Spectral tolerance determination for multivariate optical element design

Recent reports from our laboratory have described a method for all-optical multivariate chemometric prediction from optical spectroscopy. The concept behind this optical approach is that a spectral pattern (a regression vector) can be encoded into the spectrum of an optical filter. The key element of these measurement schemes is the multivariate optical element (MOE), a multiwavelength interference-based spectral discriminator that is tied to the regression vector of a particular measurement. The fabrication of these MOEs is a complex operation that requires precise techniques. However, to date, no quantitative means of determining the allowable design/ manufacturing errors for MOEs has existed. The purpose of the present report is to show how the spectroscopy of a sample is used to define the accuracy with which MOEs must be designed and manufactured. We conclude this report with a general treatment of spectral tolerance and a worked example. The worked example is based on actual experimental measurements. We show how the spectral bandpass is defined operationally in a real problem, and how the statistics of the theoretical regression vector influence both the bandpass and the minimum tolerances. In the experimental example, we demonstrate that tolerances range continuously between 1 (totally tolerant) to approximately 10^–3 (0.1% T) in this problem. Received: 21 August 2000 / Revised: 30 October 2000 / Accepted: 4 November 2000     

Spectral resolution in multivariate optical computing

An examination of spectral resolution effects on multivariate optical computing (MOC) and the design of multivariate optical elements (MOEs) is presented. A solution of napthalene and pyrene in CCl(4) is used as a test mixture, with spectra recorded in the nominal 2-2.5 microm spectral region at resolutions varying from 1 to 128 cm(-1). Spectra were treated in absorption mode and in transmission mode at sample pathlengths of 1, 0.5, and 0.2 cm. Principal components regression is used to provide comparison to MOE models. Conventional model prediction errors using all methods are presented as well as results of applying low-resolution models to high-resolution validation sets. This latter calculation is aimed at understanding the limits of calibration transfer when a model is based on spectra acquired with marginal spectral resolution. A theory is developed describing calibration transfer in the case of linear spectroscopy, which is shown to be consistent with the results observed in absorption mode and to represent the case of the short-pathlength limit in transmission mode. A definition of the necessary spectral resolution as a function of apodization function is given for linear spectroscopy, and a brief discussion of how non-linearity affects the results is provided.     

Quantitative analysis of tea using ytterbium‐based internal standard near‐infrared spectroscopy coupled with boosting least‐squares support vector regression

The present study demonstrated the possibility of utilizing the ytterbium (Yb)‐based internal standard near‐infrared (NIR) spectroscopic measurement technique coupled with multivariate calibration for quantitative analysis of tea, including total free amino acids and total polyphenols in tea. Yb is a rare earth element aimed to compensate for the spectral variation induced by the alteration of sample quantity during the spectral measurement of the powdered samples. Boosting was invoked to be combined with least‐squares support vector regression (LS‐SVR), forming boosting least‐squares support vector regression (BLS‐SVR) for the multivariate calibration task. The results showed that the tea quality could be accurately and rapidly determined via the Yb‐based internal standard NIR spectroscopy combined with BLS‐SVR method. Moreover, the introduction of boosting drastically enhanced the performance of individual LS‐SVR, and BLS‐SVR compared favorably with partial least‐squares regression. Copyright © 2013 John Wiley & Sons, Ltd.     

Least-squares support vector machines and near infrared spectroscopy for quantification of common adulterants in powdered milk

This paper proposes the use of the least-squares support vector machine (LS-SVM) as an alternative multivariate calibration method for the simultaneous quantification of some common adulterants (starch, whey or sucrose) found in powdered milk samples, using near-infrared spectroscopy with direct measurements by diffuse reflectance. Due to the spectral differences of the three adulterants a nonlinear behavior is present when all groups of adulterants are in the same data set, making the use of linear methods such as partial least squares regression (PLSR) difficult. Excellent models were built using LS-SVM, with low prediction errors and superior performance in relation to PLSR. These results show it possible to built robust models to quantify some common adulterants in powdered milk using near-infrared spectroscopy and LS-SVM as a nonlinear multivariate calibration procedure.     

Orthogonal signal correction, wavelet analysis, and multivariate calibration of complicated process fluorescence data

In this paper, multivariate calibration of complicated process fluorescence data is presented. Two data sets related to the production of white sugar are investigated. The first data set comprises 106 observations and 571 spectral variables, and the second data set 268 observations and 3997 spectral variables. In both applications, a single response, ash content, is modelled and predicted as a function of the spectral variables. Both data sets contain certain features making multivariate calibration efforts non-trivial. The objective is to show how principal component analysis (PCA) and partial least squares (PLS) regression can be used to overview the data sets and to establish predictively sound regression models. It is shown how a recently developed technique for signal filtering, orthogonal signal correction (OSC), can be applied in multivariate calibration to enhance predictive power. In addition, signal compression is tested on the larger data set using wavelet analysis. It is demonstrated that a compression down to 4% of the original matrix size — in the variable direction — is possible without loss of predictive power. It is concluded that the combination of OSC for pre-processing and wavelet analysis for compression of spectral data is promising for future use.     

Effects of sample matrix on detection limits in analytical inductively coupled plasma-Fourier transform spectrometry

The feasibility of making analytical atomic spectrometry measurements by inductively coupled plasma-Fourier transform spectrometry (ICP-FTS) is demonstrated. Analytical working curves and detection limits are presented for Al, Ni, Fe and Ca. The effects of sample matrix composition on detection limits for analytical ICP-FTS are investigated. It is shown that a multiplex disadvantage may occur in the case of a spectral bandpass encompassing stroog emission lines of a matrix element. A “worse case” example of this problem is presented. Possible approaches to overcoming the multiplex disadvantage in analytical ICP-FTS and some ideal criteria for ICP-FTS instrumentation are presented.     

一类用于多元光度分析的小波基主成分回归法

通过将变尺度小波分解滤噪与特征信息提取相结合,提出一类新的多元光度分析算法－小波基主成分回归（ＰＣＲＷ）方法。该法可有效地减小主成分向量残留噪声所引 误差显著提高多元校正准确性。将其用于分析氯霉素、醋酸对塞米松、尼泊金乙脂体系、得到满意的回收率,与ＰＣＲ法相比,分析结果的总平均相对误差从３．３８％降低到０．８３％。     

Classification of commercial apple beverages using a minimum set of mid-IR wavenumbers selected by Procrustes rotation

When infrared spectral data are used in classification and/or multivariate regression methods there can be problems related to both chemical understanding and computation speed due to the large number of wavenumbers in each spectrum. Here, it is shown that the Procrustes rotation technique can be used to select a minimum set of spectral variables (wavenumbers) to perform classification and regression. Procrustes rotation was coupled to several multivariate methods as PLS, SIMCA and potential curves (a maximum likelihood classification method). The practical problem of implementing a screening methodology for classifying apple juice-based beverages according to their contents of "pure" apple juice was addressed using attenuated total reflectance, mid-IR spectroscopy. It is found that two of the original wavenumbers are almost as good predictors as all the 176 initial ones.     

Supervised principal components: a new method for multivariate spectral analysis

The supervised principal components (SPC) method was proposed by Bair and Tibshirani for statistics regression problems where the number of variables greatly exceeds the number of samples. This case is extremely common in multivariate spectral analysis. The objective of this research is to apply SPC to near‐infrared and Raman spectral calibration. SPC is similar to traditional principal components analysis except that it selects the most significant part of wavelength from the high‐dimensional spectral data, which can reduce the risk of overfitting and the effect of collinearity in modeling according to a semi‐supervised strategy. In this study, four conventional regression methods, including principal component regression, partial least squares regression, ridge regression, and support vector regression, were compared with SPC. Three evaluation criteria, coefficient of determination (R²), external correlation coefficient (Q²), and root mean square error of prediction, were calculated to evaluate the performance of each algorithm on both near‐infrared and Raman datasets. The comparison results illustrated that the SPC model had a desirable ability of regression and prediction. We believe that this method might be an alternative method for multivariate spectral analysis. Copyright © 2013 John Wiley & Sons, Ltd.     

Multisignal calibration in spark- and ICP-OES

The advantages of multivariate calibration by using more than one selective emission line for one analyte are described in comparison with univariate calibration. Principle component regression (PCR) and partial least squares regression (PLS) are compared with classical univariate linear regression of single lines. Practical applications in spark- and inductively coupled plasma optical emission spectroscopy (ICP-OES) show that the sensitivity can be increased and thus a lower limit of detection be obtained by means of these multivariate techniques. Results from the investigations concerning the problem of collinearity are also discussed. Disturbed analyte lines are included in multisignal calibration. Their influence on the results of calibration is described.     

Determination of the enantiomeric composition of phenylalanine samples by chemometric analysis of the fluorescence spectra of cyclodextrin guest-host complexes

A novel strategy for determining the enantiomeric composition of phenylalanine samples that combines ordinary fluorescence spectroscopy, guest-host cyclodextrin chemistry, and multivariate regression modeling is investigated. Partial-least-squares regression (PLS-1) models were developed from fluorescence spectral data obtained with a series of samples containing cyclodextrin guest-host complexes of phenylalanine with different known enantiomeric compositions. The regression models were subsequently validated by determining the enantiomeric composition of a set of independently prepared phenylalanine samples. The ability of the models to correctly predict the enantiomeric compositions of future samples was evaluated in terms of the root-mean-square percent relative error (RMS%RE). The RMS%RE in the mol fraction of D-phenylalanine ranged from 1.3% to 3.0% when beta-cyclodextrin was used as the host molecule for different guest-host concentrations. The RMS%RE in the mol fraction of D-phenylalanine obtained in a similar validation study conducted with gamma-cyclodextrin ranged between 1.8% and 4.0% for different guest-host concentrations. Compared with previous studies done in absorption, fluorescence data were found to be more sensitive and the spectral differences observed as a function of enantiomeric composition were more uniformly spaced, making regression modeling more reliable. As a result, good regression models could be made at lower concentrations than were possible previously when absorption measurements were used.     

Sorting variables by using informative vectors as a strategy for feature selection in multivariate regression

A new procedure with high ability to enhance prediction of multivariate calibration models with a small number of interpretable variables is presented. The core of this methodology is to sort the variables from an informative vector, followed by a systematic investigation of PLS regression models with the aim of finding the most relevant set of variables by comparing the cross‐validation parameters of the models obtained. In this work, seven main informative vectors i.e. regression vector, correlation vector, residual vector, variable influence on projection (VIP), net analyte signal (NAS), covariance procedures vector (CovProc), signal‐to‐noise ratios vector (StN) and their combinations were automated and tested with the main purpose of feature selection. Six data sets from different sources were employed to validate this methodology. They originated from: near‐Infrared (NIR) spectroscopy, Raman spectroscopy, gas chromatography (GC), fluorescence spectroscopy, quantitative structure‐activity relationships (QSAR) and computer simulation. The results indicate that all vectors and their combinations were able to enhance prediction capability with respect to the full data sets. However, regression and NAS informative vectors from partial least squares (PLS) regression, both built using more latent variables than when building the model presented in most of tested data sets, were the best informative vectors for variable selection. In all the applications, the selected variables were quite effective and useful for interpretation. Copyright © 2008 John Wiley & Sons, Ltd.     

Kinetic Analysis Using Multivariate Non-linear Regression. I. Basic concepts

In principle, the kinetic analysis of thermal effects has limitations when based on a single measurement. Using a simulated example and the dehydration of Ca(OH)₂ , it will be shown that, through the simultaneous application of non-linear regression to several measurements run at different heating rates (multivariate non-linear regression), the difficult problem of determining the probable reaction type can be reliably solved. This revised version was published online in August 2006 with corrections to the Cover Date.     

Multivariate calibration for near-infrared spectroscopic assays of blood substrates in human plasma based on variable selection using PLS-regression vector choices

A multicomponent assay for the blood substrates of total protein, glucose, total cholesterol, triglycerides and urea in human EDTA-plasma by FT-IR spectroscopy is described based on near-infrared spectra of human plasma recorded in a 1 mm quartz transmission cell. Partial least-squares was applied for multivariate calibration taking into account absorbance or logarithmized single beam spectra. Further data reduction was applied using the pairwise selection of spectral variables suggested by the weights of the optimum full spectrum PLS-regression vector. The standard errors of prediction for protein, cholesterol, triglycerides, glucose and urea are calculated by cross-validation for the population of 124 plasma samples of different patients. These values are compared for full spectrum and reduced spectral variable set regression. Received: 16 March 1998 / Accepted: 29 May 1998     

Multivariate calibration for near-infrared spectroscopic assays of blood substrates in human plasma based on variable selection using PLS-regression vector choices

A multicomponent assay for the blood substrates of total protein, glucose, total cholesterol, triglycerides and urea in human EDTA-plasma by FT-IR spectroscopy is described based on near-infrared spectra of human plasma recorded in a 1 mm quartz transmission cell. Partial least-squares was applied for multivariate calibration taking into account absorbance or logarithmized single beam spectra. Further data reduction was applied using the pairwise selection of spectral variables suggested by the weights of the optimum full spectrum PLS-regression vector. The standard errors of prediction for protein, cholesterol, triglycerides, glucose and urea are calculated by cross-validation for the population of 124 plasma samples of different patients. These values are compared for full spectrum and reduced spectral variable set regression. Received: 16 March 1998 / Accepted: 29 May 1998     

基于激光诱导击穿光谱(LIBS)的煤灰熔点快速检测

炉内结渣是影响火电机组和气化工艺可靠运行的关键因素之一,准确预测灰熔点可以提前调整炉膛出口温度以避免结渣。本论文采用激光诱导击穿光谱（LIBS）采集煤灰样中金属元素的光谱,分别建立煤灰中的金属元素的谱线强度与煤灰熔点的随机森林模型、支持向量机回归模型和线性回归模型,直接预测煤灰熔点温度。采用基于马氏距离(MD)的异常数据剔除算法和基于稀疏矩阵的基线估计与降噪算法（BEADS）,对粉煤灰样的全光谱数据进行了预处理。随机森林模型对粉煤灰熔点的预测平均相对误差（MRE）为54.74%,支持向量机回归模型的预测平均相对误差为60.08%,而线性回归模型的预测平均相对误差达到了9.78%。研究结果表明,线性回归模型对煤灰熔点的预测结果更准确。     

New Lutetium Silicate Scintillators

Cerium-doped lutecium orthosilicate (LSO) is the most promising scintillator discovered in almost five decades. It exhibits a unique combination of important properties for x and gamma-ray spectroscopy: high density, fast decay, and large light yield. However, the practical use of LSO is hindered by difficulties related to its fabrication as a single crystal by the Czochralski method. We report on the usefulness of the sol-gel process in obtaining lutecium silicate scintillators. Upon appropriate drying and firing, lutetium silicate crystals can be grown in a silica matrix. The bulk, polycrystalline transparent scintillators are characterized by XRD, optical absorption, light decay measurement and gamma-ray spectral response. Their properties are comparable to that of traditional LSO single crystals.     

Determination of Parameter Uncertainty for Quantitative Analysis of Shaddock Peel Pectin using Linear and Nonlinear Near-infrared Spectroscopic Models

Fourier transform near-infrared spectrometry has been used in combination with multivariate chemometric methods for wide applications in agriculture and food analysis. In this paper, we used linear partial least square and nonlinear least square support vector machine regression methods to establish calibration models for Fourier transform near-infrared spectrometric determination of pectin in shaddock peel samples. In particular, the tunable kernel parameters of the linear and nonlinear models were set changing in a moderate range and were optimally selected in conjunction with a Savitzky–Golay smoother. The smoothing parameters and the linear/nonlinear modeling parameters were combined for simultaneous optimization. To investigate the robustness of calibration models, parameter uncertainty were estimated in a direct way for the optimal linear and nonlinear models. Our results show that the nonlinear least square support vector machine method gives more accurate predictive results and is substantially more robust compared to the spectral noise when compared with the linear partial least square regression. Furthermore, the optimized least square support vector machine model was evaluated by the randomly selected test samples and the model test effect was much satisfactory. We anticipate that these linear and nonlinear methods and the methodology of determination of model parameter uncertainty will be applied to other analytes in the fields of near-infrared or Fourier transform near-infrared spectroscopy.     

Optimisation of partial least squares regression calibration models in near-infrared spectroscopy: a novel algorithm for wavelength selection

A novel optimisation algorithm is presented for full spectrum calibration models in near-infrared (NIR) spectroscopy. The algorithm is used to investigate the affect of removing continuous spectral regions on parameters critical to the validity of the model (e.g. explained variance, bias etc.) and ultimately identify and remove problem areas of the spectrum. As an example of its application, this paper shows how to optimise partial least squares regression (PLSR) calibration models for predicting moisture content within an intact pharmaceutical product and how problems due to changes in the nature of samples since setting up the original model may be eliminated. On application of two validated calibration models to a new set of samples unacceptable results were obtained for bias (-0.26 and -0.21% m/m moisture content) between the NIR predicted values and the true values (Karl Fischer analysis). The optimisation algorithm identified small regions of the spectrum, which if included in development of the models contributed significant bias to the final prediction. On removal of these problem regions the calibration models were found to be equally accurate and precise, but with the added advantage of robustness to a variable region of the sample spectrum (bias reduced to -0.05 and -0.09% m/m).