Effects of nonlinearities and uncorrelated or correlated errors in realistic simulated data on the prediction abilities of augmented classical least squares and partial least squares

Comparisons of prediction models from the new augmented classical least squares (ACLS) and partial least squares (PLS) multivariate spectral analysis methods were conducted using simulated data containing deviations from the idealized model. The simulated data were based on pure spectral components derived from real near-infrared spectra of multicomponent dilute aqueous solutions. Simulated uncorrelated concentration errors, uncorrelated and correlated spectral noise, and nonlinear spectral responses were included to evaluate the methods on situations representative of experimental data. The statistical significance of differences in prediction ability was evaluated using the Wilcoxon signed rank test. The prediction differences were found to be dependent on the type of noise added, the numbers of calibration samples, and the component being predicted. For analyses applied to simulated spectra with noise-free nonlinear response, PLS was shown to be statistically superior to ACLS for most of the cases. With added uncorrelated spectral noise, both methods performed comparably. Using 50 calibration samples with simulated correlated spectral noise, PLS showed an advantage in 3 out of 9 cases, but the advantage dropped to 1 out of 9 cases with 25 calibration samples. For cases with different noise distributions between calibration and validation, ACLS predictions were statistically better than PLS for two of the four components. Also, when experimentally derived correlated spectral error was added, ACLS gave better predictions that were statistically significant in 15 out of 24 cases simulated. On data sets with nonuniform noise, neither method was statistically better, although ACLS usually had smaller standard errors of prediction (SEPs). The varying results emphasize the need to use realistic simulations when making comparisons between various multivariate calibration methods. Even when the differences between the standard error of predictions were statistically significant, in most cases the differences in SEP were small. This study demonstrated that unlike CLS, ACLS is competitive with PLS in modeling nonlinearities in spectra without knowledge of all the component concentrations. This competitiveness is important when maintaining and transferring models for system drift, spectrometer differences, and unmodeled components, since ACLS models can be rapidly updated during prediction when used in conjunction with the prediction augmented classical least squares (PACLS) method, while PLS requires full recalibration.     

近红外光谱法测定茶多酚中总儿茶素含量

以高效液相色谱(HPLC)分析结果为参考值,建立了快速测量茶多酚中总儿茶素含量的近红外光谱定标模型.将48份茶多酚样品组成定标样品集,在1000～2500nm(4000～10000cm-1)的近红外漫反射光谱为定标波长范围内,光谱经一阶导数(Firstderivative)、二阶导数(Secondderivative)、标准归一化(Stan-dardnormalvariate,SNV)和多元散射校正(multiplicativesignalcorrection,MSC)处理后结合偏最小二乘回归(PLS)定标.经内部交叉验证表明,光谱经SNV处理后建模结果最佳.模型的相关系数Corr.Coeff=0.997,校正均方根RMSEC=1.71%.比较了经典最小二乘法(CLS)、偏最小二乘法(PLS)和主成分回归(PCR)等方法建模结果,以偏最小二乘回归建模效果最好.     

Calibration of multiplexed fiber-optic spectroscopy

Large-scale commercial bioprocesses that manufacture biopharmaceutical products such as monoclonal antibodies generally involve multiple bioreactors operated in parallel. Spectra recorded during in situ monitoring of multiple bioreactors by multiplexed fiber-optic spectroscopies contain not only spectral information of the chemical constituents but also contributions resulting from differences in the optical properties of the probes. Spectra with variations induced by probe differences cannot be efficiently modeled by the commonly used multivariate linear calibration models or effectively removed by popular empirical preprocessing methods. In this study, for the first time, a calibration model is proposed for the analysis of complex spectral data sets arising from multiplexed probes. In the proposed calibration model, the spectral variations introduced by probe differences are explicitly modeled by introducing a multiplicative parameter for each optical probe, and then their detrimental effects are effectively mitigated through a "dual calibration" strategy. The performance of the proposed multiplex calibration model has been tested on two multiplexed spectral data sets (i.e., MIR data of ternary mixtures and NIR data of bioprocesses). Experimental results suggest that the proposed calibration model can effectively mitigate the detrimental effects of probe differences and hence provide much more accurate predictions than commonly used multivariate linear calibration models (such as PLS) with and without empirical data preprocessing methods such as orthogonal signal correction, standard normal variate, or multiplicative signal correction.     

Simultaneous polarographic chemometric determination of lead,copper, vanadium,cadmium and nickel

Chemometric approaches, such as classical least squares (CLS), principal component regression (PCR), partial least squares (PLS) and iterative target transformation factor analysis (ITTFA), were applied to the simultaneous determination of mixtures of lead, copper, vanadium, cadmium and nickel by differential pulse polarography (DPP). The conventional and first-derivative polarograms of the mixtures were used to perform the optimization of the calibration procedure by chemometric models. The proposed method was applied satisfactorily to the determination of a set of synthetic mixtures of metal in Britton–Robinson buffer (pH 2.87) and potassium thiocyanate and acceptable results were obtained. The results obtained by the application of the different chemometric approaches are discussed and compared. It was found that factor analysis methods generally give better results than CLS and no significant advantages were found with the application of derivative technique, except for ITTFA in this polarographic work.     

A simple method for linearizing nonlinear spectra for calibration

The development and acceptance of spectral calibration methods has been an important success story for the field of chemometrics. This paper contains a new study of a very old calibration method (K-matrix calibration, parallel calibration, or generalized inverse prediction) and partial least squares (PLS), the mainstay of modern chemometrics. We show that with some modest amount of modification, the old method of calibration is comparable, in terms of prediction, to PLS for spectroscopy involving nonlinear spectral responses.     

Importance of prediction outlier diagnostics in determining a successful inter-vendor multivariate calibration model transfer

This paper reports on the transfer of calibration models between Fourier transform near-infrared (FT-NIR) instruments from four different manufacturers. The piecewise direct standardization (PDS) method is compared with the new hybrid calibration method known as prediction augmented classical least squares/partial least squares (PACLS/PLS). The success of a calibration transfer experiment is judged by prediction error and by the number of samples that are flagged as outliers that would not have been flagged as such if a complete recalibration were performed. Prediction results must be acceptable and the outlier diagnostics capabilities must be preserved for the transfer to be deemed successful. Previous studies have measured the success of a calibration transfer method by comparing only the prediction performance (e.g., the root mean square error of prediction, RMSEP). However, our study emphasizes the need to consider outlier detection performance as well. As our study illustrates, the RMSEP values for a calibration transfer can be within acceptable range; however, statistical analysis of the spectral residuals can show that differences in outlier performance can vary significantly between competing transfer methods. There was no statistically significant difference in the prediction error between the PDS and PACLS/PLS methods when the same subset sample selection method was used for both methods. However, the PACLS/PLS method was better at preserving the outlier detection capabilities and therefore was judged to have performed better than the PDS algorithm when transferring calibrations with the use of a subset of samples to define the transfer function. The method of sample subset selection was found to make a significant difference in the calibration transfer results using the PDS algorithm, while the transfer results were less sensitive to subset selection when the PACLS/PLS method was used.     

Application of wavelet transform to extract the relevant component from spectral data for multivariate calibration

An approach aiming at extracting the relevant component for multivariate calibration is introduced, and its performance is compared with the "uninformative variable elimination" approach and with the standard PLS method for the modeling of near-infrared data. The extraction of the relevant component is carried out in the wavelet domain. The PLS results on these relevant features are better, and therefore, it seems that this approach can successfully be used to remove noise and irrelevant information from spectra for multivariate calibration.     

Quantitative analysis of low-field NMR signals in the time domain

Two novel methods are described for direct quantitative analysis of NMR free induction decay (FID) signals. The methods use adaptations of the generalized rank annihilation method (GRAM) and the direct exponential curve resolution algorithm (DECRA). With FID-GRAM, the Hankel matrix of the sample signal is compared with that of a reference mixture to obtain quantitative data about the components. With FID-DECRA, a single-sample FID matrix is split into two matrices, allowing quantitative recovery of decay constants and the individual signals in the FID. Inaccurate results were obtained with FID-GRAM when there were differences between the frequency or transverse relaxation time of signals for the reference and test samples. This problem does not arise with FID-DECRA, because comparison with a reference signal is unnecessary. Application of FID-DECRA to 19F NMR data, which contained overlapping signals from three components, gave concentrations comparable to those derived from partial least squares (PLS) analysis of the Fourier transformed spectra. However, the main advantage of FID-DECRA was that accurate (<5% error) and precise (2.3% RSD) results were obtained using only one calibration sample, whereas with PLS, a training set of 10 standard mixtures was used to give comparable accuracy and precision.     

Blank augmentation protocol for improving the robustness of multivariate calibrations

An updating procedure is described for improving the robustness of multivariate calibration models based on near-infrared spectroscopy. Employing a single blank sample containing no analyte, repeated spectra are acquired during the instrumental warm-up period. These spectra are used to capture the instrumental profile on the analysis day in a way that can be used to update a previously computed calibration model. By augmenting the original spectra of the calibration samples with a group of spectra collected from the blank sample, an updated model can be computed that incorporates any instrumental drift that has occurred. This protocol is evaluated in the context of an analysis of physiological levels of glucose in a simulated biological matrix designed to mimic blood plasma. Employing data of calibration and prediction samples acquired over approximately six months, procedures are studied for implementing the algorithm in conjunction with calibration models based on partial least squares (PLS) regression. Over the range of 1-20 mM glucose, the final algorithm achieves a standard error of prediction (SEP) of 0.79 mM when the augmented PLS model is applied to data collected 176 days after the collection of the calibration spectra. Without updating, the original PLS model produces a seriously degraded SEP of 13.4 mM.     

Multivariate determination of glucose in whole blood by attenuated total reflection infrared spectroscopy

A spectral analysis of whole EDTA blood was undertaken by using attenuated total reflection and Fourier-transform infrared spectroscopy. The concentration of blood glucose was measured by an enzymatic method using glucose dehydrogenase and ranged between 40 and 290 mg/dL with an average concentration of 90.4 mg/dL. Multivariate calibration with the partial least-squares (PLS) algorithm was performed on spectral data between 1500 and 750 cm-1 showing a varying background from different unidentified interfering compounds. Cross validation was carried out for optimizing the PLS model. PRESS was 19.8 mg/dL, which was calculated on the basis of 127 standards, whereas the estimated standard deviation for the calibration fit was computed to be 11.9 mg/dL. Infrared spectroscopy can be used for monitoring glucose levels within the normal physiological range in a complex matrix like whole blood as an alternative to electrochemical sensors.     

Cyclic subspace regression with analysis of the hat matrix

Cyclic subspace regression (CSR) is a new approach to the complex multivariate calibration problem. The simple algorithm produces solutions for principal component regression (PCR), partial least squares (PLS), least squares (LS), and other related intermediate regressions. This paper describes further analysis of CSR and shows that by using hat matrices, CSR regression vectors are formed from a summation of weighted eigenvectors where weights are determined from the hat matrix, singular values, and sample space eigenvectors. Examination of CSR weights for PCR and PLS further documents differences and similarities and provides information to assist in determining prediction rank for PCR and PLS. By redefining CSR in terms of weighted eigenvectors, it can be shown when PLS and PCR produce essentially the same results where minor differences stem from overfitting by PLS. Additionally, weights derived from the hat matrix show when PCR and PLS generate different results and why. Equations are shown for the sample space that reveal PLS to be a method based on oblique projections while PCR uses orthogonal projections. The optimal intermediate CSR model can be identified as well. A near infrared data set is studied and illustrates principles involved.     

Variable-weighted PLS

In multivariate calibration methods like partial least squares (PLS), especially when the spectra data consists of measurements at hundreds and even thousands of analytical channels, it is widely accepted that before a multivariate regression model is built, a well-performed variable selection can be helpful to improve the predictive ability of the model. In the present paper, the idea of variable selection is extended. Unlike in traditional variable selection methods, where the deleted variables and the variables included in the regression model are essentially weighted with discrete values 0 and 1, respectively, the strategy adopted in this paper is to weight the variables with continuous non-negative values. A recently proposed global optimization method, particle swarm optimization (PSO) algorithm is used to search for the weights of variables optimizing the training of a calibration set and the prediction of an independent validation set. Since variable selection is just a special case of variable weighting, the latter is expected to be more rational and flexible. Variable weighting would reduce the negative influence of wavelengths with undesirable qualities while retaining the useful information carried by them. Variable weighting would also prevent the possible spoiling of the multi-channel advantage of the model by variable selection, which would happen when the number of selected wavelengths is small. Two real data sets are investigated and the results of variable-weighted PLS and those of PLS are compared to demonstrate the advantages of the proposed method.     

Multivariate chemometric approach to fiber-optic dissolution testing

The use of fiber optics in in vitro dissolution testing opens up new possibilities for more powerful data evaluation since an entire UV-Vis spectrum can be collected at each measuring point. This paper illustrates a multivariate chemometric approach to the solution of problems of interfering absorbance of excipients in in vitro dissolution testing. Two different chemometric approaches are tested: multivariate calibration using partial least squares (PLS) regression and curve resolution using multivariate curve resolution alternating least squares (MCR-ALS), generalized rank annihilation (GRAM), and parallel factor analysis (PARAFAC). Multivariate calibration (PLS) can, following the construction of a calibration model from a calibration sample set, give selective and accurate determinations of the active ingredient in dissolution testing despite the presence of interfering absorbance from excipients. Curve resolution (MCR-ALS, GRAM, or PARAFAC) can be applied to dissolution testing data in order to determine the dissolution rate profiles and spectra for the interfering excipients as well as for the active ingredient without any precalibration. The concept of the application of these chemometric methods to fiber-optic dissolution testing data is exemplified by analysis of glibenclamide tablets enclosed in hard gelatin capsules. The results show that, despite highly overlapping spectra and unresolved raw data, it is possible with PLS to obtain an accurate dissolution rate profile of glibenclamide. Applying curve resolution makes it possible to obtain accurate estimates of both dissolution rate profiles and spectra of both the gelatin capsule and the glibenclamide. The application of multivariate chemometric methods to fiber-optic dissolution testing brings a fresh scope for a deeper understanding of in vitro dissolution testing, solving the problem of interfering absorbance of excipients and making it possible to obtain dissolution rate profiles and spectra of these. Obtaining dissolution rate profiles of multiple active pharmaceutical ingredients in tablets consisting of several active compounds is another possibility.     

Second-order calibration of excitation-emission matrix fluorescence spectra for the determination of N-phenylanthranilic acid derivatives

A spectrofluorimetric method has been developed for the quantitative determination of mefenamic, flufenamic, and meclofenamic acids in urine samples. The method is based on second-order data multivariate calibration (unfolded partial least squares (unfolded-PLS), multi-way PLS (N-PLS), parallel factor analysis (PARAFAC), self-weighted alternating trilinear decomposition (SWATLD), and bilinear least squares (BLLS)). The analytes were extracted from the urine samples in chloroform prior to the determination. The chloroform extraction was optimized for each analyte, studying the agitation time and the extraction pH, and the optimum values were 10 minutes and pH 3.5, respectively. The concentration ranges in chloroform solution of each of the analytes, used to construct the calibration matrix, were selected in the ranges from 0.15 to 0.8 microg mL-1 for flufenamic and meclofenamic acids and from 0.25 to 3.0 microg mL-1 for mefenamic acid. The combination of chloroform extraction and second-order calibration methods, using the excitation-emission matrices (EEMs) of the three analytes as analytical signals, allowed their simultaneous determination in human urine samples, in the range of approximately 80 mg L-1 to 250 mg L-1, with satisfactory results for all the assayed methods. Improved results over unfolded-PLS and N-PLS were found with PARAFAC, SWATLD, and BLLS, methods that exploit the second-order advantage.     

Pure component selectivity analysis of multivariate calibration models from near-infrared spectra

A novel procedure is proposed as a method to characterize the chemical basis of selectivity for multivariate calibration models. This procedure involves submitting pure component spectra of both the target analyte and suspected interferences to the calibration model in question. The resulting model output is analyzed and interpreted in terms of the relative contribution of each component to the predicted analyte concentration. The utility of this method is illustrated by an analysis of calibration models for glucose, sucrose, and maltose. Near-infrared spectra are collected over the 5000-4000-cm(-)(1) spectral range for a set of ternary mixtures of these sugars. Partial least-squares (PLS) calibration models are generated for each component, and these models provide selective responses for the targeted analytes with standard errors of prediction ranging from 0.2 to 0.7 mM over the concentration range of 0.5-50 mM. The concept of the proposed pure component selectivity analysis is illustrated with these models. Results indicate that the net analyte signal is solely responsible for the selectivity of each individual model. Despite strong spectral overlap for these simple carbohydrates, calibration models based on the PLS algorithm provide sufficient selectivity to distinguish these commonly used sugars. The proposed procedure demonstrates conclusively that no component of the sucrose or maltose spectrum contributes to the selective measurement of glucose. Analogous conclusions are possible for the sucrose and maltose calibration models.     

Application of partial least-squares regression to near-infrared reflectance spectroscopic determination of shive content in flax

Shive, the nonfiberous core portion of the stem, in flax fiber after retting is related to fiber quality. The objective of this study is to develop a standard calibration model for determining shive content in retted flax by using near-infrared reflectance spectroscopy. Calibration samples were prepared by manually mixing pure, ground shive and pure, ground fiber from flax retted by three different methods (water, dew, and enzyme retting) to provide a wide range of shive content from 0 to 100%. Partial least-squares (PLS) regression was used to generate a calibration model, and spectral data were processed using various pretreatments such as a multiplicative scatter correction (MSC), normalization, derivatives, and Martens' Uncertainty option to improve the calibration model. The calibration model developed with a single sample set resulted in a standard error of 1.8% with one factor. The best algorithm was produced from first-derivative processing of the spectral data. MSC was not effective processing for this model. However, a big bias was observed when independent sample sets were applied to this calibration model to predict shive content in flax fiber. The calibration model developed using a combination sample set showed a slightly higher standard error and number of factors compared to the model for a single sample set, but this model was sufficiently accurate to apply to each sample set. The best algorithm for the combination sample set was generated from second derivatives followed by MSC processing of spectral data and from Martens' Uncertainty option; it resulted in a standard error of 2.3% with 2 factors. The value of the digital second derivative centered at 1674 nm for these spectral data was highly correlated to shive content of flax and could form the basis for a simple, low-cost sensor for the shive or fiber content in retted flax.     

Multi-scale extension of PLS algorithm for advanced on-line process monitoring

Typical process measurements are usually correlated with each other and compounded with various phenomena occurring at different time and frequency domains. To take into account this multivariate and multi-scale nature of process dynamics, a multi-scale PLS (MSPLS) algorithm combining PLS and wavelet analysis is proposed. The MSPLS first decomposes the process measurements into separated multi-scale components using on-line wavelet transform, and then the resultant multi-scale data blocks are modeled in the framework of multi-block PLS algorithm which can describe the global relationships across the entire scale blocks as well as the localized features within each sub-block at detailed resolutions. To demonstrate the feasibility of the MSPLS method, its process monitoring abilities were tested not only for the simulated data sets containing several fault scenarios but also for a real industrial data set, and compared with the monitoring abilities of the standard PLS method on the quantitative basis. The results clearly showed that the MSPLS was superior to the standard PLS for all cases especially in that it could provide additional scale-level information about the fault characteristics as well as more sensitive fault detection ability.     

预浸料生产中智能控制系统的应用

用近红外光谱技术对无碱布/酚醛预浸料的树脂含量、可溶树脂含量和挥发分含量进行在线检测,通过偏最小二乘方法分别建立标准模型,选择光谱预处理方法和PLS的因子数.用近红外方法和标准方法对未知样品进行分析,通过t检验结果显示两种方法没有显著性的差别,利用该方法可以同时预测三项指标,1分钟之内就可以分析一个样品,没有破坏性.如果质量指标不合格,通过自动控制系统发出指令,及时调节工艺参数.研究表明近红外光谱方法能够十分有效和准确对分析预浸料质量.     

Time-alignment of bidimensional chromatograms in the presence of uncalibrated interferences using parallel factor analysis: Application to multi-component determinations using liquid-chromatography with spectrofluorimetric detection

A new methodology for the alignment of matrix chromatographic data is proposed, based on the decomposition of a three-way array composed of a test and a reference data matrix using a suitably initialized and constrained parallel factor (PARAFAC) model. It allows one to perform matrix alignment when the test data matrix contains unexpected chemical interferences, in contrast to most of the available algorithms. A series of simulated analytical systems is studied, as well as an experimental one, all having calibrated analytes and also potential interferences in the test samples, i.e., requiring the second-order advantage for successful analyte quantitation. The results show that the newly proposed method is able to properly align the different data matrix, restoring the trilinearity which is required to process the calibration and test data with second-order multivariate calibration algorithms such as PARAFAC. Recent models including unfolded partial least-squares regression (U-PLS) and N-dimensional PLS (N-PLS), combined with residual bilinearization (RBL), are also applied to both simulated and experimental data. The latter one corresponds to the determination of the polycyclic aromatic hydrocarbons benzo[b]fluoranthene and benzo[k]fluoranthene in the presence of benzo[j]fluoranthene as interference. The analytical figures of merit provided by the second-order calibration models are compared and discussed.     

New robust bilinear least squares method for the analysis of spectral-pH matrix data

A new second-order multivariate method has been developed for the analysis of spectral-pH matrix data, based on a bilinear least-squares (BLLS) model achieving the second-order advantage and handling multiple calibration standards. A simulated Monte Carlo study of synthetic absorbance-pH data allowed comparison of the newly proposed BLLS methodology with constrained parallel factor analysis (PARAFAC) and with the combination multivariate curve resolution-alternating least-squares (MCR-ALS) technique under different conditions of sample-to-sample pH mismatch and analyte-background ratio. The results indicate an improved prediction ability for the new method. Experimental data generated by measuring absorption spectra of several calibration standards of ascorbic acid and samples of orange juice were subjected to second-order calibration analysis with PARAFAC, MCR-ALS, and the new BLLS method. The results indicate that the latter method provides the best analytical results in regard to analyte recovery in samples of complex composition requiring strict adherence to the second-order advantage. Linear dependencies appear when multivariate data are produced by using the pH or a reaction time as one of the data dimensions, posing a challenge to classical multivariate calibration models. The presently discussed algorithm is useful for these latter systems.