Optimization in locally weighted regression

The application of locally weighted regression (LWR) to nonlinear calibration problems and strongly clustered calibration data often yields more reliable predictions than global linear calibration models. This study compares the performance of LWR that uses PCR and PLS regression, the Euclidean and Mahalanobis distance as a distance measure, and the uniform and cubic weighting of calibration objects in local models. Recommendations are given on how to apply LWR to near-infrared data sets without spending too much time in the optimization phase.     

Evaluation of a new local modelling approach for large and heterogeneous NIRS data sets

The industry is demanding quality control systems that enable not only certified safety of an end-product but also a secure and efficient production system. Due to this, fast and accurate technologies are required for developing real time decision systems. Sensors based on Near-Infrared Spectroscopy (NIRS), together with the use of chemometrics models, have been studied for on-line quality control as a Process Analytical Technology (PAT) tool in several industries. A critical issue is the development of robust and sufficiently accurate mathematical models that can contain hundreds of very heterogeneous samples representing the large natural variability of the process and product; this especially holds for the agro-food production. This paper evaluates the performance of different linear (PLS) and non-linear regression algorithms (LOCAL and Locally Weighted Regression — LWR) plus a new local approach for the prediction of ingredient composition in compound feeds (called, Local Central Algorithm — LCA). The comparison is based on complexity, accuracy and predicted percentages in test set samples. The new local modelling approach is based on the use of Principal Component Analysis (PCA) and the Mahalanobis Distance (MD) for selecting a training set and calculating the final prediction estimate using a central tendency statistics such as mean of the local neighbours for the unknown samples. The results show that the local strategy proposed in this work enables the prediction in seconds of all the unknown samples in the test set and performed comparable to LWR, although the RMSEP was somewhat higher than using LWR or LOCAL. However, it was found that this approach produced smaller prediction errors than the other methods for less commonly present ingredients that are not well represented by even a large number of training samples. This finding could be relevant for the start-up phase in the implementation of NIRS sensors in the feed industry at which stage the libraries build only on-line contain data of a limited production period.     

Short-wave near-infrared spectroscopy of biological fluids. 1. Quantitative analysis of fat, protein, and lactose in raw milk by partial least-squares regression and band assignment

The present study has aimed at providing new insight into short-wave near-infrared (NIR) spectroscopy of biological fluids. To do that, we analyzed NIR spectra in the 800-1,100-nm region of 100 raw milk samples. The contents of fat, proteins, and lactose were predicted by partial least-squares (PLS) regression and band assignment in that region was investigated based upon PLS loading plots and regression coefficients. For the fat prediction, the whole set of samples was divided into two groups and the fat concentration was predicted for the samples that were not included in the calibration procedures. The correlation coefficient and root-mean-square error of prediction (RM-SEP) in the better prediction run were found to be 0.996 and 0.087 wt %, respectively. Assignment of the bands due to fat was proposed based upon the regression coefficients and PLS loading weights, and the importance of a pretreatment in the prediction was discussed. Milk proteins also yielded sufficient correlation coefficients and RMSEP although the contributions of protein bands to the milk spectra were much smaller than those of the fat bands. The sizes of the calibration models for protein prediction were considered. This is the first time that good correlation coefficients and RMSEP of proteins have ever been obtained for the short-wave NIR spectra of milk. For lactose, noisy regression coefficients with limited prediction ability were obtained. Band assignment was investigated also for bands due to proteins and lactose. We propose the detailed band assignment for the short-wave NIR region useful for various biological fluids. The results presented here demonstrate that the short-wave NIR region is promising for the fast and reliable determination of major components in biological and biomedical fluids.     

Noninvasive, quantitative analysis of drug mixtures in containers using spatially offset Raman spectroscopy (SORS) and multivariate statistical analysis

In this paper, spatially offset Raman spectroscopy (SORS) is demonstrated for noninvasively investigating the composition of drug mixtures inside an opaque plastic container. The mixtures consisted of three components including a target drug (acetaminophen or phenylephrine hydrochloride) and two diluents (glucose and caffeine). The target drug concentrations ranged from 5% to 100%. After conducting SORS analysis to ascertain the Raman spectra of the concealed mixtures, principal component analysis (PCA) was performed on the SORS spectra to reveal trends within the data. Partial least squares (PLS) regression was used to construct models that predicted the concentration of each target drug, in the presence of the other two diluents. The PLS models were able to predict the concentration of acetaminophen in the validation samples with a root-mean-square error of prediction (RMSEP) of 3.8% and the concentration of phenylephrine hydrochloride with an RMSEP of 4.6%. This work demonstrates the potential of SORS, used in conjunction with multivariate statistical techniques, to perform noninvasive, quantitative analysis on mixtures inside opaque containers. This has applications for pharmaceutical analysis, such as monitoring the degradation of pharmaceutical products on the shelf, in forensic investigations of counterfeit drugs, and for the analysis of illicit drug mixtures which may contain multiple components.     

Waveband selection for NIR spectroscopy analysis of soil organic matter based on SG smoothing and MWPLS methods

Savitzky-Golay (SG) smoothing and moving window partial least square (MWPLS) methods were applied to the model optimization and the waveband selection for near-infrared (NIR) spectroscopy analysis of soil organic matter. The optimal single wavelength prediction bias (OSWPB) was used to evaluate the similarity of calibration set and prediction set, and a new division method for calibration set and prediction set was proposed. SG smoothing modes were expanded to 540 kinds. The specific computer algorithm platforms for optimization of SG smoothing mode combined with PLS factor and for MWPLS method with changeable parameters were built up. The optimal waveband for soil organic matter was 1926-2032 nm, the optimal smoothing mode was the 2nd order derivative, 6th degree polynomial, 45 smoothing points, the PLS factor, RMSEP and R_P were 8, 0.260 (%) and 0.877 respectively. The prediction effect was obviously better than that in the whole spectral collecting region. To get stable results, all the optimization processes were based on the average prediction effect on 50 different divisions of calibration set and prediction set.     

Optimization of near-infrared spectroscopic process monitoring at low signal-to-noise ratio

An approach for the optimization of near-infrared (NIR) spectroscopic process monitoring at low signal-to-noise ratio is presented. It compromises the combined adjustment of different measurement variables and data pretreatments considering the prediction error, economic aspects of the application, and process constraints. The integration time, light intensity, and number of averaged spectra were varied; their mutual influence on the prediction error of partial least squares (PLS) models (i.e., root-mean-square error of cross-validation (RMSECV)) was evaluated in the laboratory. At low signal levels, the spectral uncertainty had a strong impact on the prediction error. It leveled off with increasing values of all three parameters and was finally dominated by other sources of uncertainty. The experimental findings could be characterized and explained by a mathematical equation, which was deduced from theoretical principles. The knowledge about the interaction of the measurement variables allowed their combined adjustment resulting in a reduced impact of spectral uncertainty on the prediction error (i.e., root-mean-square error of prediction (RMSEP)) without additional costs or process modifications. Moreover, a convenient procedure to compensate the stray light caused by strongly absorbing windows was developed. The whole approach was successfully applied to a challenging process, namely, the NIR inline monitoring of the liquid content of two model substances in a rotating suspension dryer.     

On-line dissolution determination of Baicalin in solid dispersion based on near infrared spectroscopy and circulation dissolution system

Drug on-line circulation dissolution system with near infrared spectrophotometer for dissolution determination was reported in this paper and subsequently partial least squares (PLS) calibration model was established for concentration prediction of Baicalin in solid dispersion. When the main factor number in PLS calibration model was 6, the correlation coefficients of PLS calibration samples and prediction ones were all 0.9999 and the relative standard deviations were 0.69% and 1.10%, respectively, which showed good robustness and predictability. Combining drug circulation dissolution system with the PLS calibration model, dissolution of Baicalin in raw material drug and solid dispersion were obtained at different times. The results indicated that the dissolution property of Baicalin in solid dispersion (especially at the early time) had been significantly improved. The accumulated dissolution of Baicalin in the solid dispersion at 45 min reached nearly 40%, increasing by 15% compared with raw material drug (about 25%). The aforementioned PLS model associated with drug circulation dissolution system provided a simple, accurate and on-line support for dissolution determination of drug, especially at the early time of rapid dissolution.     

Quantitative analysis of bayberry juice acidity based on visible and near-infrared spectroscopy

Visible and near-infrared (Vis/NIR) reflectance spectroscopy has been investigated for its ability to nondestructively detect acidity in bayberry juice. What we believe to be a new, better mathematic model is put forward, which we have named principal component analysis-stepwise regression analysis-backpropagation neural network (PCA-SRA-BPNN), to build a correlation between the spectral reflectivity data and the acidity of bayberry juice. In this model, the optimum network parameters, such as the number of input nodes, hidden nodes, learning rate, and momentum, are chosen by the value of root-mean-square (rms) error. The results show that its prediction statistical parameters are correlation coefficient (r) of 0.9451 and root-mean-square error of prediction (RMSEP) of 0.1168. Partial least-squares (PLS) regression is also established to compare with this model. Before doing this, the influences of various spectral pretreatments (standard normal variate, multiplicative scatter correction, S. Golay first derivative, and wavelet package transform) are compared. The PLS approach with wavelet package transform preprocessing spectra is found to provide the best results, and its prediction statistical parameters are correlation coefficient (r) of 0.9061 and RMSEP of 0.1564. Hence, these two models are both desirable to analyze the data from Vis/NIR spectroscopy and to solve the problem of the acidity prediction of bayberry juice. This supplies basal research to ultimately realize the online measurements of the juice's internal quality through this Vis/NIR spectroscopy technique.     

Prediction of Drug Content and Hardness of Intact Tablets Using Artificial Neural Network and Near-Infrared Spectroscopy

The purpose of this study was to predict drug content and hardness of intact tablets using artificial neural networks (ANN) and near-infrared spectroscopy (NIRS). Tablets for the drug content study were compressed from mixtures of Avicel® PH-101, 0.5% magnesium stearate, and varying concentrations (0%, 1%, 2%, 5%, 10%, 20%, and 40% w/w) of theophylline. Tablets for the hardness study were compressed from mixtures of Avicel PH-101 and 0.5% magnesium stearate at varying compression forces ranging from 0.4 to 1 ton. An Intact Analyzer™ was used to obtain near infrared spectra from the tablets with varying drug contents, whereas a Rapid Content Analyzer™ (RCA) was used to obtain spectral data from the tablets with varying hardness. Two sets of tablets from each batch (i.e., tablets with varying drug content and hardness) were randomly selected. One set of tablets was used to generate appropriate calibration models, while the other set was used as the unknown (test) set. A total of 10 ANN calibration models (5 each with 10 and 160 inputs at appropriate wavelengths) and five separate 4-factor partial least squares (PLS) calibration models were generated to predict drug contents of the test tablets from the spectral data. For the prediction of tablet hardness, two ANN calibration models (one each with 10 and 160 inputs) and two 4-factor PLS calibration models were generated and used to predict the hardness of test tablets. The PLS calibration models were generated using Vision® software. Prediction of drug contents of test tablets using the ANN calibration models generated with 10 inputs was significantly better than the prediction obtained with the ANN calibration models with 160 inputs. For tablets with low drug concentrations (less than or equal to 2%w/w), prediction of drug content was better with either of the two ANN calibration models than with the PLS calibration models. However, prediction of drug contents of tablets with greater than or equal to 5% w/w drug was better with the PLS calibration models than with the ANN calibration models. Prediction of tablet hardness was better with the ANN calibration models generated with either 10 or 160 inputs than with the PLS calibration models. This work demonstrated that a well-trained ANN model is a powerful alternative technique for analysis of NIRS data. Moreover, the technique could be used in instances when the conventional modeling of data does not work adequately.     

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.     

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.     

Spectral fluorescence signatures and partial least squares regression: model to predict dissolved organic carbon in water

Spectro-fluorescence signature (SFS) of water samples contains information that may be used to quantify dissolved organic carbon (DOC) if combined with multivariate analyses. A model was built through SFS and partial least squared (PLS) regression. The SFSs of 219 samples of natural water along the Raritan River and Millstone River watersheds located in central New Jersey, and their corresponding DOC concentrations were used to build the model. Calibration, full cross-validation, and prediction performances of various models were statistically compared before optimal model selection. The final selected model, tested on the Passaic River watershed in northern New Jersey, provided a bias of 0.028 mg/l and a root mean squared error of prediction (RMSEP) of 0.35 mg/l. Linked to PLS, SFS can be a quality and cost effective method to perform on-line rapid DOC measurements.     

近红外光谱测量中的多尺度建模新方法

近红外光谱学是近十年来发展最快、最引人注目的光谱分析技术之一,其高精度测量依赖于化学计量学方法以准确提取光谱信息.针对近红外光谱单尺度传统建模方法中存在的信息易丢失问题,发展了一种多尺度建模新方法.多尺度建模可有效协同利用信号的时/频多尺度特性,并将多尺度特性以加权形式统一映射到多元校正空间,有效避免了信息丢失.该算法成功地应用于面粉中掺杂有毒非法添加剂硼砂含量检测,经验证后模型的预测值与真实值的相关系数和预测均方根误差分别为0.974和0.0019,其预测相对误差为1.9%.研究结果表明,多尺度建模方法完全满足近红外光谱高精度测量的要求.     

Prediction of oil and oleic acid concentrations in individual corn (Zea mays L.) kernels using near-infrared reflectance hyperspectral imaging and multivariate analysis

Due to their heterogeneous structure and variability in form, individual corn (Zea mays L.) kernels present an optical challenge for nondestructive spectroscopic determination of their chemical composition. Increasing demand in agricultural science for knowledge of specific traits in kernels is driving the need to find high-throughput methods of examination. In this study macroscopic near-infrared (NIR) reflectance hyperspectral imaging was used to measure small sets of kernels in the spectroscopic range of 950 nm to 1700 nm. Image analysis and principal component analysis (PCA) were used to determine kernel germ from endosperm regions as well as to define individual kernels as objects out of sets of kernels. Partial least squares (PLS) analysis was used to predict oil or oleic acid concentrations derived from germ or full kernel spectra. The relative precision of the minimum cross-validated root mean square error (RMSECV) and root mean square error of prediction (RMSEP) for oil and oleic acid concentration were compared for two sets of two hundred kernels. An optimal statistical prediction method was determined using a limited set of wavelengths selected by a genetic algorithm. Given these parameters, oil content was predicted with an RMSEP of 0.7% and oleic acid content with an RMSEP of 14% for a given corn kernel.     

Conductometric simultaneous determination of acetic acid, monochloroacetic acid and trichloroacetic acid using orthogonal signal correction-partial least squares

A simultaneous conductometric titration method for determination of mixtures of acetic acid, monochloroacetic acid and trichloroacetic acid based on the multivariate calibration partial least squares is proposed. It is possible to obtain an adjustable model to relate squared concentration values of the mixtures used in the calibration range by conductance. The effect of orthogonal signal correction (OSC) as a preprocessing technique used to remove the information unrelated to the target variables is studied. The calibration model was build using conductometric titrations data of 16 mixtures of three acids. The concentration matrix was designed by a orthogonal design. The root mean squares error of prediction (RMSEP) for acetic acid, monochloroacetic acid and trichloroacetic acid with and without OSC were 0.08, 0.30 and 0.08, and 0.15, 0.40 and 0.18, respectively. The results obtained by OSC-PLS are better than the PLS and this indicate the successful application of the OSC filter as a good preprocessing method in multivariate calibration methods. The proposed procedure allows the simultaneous determination of these acids, in the synthetic mixtures.     

Rapid nondestructive on-site screening of methylamphetamine seizures by attenuated total reflection fourier transform infrared spectroscopy

The identification and quantification of illicit substances in the field is often desirable. Fourier transform infrared spectroscopy (FT-IR) has both qualitative and quantitative capabilities and field portable instruments are commercially available. Transmission infrared spectra of mixtures containing ephedrine hydrochloride, glucose, and caffeine and attenuated total reflection (ATR) infrared spectra of mixtures composed of methylamphetamine hydrochloride, glucose, and caffeine were used to develop principal component regression (PCR) calibration models. The root mean sum of errors of predictions (RMSEP) of all individual components in a mixture from a single measurement was <6% w/w, which reduced to approximately 3% w/w when triplicates were averaged. Sample mixing and grinding are essential to minimize the effect of heterogeneity, as deviations of up to 20% w/w were observed for single measurements of unground samples. Poor predictions of the components in a mixture occurred when samples were "contaminated" with substances not present in the calibration set, as would be expected. When only a single analyte (drug) was targeted, using a calibration set that contained both contaminated and uncontaminated samples, an RMSEP of approximately 4% w/w was achieved. The results demonstrate that ATR-FT-IR has the potential to quantify methylamphetamine samples, and possibly other licit or illicit substances, in at-seizure and on-site scenarios.     

一种基于LMS加权的残差补偿光谱降维模型研究

目的在PCA算法的基础上提出一种基于LMS锥响应加权的残差补偿光谱降维模型。方法介绍以LMS为加权函数对源光谱加权以及用残差光谱对模型补偿的基本框架。以Munsell色卡作为训练样本,以多光谱图像和SG色卡为检测样本,用文中算法与主成分分析算法分别对其进行降维、重构。结果在不同维数下,采用文中算法重构都具有较高的色度精度,该算法有效提高了主成分分析算法的色度精度,且在变光源情况下仍具有较高的色度稳定性。结论该降维算法采用LMS加权并对残差光谱补偿是一种精度较高的光谱降维模型。     

Multivariate calibration and instrument standardization for the rapid detection of diethylene glycol in glycerin by Raman spectroscopy

The transfer of a multivariate calibration model for quantitative determination of diethylene glycol (DEG) contaminant in pharmaceutical-grade glycerin between five portable Raman spectrometers was accomplished using piecewise direct standardization (PDS). The calibration set was developed using a multi-range ternary mixture design with successively reduced impurity concentration ranges. It was found that optimal selection of calibration transfer standards using the Kennard-Stone algorithm also required application of the algorithm to multiple successively reduced impurity concentration ranges. Partial least squares (PLS) calibration models were developed using the calibration set measured independently on each of the five spectrometers. The performance of the models was evaluated based on the root mean square error of prediction (RMSEP), calculated using independent validation samples. An F-test showed that no statistical differences in the variances were observed between models developed on different instruments. Direct cross-instrument prediction without standardization was performed between a single primary instrument and each of the four secondary instruments to evaluate the robustness of the primary instrument calibration model. Significant increases in the RMSEP values for the secondary instruments were observed due to instrument variability. Application of piecewise direct standardization using the optimal calibration transfer subset resulted in the lowest values of RMSEP for the secondary instruments. Using the optimal calibration transfer subset, an optimized calibration model was developed using a subset of the original calibration set, resulting in a DEG detection limit of 0.32% across all five instruments.     

Quantitative analysis of cotton-polyester textile blends from near-infrared spectra

Quantitative analysis of textile blends and textile fabrics is currently of particular interest in the industrial context. In this frame, this work investigates whether the use of Fourier transform (FT) near-infrared (NIR) spectroscopy and chemometrics is powerful for rapid and accurate quantitative analysis of cotton-polyester content in blend products. As samples of the same composition have many sources of variability that affect NIR spectra, indirect prediction is particularly challenging and a large sample population is required to design robust calibration models. Thus, a total of more than three-hundred cotton-polyester samples were selected covering the range from the 0% to 100% cotton and the corresponding NIR reflectance spectra were measured on raw fabrics. The data set obtained was used to develop multivariate models for quantitative prediction from reference measurements. A successful approach was found to rely on partial least squares (PLS) regression combined with genetic algorithms (GAs) for wavelength selection. It involved evaluating a set of calibration models considering different spectral regions. The results obtained considering 27.5% of the original variables yielded a prediction error (RMSEP) of 2.3 in percent cotton content. It demonstrates that FT-NIR spectroscopy has the potential to be used in the textile industry for the prediction of the composition of cotton-polyester blends. As a further consequence, it was observed that the spectral preprocessing and the complexity of the model are simplified compared to the full-spectrum approach. Also, the relevancy of the spectral intervals retained after variable selection can be discussed.     

Temperature-independent near-infrared analysis of lysozyme aqueous solutions

Digital Fourier filtering is used to produce a temperature-insensitive univariate calibration model for measuring lysozyme in aqueous solutions. Absorbance spectra over the 5000-4000 cm-1 spectral range are collected for lysozyme standards maintained at 14 degrees C. These spectra are used to compute the calibration model while a set of spectra collected at temperatures ranging from 4 to 24 degrees C are used to validate the accuracy of this model. The root-mean-square error of prediction (RMSEP) is 0.279 mg/mL over a tested lysozyme concentration range of 0.036-51.6 mg/mL. The detection limit is 0.68 mg/mL. In addition, multivariate calibration models based on partial least-squares regression (PLS) are evaluated and compared to the results from the univariate model. PLS outperforms the univariate model by providing a RMSEP of 0.090 mg/mL. Analysis of variance showed that both calibration methods effectively eliminate the adverse affects created by variations in solution temperature.