse voltammetry, for the simultaneous determination of Imipramine and its metabolite Desipramine is reported. Both compounds produce, at glassy carbon electrode, an electrochemical signal due to an adsorptive‐oxidative process. The voltammograms show a very high overlap degree between IM and DE peaks. The multivariate calibration method PLS‐1 was employed for the simultaneous determination of both compounds. An experimental design together with the response surface methodology has been used to find the optimum experimental conditions. The developed procedure has been utilized in the analysis of fortified human serum samples with good recovery values for each analyte.     

Construction of stable multivariate calibration models using unsupervised segmented principal component regression

In multivariate spectral calibration by principal component regression (PCR), the principal components (PCs) are calculated from the response data measured at all employed instrument channels; however some channels are redundant and their responses do not possess useful information. Thus, the extracted PCs possess mixed information from both useful and redundant channels. In this work, we propose a segmentation approach based on unsupervised pattern recognition to identify the most informative spectral region and then to construct a stable multivariate calibration model by PCR. In this method, the instrument channels are clustered into different segments via Kohonen self‐organization map. The spectral data of each segment are then subjected to PCA and the derived PCs are used as input variables for an inverse least square (ILS) regression model employing stepwise selection of the informative PCs. The proposed method was evaluated by the analysis of four simulated and six experimental data sets. It was found that our proposed method can model the above data sets with prediction errors lower than conventional partial least squares (PLS) and PCR methods. In addition, the prediction ability of our method was better than the previously reported models for these data sets. Copyright © 2011 John Wiley & Sons, Ltd.     

Application of an optimization procedure in adsorptive stripping voltammetry for the determination of trace contaminant metals in aqueous medium

A procedure for the determination of the contaminant metal In(III) by differential pulse adsorptive stripping voltammetry (DPAdSV) using ammonium pyrrolidine dithiocarbamate (APDC) as a complexing agent, has been optimized. The selection of the experimental conditions was made using experimental design methodology by means of a robust regression method which allows the elimination of anomalous points. The detection limit obtained was 1.3×10⁻⁹ mol dm⁻³. Possible interferences from concomitant metal ions were evaluated. Among all the metals analyzed, only Cd(II) was found to create an interference. This fact made impossible to carry out the determination of In(III) in the presence of Cd(II) using a univariate calibration. This problem was solved using multivariate regression techniques such as partial least squares (PLS). The procedure was successfully applied to the determination of indium in different aqueous samples.     

Net analyte signal-based simultaneous determination of antazoline and naphazoline using wavelength region selection by experimental design-neural networks

Net analyte signal (NAS)-based multivariate calibration methods were employed for simultaneous determination of anthazoline and naphazoline. The NAS vectors calculated from the absorbance data of the drugs mixture were used as input for classical least squares (CLS), principal component and partial least squares regression PCR and PLS methods. A wavelength selection strategy was used to find the best wavelength region for each drug separately. As a new procedure, we proposed an experimental design-neural network strategy for wavelength region optimization. By use of a full factorial design method, some different wavelength regions were selected by taking into account different spectral parameters including the starting wavelength, the ending wavelength and the wavelength interval. The performance of all the multivariate calibration methods, in all selected wavelength regions for both drugs, was evaluated by calculating a fitness function based on the root mean square error of calibration and validation. A three-layered feed-forward artificial neural network (ANN) model with back-propagation learning algorithm was employed to model the nonlinear relationship between the spectral parameters and fitness of each regression method. From the resulted ANN models, the spectral regions in which lowest fitness could be obtained were chosen. Comparison of the results revealed that the net NAS-PLS resulted in lower prediction error than the other models. The proposed NAS-based calibration method was successfully applied to the simultaneous analyses of anthazoline and naphazoline in a commercial eye drop sample.     

Simultaneous wavelength selection and outlier detection in multivariate regression of near-infrared spectra.

Near-infrared (NIR) spectrometry will present a more promising tool for quantitative measurement if the robustness and predictive ability of the partial least square (PLS) model are improved. In order to achieve the purpose, we present a new algorithm for simultaneous wavelength selection and outlier detection; at the same time, the problems of background and noise in multivariate calibration are also solved. The strategy is a combination of continuous wavelet transform (CWT) and modified iterative predictors and objects weighting PLS (mIPOW-PLS). CWT is performed as a pretreatment tool for eliminating background and noise synchronously; then, mIPOW-PLS is proposed to remove both the useless wavelengths and the multiple outliers in CWT domain. After pretreatment with CWT-mIPOW-PLS, a PLS model is built finally for prediction. The results indicate that the combination of CWT and mIPOW-PLS produces robust and parsimonious regression models with very few wavelengths.     

Improvement of multivariate calibration techniques applied to 1-to-N component mixtures through an optimized experimental design

This work describes a novel experimental design aimed at building a calibration set constituted by samples containing a different number of components. The algorithm performs a reiteration process to maintain the number of samples at the lower value as possible and to ensure an homogeneous presence of all the concentration levels. The mixture design was applied to a drug system composed by one-to-four components in different combination. The resolution of the system was performed by three multivariate UV spectrophotometric methods utilizing principal component regression (PCR) and partial last squares (PLS1 and PLS2) algorithms. The calibration set was composed by 61 references on four concentration levels, including 15 samples for each quaternary, ternary and binary composition and 16 one-component samples. The calibration models were optimized through a careful selection of number of factors and wavelength zones, in such a way as to remove interferences from instrumental noise and excipients present in the pharmaceutical formulations. The prediction power of the regression models were verified and compared by analysis of an external prediction set. The models were finally used to assay pharmaceutical specialities containing the studied drugs in one-to-four formulations.     

Prediction of wood property in Chinese Fir based on visible/near-infrared spectroscopy and least square-support vector machine

A method for the quantification of density of Chinese Fir samples based on visible/near-infrared (vis–NIR) spectrometry and least squares-support vector machine (LS-SVM) was proposed. Sample set partitioning based on joint x–y distances (SPXY) algorithm was used for dividing calibration and prediction samples, it is of value for prediction of property involving complex matrices. A stepwise procedure is employed to select samples according to their differences in both x (instrumental responses) and y (predicted parameter) spaces. For comparison, the models were also constructed by Kennard–Stone method, as well as by using the duplex and random sampling methods for subset partitioning. The results revealed that the SPXY algorithm may be an advantageous alternative to the other three strategies. To validate the reliability of LS-SVM, comparisons were made among other modeling methods such as support vector machine (SVM) and partial least squares (PLS) regression. Satisfactory models were built using LS-SVM, with lower prediction errors and superior performance in relation to SVM and PLS. These results showed possibility of building robust models to quantify the density of Chinese Fir using near-infrared spectroscopy and LS-SVM combined SPXY algorithm as a nonlinear multivariate calibration procedure.