An adaptive strategy for selecting representative calibration samples in the continuous wavelet domain for near-infrared spectral analysis

Sample selection is often used to improve the cost-effectiveness of near-infrared (NIR) spectral analysis. When raw NIR spectra are used, however, it is not easy to select appropriate samples, because of background interference and noise. In this paper, a novel adaptive strategy based on selection of representative NIR spectra in the continuous wavelet transform (CWT) domain is described. After pretreatment with the CWT, an extension of the Kennard–Stone (EKS) algorithm was used to adaptively select the most representative NIR spectra, which were then submitted to expensive chemical measurement and multivariate calibration. With the samples selected, a PLS model was finally built for prediction. It is of great interest to find that selection of representative samples in the CWT domain, rather than raw spectra, not only effectively eliminates background interference and noise but also further reduces the number of samples required for a good calibration, resulting in a high-quality regression model that is similar to the model obtained by use of all the samples. The results indicate that the proposed method can effectively enhance the cost-effectiveness of NIR spectral analysis. The strategy proposed here can also be applied to different analytical data for multivariate calibration.     

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.     

A new hybrid strategy for constructing a robust calibration model for near-infrared spectral analysis

A new hybrid algorithm is proposed for construction of a high-quality calibration model for near-infrared (NIR) spectra that is robust against both spectral interference (including background and noise) and multiple outliers. The algorithm is a combination of continuous wavelet transform (CWT) and a modified iterative reweighted PLS (mIRPLS) procedure. In the proposed algorithm the spectral interference is filtered by CWT at the first stage then mIRPLS is proposed to detect the multiple outliers in the CWT domain. Compared with the original IRPLS method, mIRPLS does not need to adjust variable parameters to achieve optimum calibration results, which makes it very convenient to perform in practice. The final PLS model is constructed robustly because both the spectral interference and multiple outliers are eliminated. In order to validate the effectiveness and universality of the algorithm, it was applied to two different sets of NIR spectra. The results indicate that the proposed strategy can greatly enhance the robustness and predictive ability of NIR spectral analysis.     

Determination of α-linolenic acid and linoleic acid in edible oils using near-infrared spectroscopy improved by wavelet transform and uninformative variable elimination

This paper proposes an analytical method for simultaneous near-infrared (NIR) spectrometric determination of α-linolenic and linoleic acid in eight types of edible vegetable oils and their blending. For this purpose, a combination of spectral wavelength selection by wavelet transform (WT) and elimination of uninformative variables (UVE) was proposed to obtain simple partial least square (PLS) models based on a small subset of wavelengths. WT was firstly utilized to compress full NIR spectra which contain 1413 redundant variables, and 42 wavelet approximate coefficients were obtained. UVE was then carried out to further select the informative variables. Finally, 27 and 19 wavelet approximate coefficients were selected by UVE for α-linolenic and linoleic acid, respectively. The selected variables were used as inputs of PLS model. Due to original spectra were compressed, and irrelevant variables were eliminated, more parsimonious and efficient model based on WT-UVE was obtained compared with the conventional PLS model with full spectra data. The coefficient of determination (r²) and root mean square error prediction set (RMSEP) for prediction set were 0.9345 and 0.0123 for α-linolenic acid prediction by WT-UVE-PLS model. The r² and RMSEP were 0.9054, 0.0437 for linoleic acid prediction. The good performance showed a potential application using WT-UVE to select NIR effective variables. WT-UVE can both speed up the calculation and improve the predicted results. The results indicated that it was feasible to fast determine α-linolenic acid and linoleic acid content in edible oils using NIR spectroscopy.     

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.     

离散小波变换-遗传算法-交互检验法用于近红外光谱数据的高倍压缩与变量筛选

用遗传算法(GA)与交互检验(CV)相结合建立了一种用于对近红外光谱(NIR)数据及其离散小波变换(DWT)系数进行变量筛选的方法，并应用于烟草样品中总挥发碱和总氮的同时测定。结果表明：NIR数据经DWT压缩为原始大小的3．3％时基本没有光谱信息的丢失；有效的变量筛选可以极大地减少模型中的变量个数，降低模型的复杂程度，改善预测的准确度。     

Determination of Total Sugar in Tobacco by Near-Infrared Spectroscopy and Wavelet Transformation-Based Calibration

Based on wavelet transformation (WT) and mutual information (MI), a simple and effective procedure is proposed for multivariate calibration of near-infrared spectroscopy. In such a procedure, the original spectra of the training set are first transformed into a set of wavelet representations by wavelet prism transform. Then, the MI value between each wavelet coefficient variable and the dependent variable is calculated, resulting in a MI spectrum; by retaining a subset set of coefficients with higher MI, an update training set consisting of wavelet coefficients is obtained and reconstructed/converted back to the original domain. Based on this, a partial least square (PLS) model can be constructed and optimized. The optimal wavelet and decomposition level are determined by experiment. A NIR quantitative problem involving the determination of total sugar in tobacco is used to demonstrate the overall performance of the proposed procedure, named RPLS, meaning PLS in reconstructed original domain coupled with MI-induced variable selection in wavelet domain (RPLS). Three kinds of procedures, that is, conventional full-spectrum PLS in original domain (FPLS), PLS in original domain coupled with MI-induced variable selection (OPLS), and direct PLS in MI-based wavelet coefficients (WPLS), are used as reference. The result confirms that it can build more accurate and robust calibration models without increasing the complexity.     

Removal of interference signals due to water from in vivo near-infrared (NIR) spectra of blood glucose by region orthogonal signal correction (ROSC).

A novel chemometric method, region orthogonal signal correction (ROSC), is proposed and applied to pretreat near-infrared (NIR) spectra of blood glucose measured in vivo. Water is the most serious interference component in such kinds of noninvasive measurements, because it shows very high absorbance in the spectra. In the present study, the spectra of blood glucose in the range of 1212 - 1889 nm are used, in which the absorption of water around 1440 nm is very high. ROSC aims at removing the interference signal due to water from the spectra by selecting a set of spectra with a special region of 1404 - 1454 nm that mainly contain information about the variation of the interference component, water, and calculating the orthogonal components to the concentrations of glucose that will be removed. The difference between ROSC and orthogonal signal correction (OSC) is that ROSC uses a special region of spectra for the estimation of scores and loading weights of orthogonal components to pretreat the spectra in other regions, while OSC only uses one fixed region of spectra to calculate loadings, scores and weights of OSC components and removes the OSC components in the same region. A clear advantage of ROSC is that it is more interpretable than OSC, because one can select a spectral region to remove the variation of a special component such as water. Another chemometric method, moving window partial least squares (MWPLSR), is also used to select informative regions of glucose from the NIR spectra of blood glucose measured in vivo, leading to improved PLS models. Results of the application of ROSC demonstrate that ROSC-pretreated spectra including the whole spectral region of 1212 - 1889 nm or an informative region of 1600- 1730 nm selected by MWPLSR provide very good performance of the PLS models. Especially, the later region yields a model with RMSECV of 15.8911 mg/dL for four PLS components. ROSC is a potential chemometric technique in the pretreatment of various spectra.     

A strategy that iteratively retains informative variables for selecting optimal variable subset in multivariate calibration

Nowadays, with a high dimensionality of dataset, it faces a great challenge in the creation of effective methods which can select an optimal variables subset. In this study, a strategy that considers the possible interaction effect among variables through random combinations was proposed, called iteratively retaining informative variables (IRIV). Moreover, the variables are classified into four categories as strongly informative, weakly informative, uninformative and interfering variables. On this basis, IRIV retains both the strongly and weakly informative variables in every iterative round until no uninformative and interfering variables exist. Three datasets were employed to investigate the performance of IRIV coupled with partial least squares (PLS). The results show that IRIV is a good alternative for variable selection strategy when compared with three outstanding and frequently used variable selection methods such as genetic algorithm-PLS, Monte Carlo uninformative variable elimination by PLS (MC-UVE-PLS) and competitive adaptive reweighted sampling (CARS). The MATLAB source code of IRIV can be freely downloaded for academy research at the website: http://code.google.com/p/multivariate-calibration/downloads/list.     

A consensus least squares support vector regression (LS-SVR) for analysis of near-infrared spectra of plant samples

Consensus modeling of combining the results of multiple independent models to produce a single prediction avoids the instability of single model. Based on the principle of consensus modeling, a consensus least squares support vector regression (LS-SVR) method for calibrating the near-infrared (NIR) spectra was proposed. In the proposed approach, NIR spectra of plant samples were firstly preprocessed using discrete wavelet transform (DWT) for filtering the spectral background and noise, then, consensus LS-SVR technique was used for building the calibration model. With an optimization of the parameters involved in the modeling, a satisfied model was achieved for predicting the content of reducing sugar in plant samples. The predicted results show that consensus LS-SVR model is more robust and reliable than the conventional partial least squares (PLS) and LS-SVR methods.     

基于近红外光谱的食用植物油中反式脂肪酸含量快速定量检测及模型优化研究

利用近红外光谱技术对食用植物油中反式脂肪酸(Trans fatty acids,TFA)含量进行快速定量检测,并通过波段选择、预处理方法、变量筛选及建模方法对TFA含量预测模型进行优化.采用AntarisⅡ傅里叶变换近红外光谱仪在4000~10000 cm-1光谱范围采集98个食用植物油样本的近红外透射光谱,然后采用气相色谱法测定TFA的真实含量.首先,对样本原始光谱进行波段、预处理方法优选;在此基础上,采用竞争自适应重加权法(Competitive adaptive reweighted sampling,CARS)筛选TFA相关的重要变量,最后应用主成分回归、偏最小二乘和最小二乘支持向量机方法分别建立食用植物油中TFA含量的预测模型.研究结果表明,近红外光谱技术检测食用植物油中的TFA含量是可行的,优化后的最佳预测模型的校正集和预测集R2分别为0.992和0.989,RMSEC和RMSEP分别为0.071%和0.075%.最佳预测模型所用的变量仅26个,占全波段变量的0.854%.此外,与全波段偏最小二乘预测模型相比,其预测集R2由0.904上升为0.989,RMSEP由0.230%下降为0.075%.由此表明,模型优化非常必要,CARS能有效筛选TFA相关的重要变量,极大减少建模变量数,从而简化预测模型,并较大提高预测模型的精度和稳定性.     

Determination of polyphenols in oats by near-infrared spectroscopy (NIRS) and two-dimensional correlation spectroscopy

Two-dimensional correlation spectroscopy (2DCOS) and near-infrared spectroscopy (NIRS) were used to determine the polyphenol content in oat grain. A partial least squares (PLS) algorithm was used to perform the calibration. A total of 116 representative oat samples from four locations in China were prepared and the corresponding near-infrared spectra were measured. Two-dimensional correlation spectroscopy was employed to select wavelength bands for the PLS regression model for the polyphenol determination. The number of PLS components and intervals was optimized according to the coefficients of determination (R²) and root mean square error of cross validation (RMSECV) in the calibration set. The performance of the final model was evaluated using the correlation coefficient (R) and the root mean square error of validation (RMSEV) in the prediction set. The results showed the band corresponding to the optimal calibration model was between 1350 and 1848?nm and the optimal spectral preprocessing combination was second derivative with second smoothing. The optimal regression model was obtained with an R² of 0.8954 and an RMSECV of 0.06651 in the calibration set and R of 0.9614 and RMSEV of 0.04573 in the prediction set. These measurements reveal the calibration model had qualified predictive accuracy. The results demonstrated that the 2DCOS with PLS was a simple and rapid method for the quantitative determination of polyphenols in oats.     

A comparative study between PCR and PLS in simultaneous spectrophotometric determination of diphenylamine, aniline, and phenol: Effect of wavelength selection

Partial least squares (PLS) and principal component regression (PCR) have received considerable attention in the chemometrics for multicomponent analysis where superiority of one over another is a challenging problem yet. Considering the effect of wavelength selection, a comparison was made between PCR and PLS methods by application those to simultaneous spectrophotometric determination of diphenylamine (DPA), a compound from the third European Union list of priority pollutants, and its environmentally related products aniline and phenol. The UV absorbance spectra of the methanolic solutions of the analytes were measured in the concentration ranges of 1.0-10.0 microg mL(-1) and then subjected to PCR and PLS. The models refinement procedure and validation was performed by cross-validation. A modified changeable size moving windows strategy, where optimized the intervals between the sensors in a selected windows, was also proposed to select the more informative spectral regions for each of the analytes. It was found that wavelength selection improved the quality of predictions for both regression methods whereas more reliable results were obtained by removing of the highly collinear neighboring wavelengths. The resultant data explained that PLS produced more or less better results when whole spectral data were used but in the case of selected wavelength regions both methods produced similar results and no comments could be given about the superiority of one against another. The major difference was obtaining the higher number of factors for PCR, which is not a significant problem.     

连续小波变换-独立成分回归算法及其在多组分分析中的应用

采用连续小波变换（CWT）对光谱数据进行处理，用独立成分分析（ICA）进行特征提取，再用回归分析方法对被测组分进行测定，建立了连续小波变换一独立成分回归（CWT-ICR）方法。方法用于肉样品中水分、脂肪和蛋白质多组分的同时测定，所得结果与化学法测得结果相符。     

Comparison of Different PLS Algorithms for Simultaneous Determination of Cd(II), Cu(II), Pb(II), and Zn(II) by Anodic Stripping Voltammetry at Bismuth Film Electrode

In this work we evaluated the use of different variable selection techniques combined with partial least‐squares regression (PLS) – genetic algorithm PLS (GA‐PLS), interval PLS (iPLS), and synergy interval PLS (siPLS) – in the simultaneous determination of Cd(II), Cu(II), Pb(II) and Zn(II) by anodic stripping voltammetry at a bismuth film. Generally, variable selection provided an improvement in prediction results when compared to full‐voltammogram PLS. The use of interval selection based algorithms have shown to be most adequate than the selection of discrete variables by GA. Excellent analytical performances were obtained despite the inherent complexity of the simultaneous determination.     

Spectral regions selection to improve prediction ability of PLS models by changeable size moving window partial least squares and searching combination moving window partial least squares

Changeable size moving window partial least squares (CSMWPLS) and searching combination moving window partial least squares (SCMWPLS) are proposed to search for an optimized spectral interval and an optimized combination of spectral regions from informative regions obtained by a previously proposed spectral interval selection method, moving window partial least squares (MWPLSR) [Anal. Chem. 74 (2002) 3555]. The utilization of informative regions aims to construct better PLS models than those based on the whole spectral points. The purpose of CSMWPLS and SCMWPLS is to optimize the informative regions and their combination to further improve the prediction ability of the PLS models. The results of their application to an open-path (OP)/FT-IR spectra data set show that the proposed methods, especially SCMWPLS can find out an optimized combination, with which one can improve, often significantly, the performance of the corresponding PLS model, in terms of low prediction error, root mean square error of prediction (RMSEP) with the reasonable latent variable (LVs) number, comparing with the results obtained using whole spectra or direct combination of informative regions for a compound. Regions consisting of the combinations obtained can easily be explained by the existence of IR absorption bands in those spectral regions.