Non-linear calibration models for near infrared spectroscopy

Different calibration techniques are available for spectroscopic applications that show nonlinear behavior. This comprehensive comparative study presents a comparison of different nonlinear calibration techniques: kernel PLS (KPLS), support vector machines (SVM), least-squares SVM (LS-SVM), relevance vector machines (RVM), Gaussian process regression (GPR), artificial neural network (ANN), and Bayesian ANN (BANN). In this comparison, partial least squares (PLS) regression is used as a linear benchmark, while the relationship of the methods is considered in terms of traditional calibration by ridge regression (RR). The performance of the different methods is demonstrated by their practical applications using three real-life near infrared (NIR) data sets. Different aspects of the various approaches including computational time, model interpretability, potential over-fitting using the non-linear models on linear problems, robustness to small or medium sample sets, and robustness to pre-processing, are discussed. The results suggest that GPR and BANN are powerful and promising methods for handling linear as well as nonlinear systems, even when the data sets are moderately small. The LS-SVM is also attractive due to its good predictive performance for both linear and nonlinear calibrations.     

An expeditious method for determining particle size distribution by near infrared spectroscopy: Comparison of PLS2 and ANN models

The particle size distribution of a solid product can be crucial parameter considering its application to different kinds of processes. The influence of particle size on near infrared (NIR) spectra has been used to develop effective alternative methods to traditional ones in order to determine this parameter. In this work, we used the chemometrical techniques partial least squares 2 (PLS2) and artificial neural networks (ANNs) to simultaneously predict several variables to the rapid construction of particle size distribution curves. The PLS2 algorithm relies on linear relations between variables, while the ANN technique can model non-linear systems.Samples were passed through sieves of different sieve opening in order to separate several size fractions that were used to construct two types of particle size distribution curves. The samples were recorded by NIR and their spectra were used with PLS2 and ANN to develop two calibration models for each. The correlation coefficients and relative standard errors of prediction (RSEP) have been used to assess the goodness of fit and accuracy of the results.The four calibration models studied provided statistically identical results based on RSEP values. Therefore, the combined use of NIR spectroscopy and PLS2 or ANN calibration models allows determining the particle size distributions accurately. The results obtained by ANN or PLS2 are statistically similar.     

Variable-weighted least-squares support vector machine for multivariate spectral analysis

Multivariate spectral analysis has been widely applied in chemistry and other fields. Spectral data consisting of measurements at hundreds and even thousands of analytical channels can now be obtained in a few seconds. 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 this paper, the concept of traditional wavelength variable selection has been extended and the idea of variable weighting is incorporated into least-squares support vector machine (LS-SVM). A recently proposed global optimization method, particle swarm optimization (PSO) algorithm is used to search for the weights of variables and the hyper-parameters involved in LS-SVM optimizing the training of a calibration set and the prediction of an independent validation set. All the computation process of this method is automatic. Two real data sets are investigated and the results are compared those of PLS, uninformative variable elimination-PLS (UVE-PLS) and LS-SVM models to demonstrate the advantages of the proposed method.     

人工神经网络用于近红外光谱测定柴油闪点

采用主成分－人工神经网络对不同留程柴油的近红外光谱进行校正,预测其闪点。采用监控集控制网络训练过程,以避免过训练。探讨了人工神经网络（ＡＮＮ）、直接线性连接人工神经网络（ＬＡＮＮ）的校正效果,并与局部权重回归（ＬＷＲ）、主成分回归（ＰＣＲ）及偏最小二乘（ＰＬＳ）等校正方法进行了比较,认为人工神经及直接线性关联的较好手段。     

Combination of mid- and near-infrared spectroscopy for the determination of the quality properties of beers

The combination of infrared (MIR) and near-infrared (NIR) spectroscopy has been employed for the determination of important quality parameters of beers, such as original and real extract and alcohol content. A population of 43 samples obtained from the Spanish market and including different types of beer, was evaluated. For each technique, spectra were obtained in triplicate. In the case of NIR a 1 mm pathlength quartz flow cell was used, whereas attenuated total reflectance measurements were used in MIR. Cluster hierarchical analysis was employed to select calibration and validation data sets. The calibration set was composed of 15 samples, thus leaving 28 for validation. A critical evaluation of the prediction capability of multivariate methods established from the combination of NIR and MIR spectra was made. Partial least squares (PLS) and artificial neural networks (ANN) were evaluated for the treatment of data obtained in each individual technique and the combination of both. Different parameters of each methodology were optimized. A slightly better predictive performance was obtained for NIR-MIR combined spectra, and in all the cases ANN performs better than PLS, which may be interpreted from the existence of some non-linearity in the data. The root-mean-sqare-error of prediction (RMSEP) values obtained for the combined NIR-MIR spectra for the determination of real extract, original extract and ethanol were 0.076% w/w, 0.14% w/w and 0.091% v/v.     

A comparative study of diesel analysis by FTIR, FTNIR and FT-Raman spectroscopy using PLS and artificial neural network analysis

Diesel properties determined by ASTM reference methods as cetane index, density, viscosity, distillation temperatures at 50% (T50) and 85% (T85) recovery, and the total sulfur content (%, w/w) were modeled by FTIR-ATR, FTNIR, and FT-Raman spectroscopy using partial last square regression (PLS) and artificial neural network (ANN) spectral analysis. In the PLS models, 45 diesel samples were used in the training group and the other 45 samples were used in the validation. In the ANN analysis a modular feedforward network was used. Sixty diesel samples were used in the neural network training and other 30 samples were used in the validation. Two different ATR configurations were compared in the FTIR, a conventional (ATR1) and an immersion (ATR2) cell. The ATR1 cell presented the best results, with smaller prediction errors (root mean square error of prediction, RMSEP). The comparison of the three PLS models (FTIR-ATR1, FTNIR, and FT-Raman) shows that reasonable values of R² and RMSEP were obtained by the FTIR-ATR1 and FTNIR models in the evaluation of density, viscosity, and T50. The PLS/FT-Raman models presented reasonable results only for the T50 property. None of the techniques was able to generate suitable PLS calibration models for the determination of sulfur content. The ANN/FT-Raman models presented the best performances, with all models presenting R²-values above 85% some of them with RMSEP values significantly smaller than those obtained with FTIR-ATR and FTNIR. The ANN/FT-Raman and ANN/FTIR-ATR1 models were able to estimate the total sulfur content of diesel with 0.01% (w/w) accuracy.     

Multicomponent analysis of electrochemical signals in the wavelet domain

Successful applications of multivariate calibration in the field of electrochemistry have been recently reported, using various approaches such as multilinear regression (MLR), continuum regression, partial least squares regression (PLS) and artificial neural networks (ANN). Despite the good performance of these methods, it is nowadays accepted that they can benefit from data transformations aiming at removing baseline effects, reducing noise and compressing the data. In this context the wavelet transform seems a very promising tool. Here, we propose a methodology, based on the fast wavelet transform, for feature selection prior to calibration. As a benchmark, a data set consisting of lead and thallium mixtures measured by differential pulse anodic stripping voltammetry and giving seriously overlapped responses has been used. Three regression techniques are compared: MLR, PLS and ANN. Good predictive and effective models are obtained. Through inspection of the reconstructed signals, identification and interpretation of significant regions in the voltammograms are possible.     

Determination of methyl ester contents in biodiesel blends by FTIR-ATR and FTNIR spectroscopies

Partial last square regression (PLS) and artificial neural network (ANN) combined to FTIR-ATR and FTNIR spectroscopies have been used to design calibration models for the determination of methyl ester content (%, w/w) in biodiesel blends (methyl ester + diesel). Methyl esters were obtained by the methanolysis of soybean, babassu, dende, and soybean fried oils. Two sets of samples have been used: Group I, binary mixtures (diesel + one kind of methyl ester), corresponding to 96 biodiesel blends (0–100%, w/w), and Group II, quaternary mixtures (diesel + three types of methyl esters), corresponding to 60 biodiesel blends (0–100%, w/w). The PLS results have shown that the FTNIR model for Group I is more precise and accurate (±0.02 and ±0.06%, w/w). In the case of Group II the PLS models (FTIR-ATR and FTNIR) have shown the same accuracies, while the ANN/FTNIR models has presented better performance than the ANN/FTIR-ATR models. The best accuracy was achieved by the ANN/FTNIR model for diesel determination (0.14%, w/w) while the worthiest was that of dende ANN/FTIR-ATR model (0.6%, w/w). Precisions in Group II analysis ranged from 0.06 to 0.53% (w/w) and coefficients of variation were better than 3% indicating that these models are suitable for the determination of diesel–biodiesel blends composed of methyl esters derived from different vegetable oils.     

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.     

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.     

Improvement of the prediction ability of multivariate calibration by a method based on the combination of data fusion and least squares support vector machines

This paper suggests a novel method named DF-LS-SVM, which is based on least squares support vector machines (LS-SVM) regression combined with data fusion (DF) to enhance the ability to extract characteristic information and improve the quality of the regression. Simultaneous multicomponent determination of Fe(III), Co(II) and Cu(II) was conducted for the first time by using the proposed method. Data fusion is a technique that integrates information from disparate sources to produce a single model or decision. The LS-SVM technique allows for learning a high-dimensional feature with fewer training data, and reduces the computational complexity by only requiring the solution of a set of linear equations instead of a quadratic programming problem. Experimental results showed that the DF-LS-SVM method was successful for simultaneous multicomponent determination even when severe overlap of spectra existed. The DF-LS-SVM method is an attractive and promising hybrid approach that combines the best properties of the two techniques. The results obtained from an additional test case, simultaneous differential pulse voltammetric determination of o-nitrophenol, m-nitrophenol and p-nitrophenol, also demonstrated that the DF-LS-SVM method performed somewhat better than LS-SVM and PLS methods.     

Comparison of Artificial Neural Networks with Partial Least Squares Regression for Simultaneous Determinations by ICP-AES

Simultaneous determination of several elements （U, Ta, Mn, Zr and W） with inductively coupled plasma atomic emission spectrometry （ICP-AES） in the presence of spectral interference was performed using chemometrics methods. True comparison between artificial neural network （ANN） and partial least squares regression （PLS） for simultaneous determination in different degrees of overlap was investigated. The emission spectra were recorded at uranium analytical line （263.553 nm） with a 0.06 nm spectral window by ICP-AES. Principal component analysis was applied to data and scores on 5 dominant principal components were subjected to ANN. A 5-5-5 （input, hidden and output neurons） network was used with linear transfer function after both hidden and output layers. The PI,S model was trained with five latent variables and 20 samples in calibration set. The relative errors of predictions （REP） in test set were 3.75% and 3.56% for ANN and PLS respectively.     

Combined wavelet transform-artificial neural network use in tablet active content determination by near-infrared spectroscopy

The pharmaceutical industry faces increasing regulatory pressure to optimize quality control. Content uniformity is a basic release test for solid dosage forms. To accelerate test throughput and comply with the Food and Drug Administration's process analytical technology initiative, attention is increasingly turning to nondestructive spectroscopic techniques, notably near-infrared (NIR) spectroscopy (NIRS). However, validation of NIRS using requisite linearity and standard error of prediction (SEP) criteria remains a challenge. This study applied wavelet transformation of the NIR spectra of a commercial tablet to build a model using conventional partial least squares (PLS) regression and an artificial neural network (ANN). Wavelet coefficients in the PLS and ANN models reduced SEP by up to 60% compared to PLS models using mathematical spectra pretreatment. ANN modeling yielded high-linearity calibration and a correlation coefficient exceeding 0.996.     

Boosted regression trees, multivariate adaptive regression splines and their two-step combinations with multiple linear regression or partial least squares to predict blood-brain barrier passage: a case study

The use of some unconventional non-linear modeling techniques, i.e. classification and regression trees and multivariate adaptive regression splines-based methods, was explored to model the blood-brain barrier (BBB) passage of drugs and drug-like molecules. The data set contains BBB passage values for 299 structural and pharmacological diverse drugs, originating from a structured knowledge-based database. Models were built using boosted regression trees (BRT) and multivariate adaptive regression splines (MARS), as well as their respective combinations with stepwise multiple linear regression (MLR) and partial least squares (PLS) regression in two-step approaches. The best models were obtained using combinations of MARS with either stepwise MLR or PLS. It could be concluded that the use of combinations of a linear with a non-linear modeling technique results in some improved properties compared to the individual linear and non-linear models and that, when the use of such a combination is appropriate, combinations using MARS as non-linear technique should be preferred over those with BRT, due to some serious drawbacks of the BRT approaches.     

Performance of multicomponent self-organizing regression (MCSOR) in QSAR, QSPR, and multivariate calibration: comparison with partial least-squares (PLS) and validation with large external data sets

A novel method for underdetermined regression problems, multicomponent self-organizing regression (MCSOR), has been recently introduced. Here, its performance is compared with partial least-squares (PLS), which is perhaps the most widely adopted multivariate method in chemometrics. A potpourri of models is presented, and MCSOR appears to provide highly predictive models that are comparable with or better than the corresponding PLS models in large internal (leave-one-out, LOO) and pseudo-external (leave-many-out, LMO) validation tests. The "blind" external predictive ability of MCSOR and PLS is demonstrated employing large melting point, factor Xa, log P and log S data sets. In a nutshell, MCSOR is fast, conceptually simple (employing multiple linear regression, MLR, as a statistical tool), and applicable to all kinds of multivariate problems with single Y-variable.     

人工神经网络紫外光度法同时测定甲基苯甲醛的三种同分异构体及其与偏最小二乘法的比较

同分异构体的同时测定一直是分析化学领域的热点和难点问题,本文将化学计量学中的多元校正方法,如偏最小二乘法和人工神经网络法与紫外分光光度法相结合,同时测定了紫外吸收光谱严重重叠的甲基苯甲醛的三种同分异构体混合体系中各组分的含量。确定了测定的最佳波长范围为230～304 nm;测得48个混合标样的吸光度值用于建立模型,其中,邻、间、对甲基苯甲醛的浓度范围分别为6.0～15.0、7.0～16.0和8.0～19.0 μg·mL-1。7个模拟样品作为监测集用于检验所建立模型的预测性能。本文还讨论了三种组分浓度比例对所建立模型预测性能的影响并确定了可以准确测定的浓度比例范围。所建立的方法用于模拟样品的测定,其回收率在84.00%与109.60%之间。与偏最小二乘法的测定结果比较,经成对t检验表明,两种方法对邻、间甲基苯甲醛测定结果无显著性差异;而对甲基苯甲醛的测定,人工神经网络法的测定结果优于偏最小二乘法。