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).     

Simultaneous determination of Sb(III) and Sb(V) by partial least squares regression

A method for simultaneous spectrophotometric determination of Sb(III) and Sb(V) using multivariate calibration method is proposed. This method is based on the development of the reaction between the analytes and pyrogallol red at pH 2.00. The selection of variables was studied. A series of synthetic solutions containing different concentrations of Sb(III) and Sb(V) were used to check the prediction ability of the partial least squares model. The calibration curves were linear over the range of 0.3-3.4 and 0.3-3.0 μg ml⁻¹ for Sb(III) and Sb(V), respectively. The detection limits were 0.177 and 0.200 μg ml⁻¹ for Sb(III) and Sb(V), respectively.     

Source contributions to ambient aerosol calculated by discriminat partial least squares regression (PLS)

Partial least squares regression (PLS) is proposed for solving ir pollution source apportionment problems as an alternative method to the frequently used chemical mass balance technique. A discriminant PLS is used to calculate linear mixing proportions for a synthetic ambient aerosol data set where the truth is known. Without sacrificing orthogonality of the source profiles, PLS can resolve the emission sources and accurately predict the emission source contributions. Further extensions of the PLS approach to environmental receptor modelling are discussed.     

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.     

Iterative weighting of multiblock data in the orthogonal partial least squares framework

The integration of multiple data sources has emerged as a pivotal aspect to assess complex systems comprehensively. This new paradigm requires the ability to separate common and redundant from specific and complementary information during the joint analysis of several data blocks. However, inherent problems encountered when analysing single tables are amplified with the generation of multiblock datasets. Finding the relationships between data layers of increasing complexity constitutes therefore a challenging task. In the present work, an algorithm is proposed for the supervised analysis of multiblock data structures. It associates the advantages of interpretability from the orthogonal partial least squares (OPLS) framework and the ability of common component and specific weights analysis (CCSWA) to weight each data table individually in order to grasp its specificities and handle efficiently the different sources of Y-orthogonal variation.     

Quantification of brain lipids by FTIR spectroscopy and partial least squares regression

Brain tissue is characterized by high lipid content. Its content decreases and the lipid composition changes during transformation from normal brain tissue to tumors. Therefore, the analysis of brain lipids might complement the existing diagnostic tools to determine the tumor type and tumor grade. Objective of this work is to extract lipids from gray matter and white matter of porcine brain tissue, record infrared (IR) spectra of these extracts and develop a quantification model for the main lipids based on partial least squares (PLS) regression. IR spectra of the pure lipids cholesterol, cholesterol ester, phosphatidic acid, phosphatidylcholine, phosphatidylethanolamine, phosphatidylserine, phosphatidylinositol, sphingomyelin, galactocerebroside and sulfatide were used as references. Two lipid mixtures were prepared for training and validation of the quantification model. The composition of lipid extracts that were predicted by the PLS regression of IR spectra was compared with lipid quantification by thin layer chromatography.     

偏最小二乘线性拟合滴定甘蔗糖蜜中多组分有机酸

将滴定体系调节至pH 2.0,用碱标准溶液滴定至特定pH所消耗滴定荆为测量指标,构建了多组分有机酸滴定数据阵,分别以主成分回归法、偏最小二乘法以及人工神经元网络法进行多组分拟合.结果表明,偏最小二乘法的拟合结果最佳,对混合体系中乙酸、乳酸、草酸、琥珀酸、柠檬酸和乌头酸总量的相对预测均方根误差分别为5.80%、8.88%...     

On estimation of multivariate prediction regions in partial least squares regression

The estimation of the prediction region of partial least squares (PLS) is necessary in many engineering applications. However, research in this area focuses on the estimation of prediction intervals only. In this work, a new recursive formulation of PLS is proposed to facilitate the calculation of the Jacobian matrix of the estimated coefficient matrix. Furthermore, the computational complexity analysis indicates that the proposed algorithm is O(m²N + mpN + mpN² + mN³ + mpN⁴) per number of component. The prediction region of the multivariate PLS is obtained through local linearization. The new formulation provides one way to obtain the prediction region of the multivariate PLS. Simulation and near‐infrared spectra of corn case studies indicate the utility of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.     

Sparse matrix transform based weight updating in partial least squares regression

Regression from high dimensional observation vectors is particularly difficult when training data is limited. Partial least squares (PLS) partly solves the high dimensional regression problem by projecting the data to latent variables space. The key issue in PLS is the computation of weight vector which describes the covariance between the responses and observations. For small-sample-size and high-dimensional regression problem, the covariance estimation is usually inaccurate and the correlated components in the predictors will distort the PLS weight. In this paper, we propose a sparse matrix transform (SMT) based PLS (SMT-PLS) method for high-dimensional spectroscopy regression. In SMT-PLS, the observation data is first decorrelated by SMT. Then, in the decorrelated data space, the PLS loading weight is computed by least squares regression. SMT technique provides an accurate data covariance estimation, which can overcome the effect of small-sample-size and benefit both the PLS weight computation and subsequent regression prediction. The proposed SMT-PLS method is compared, in terms of root mean square errors of prediction, to PLS, Power PLS and PLS with orthogonal scatter correction on four real spectroscopic data sets. Experimental results demonstrate the efficacy and effectiveness of our proposed method.     

Influence of variable selection on partial least squares discriminant analysis models for explosive residue classification

Using a series of thirteen organic materials that includes novel high-nitrogen energetic materials, conventional organic military explosives, and benign organic materials, we have demonstrated the importance of variable selection for maximizing residue discrimination with partial least squares discriminant analysis (PLS-DA). We built several PLS-DA models using different variable sets based on laser induced breakdown spectroscopy (LIBS) spectra of the organic residues on an aluminum substrate under an argon atmosphere. The model classification results for each sample are presented and the influence of the variables on these results is discussed. We found that using the whole spectra as the data input for the PLS-DA model gave the best results. However, variables due to the surrounding atmosphere and the substrate contribute to discrimination when the whole spectra are used, indicating this may not be the most robust model. Further iterative testing with additional validation data sets is necessary to determine the most robust model.     

Quantitative analysis of thymine with surface-enhanced Raman spectroscopy and partial least squares (PLS) regression

Silver sol surface-enhanced Raman spectroscopy (SERS) was considered as a technique in the quantitative analysis of low-concentration thymine. Because of the poor stability and reproducibility of SERS signal, a polymer of polyacrylic acid sodium was selected as a stable medium to add into silver sol in order to obtain a surface-enhanced Raman spectroscopy signal. Assignments of Raman shift for solid thymine, SERS of thymine, and SERS of thymine containing stable medium were given. The comparison of Raman peaks between them showed that the addition of stable medium had a little influence on the SERS of thymine and is suitable for the quantitative analysis of low-concentration thymine.     

Multi-analyte quantification in bioprocesses by Fourier-transform-infrared spectroscopy by partial least squares regression and multivariate curve resolution

This paper presents the quantification of Penicillin V and phenoxyacetic acid, a precursor, inline during Pencillium chrysogenum fermentations by FTIR spectroscopy and partial least squares (PLS) regression and multivariate curve resolution – alternating least squares (MCR-ALS). First, the applicability of an attenuated total reflection FTIR fiber optic probe was assessed offline by measuring standards of the analytes of interest and investigating matrix effects of the fermentation broth. Then measurements were performed inline during four fed-batch fermentations with online HPLC for the determination of Penicillin V and phenoxyacetic acid as reference analysis. PLS and MCR-ALS models were built using these data and validated by comparison of single analyte spectra with the selectivity ratio of the PLS models and the extracted spectral traces of the MCR-ALS models, respectively. The achieved root mean square errors of cross-validation for the PLS regressions were 0.22 g L⁻¹ for Penicillin V and 0.32 g L⁻¹ for phenoxyacetic acid and the root mean square errors of prediction for MCR-ALS were 0.23 g L⁻¹ for Penicillin V and 0.15 g L⁻¹ for phenoxyacetic acid. A general work-flow for building and assessing chemometric regression models for the quantification of multiple analytes in bioprocesses by FTIR spectroscopy is given.     

Simultaneous kinetic spectrophotometric determination of cyanide and thiocyanate using the partial least squares (PLS) regression

The partial least squares (PLS-1) calibration model based on spectrophotometric measurement, for the simultaneous determination of CN⁻ and SCN⁻ ions is described. The method is based on the difference in the rate of the reaction between CN⁻ and SCN⁻ ions with chloramine-T in a pH 4.0 buffer solution and at 30 °C. The produced cyanogen chloride (CNCl) reacts with pyridine and the product condenses with barbituric acid and forms a final colored product. The absorption kinetic profiles of the solutions were monitored by measuring absorbance at 578 nm in the time range 20-180 s after initiation of the reaction with 2 s intervals. The experimental calibration matrix for partial least squares (PLS-1) calibration was designed with 31 samples. The cross-validation method was used for selecting the number of factors. The results showed that simultaneous determination could be performed in the range 10.0-900.0 and 50.0-1200.0 ng mL⁻¹ for CN⁻ and SCN⁻ ions, respectively. The proposed method was successfully applied to the simultaneous determination of cyanide and thiocyanate in water samples.     

Multivariate NIR spectroscopy models for moisture, ash and calorific content in biofuels using bi-orthogonal partial least squares regression

The multitude of biofuels in use and their widely different characteristics stress the need for improved characterisation of their chemical and physical properties. Industrial use of biofuels further demands rapid characterisation methods suitable for on-line measurements. The single most important property in biofuels is the calorific value. This is influenced by moisture and ash content as well as the chemical composition of the dry biomass. Near infrared (NIR) spectroscopy and bi-orthogonal partial least squares (BPLS) regression were used to model moisture and ash content as well as gross calorific value in ground samples of stem and branches wood. Samples from 16 individual trees of Norway spruce were artificially moistened into five classes (10, 20, 30, 40 and 50%). Three different models for decomposition of the spectral variation into structure and noise were applied. In total 16 BPLS models were used, all of which showed high accuracy in prediction for a test set and they explained 95.4-99.8% of the reference variable variation. The models for moisture content were spanned by the O-H and C-H overtones, i.e. between water and organic matter. The models for ash content appeared to be based on interactions in carbon chains. For calorific value the models was spanned by C-H stretching, by O-H stretching and bending and by combinations of O-H and C-O stretching. Also -C=C- bonds contributed in the prediction of calorific value. This study illustrates the possibility of using the NIR technique in combination with multivariate calibration to predict economically important properties of biofuels and to interpret models. This concept may also be applied for on-line prediction in processes to standardize biofuels or in biofuelled plants for process monitoring.     

Prediction of humic acid content and respiration activity of biogenic waste by means of Fourier transform infrared (FTIR) spectra and partial least squares regression (PLS-R) models

Fourier transform infrared (FTIR) spectroscopy has been proven to be an appropriate analytical method for the qualitative assessment of compost stability. This study focuses on quantitative determination of two time-consuming parameters: humic acid (HA) contents and respiration activity. Reactivity/stability and humification were quantified by respiration activities (oxygen uptake) and humic acid contents. These features are also reflected by a specific infrared spectroscopic pattern. Based on this relationship partial least squares regression (PLS-R) models for the prediction of respiration activities and humic acid contents were calculated. Characteristic wavenumber regions that are assigned to the biological/chemical parameter were selected for multivariate data analysis. The coefficient of determination (R²) obtained for the humic acid prediction model from infrared spectra was 87% with a root mean square error of cross-validation (RMSECV) of 2.6% organic dry matter (ODM). The prediction model for respiration activity resulted in a R² of 94% and a RMSECV for oxygen uptake of 2.9 mg g⁻¹ dry matter (DM).     

Quantifying silica in filter-deposited mine dusts using infrared spectra and partial least squares regression

The feasibility of measuring airborne crystalline silica (α-quartz) in noncoal mine dusts using a direct-on-filter method of analysis is demonstrated. Respirable α-quartz was quantified by applying a partial least squares (PLS) regression to the infrared transmission spectra of mine-dust samples deposited on porous polymeric filters. This direct-on-filter method deviates from the current regulatory determination of respirable α-quartz by refraining from ashing the sampling filter and redepositing the analyte prior to quantification using either infrared spectrometry for coal mines or x-ray diffraction (XRD) from noncoal mines. Since XRD is not field portable, this study evaluated the efficacy of Fourier transform infrared spectrometry for silica determination in noncoal mine dusts. PLS regressions were performed using select regions of the spectra from nonashed samples with important wavenumbers selected using a novel modification to the Monte Carlo unimportant variable elimination procedure. Wavenumber selection helped to improve PLS prediction, reduce the number of required PLS factors, and identify additional silica bands distinct from those currently used in regulatory enforcement. PLS regression appeared robust against the influence of residual filter and extraneous mineral absorptions while outperforming ordinary least squares calibration. These results support the quantification of respirable silica in noncoal mines using field-portable infrared spectrometers.

Analysis of elements in wine using near infrared spectroscopy and partial least squares regression

The use of visible (VIS) and near infrared spectroscopy (NIRS) to measure the concentration of elements in Australian wines was investigated. Both white (n=32) and red (n=94) wine samples representing a wide range of varieties and regions were analysed by inductively coupled plasma mass spectrometry (ICP-MS) for the concentrations of calcium (Ca), potassium (K), magnesium (Mg), phosphorus (P), sodium (Na), sulphur (S), iron (Fe), boron (B) and manganese (Mn). Samples were scanned in transmittance mode (1mm path length) in a monochromator instrument (400-2500nm). The spectra were pre-treated by second derivative and standard normal variate (SNV) prior to developing calibration models using partial least squares (PLS) regression method with cross-validation. The highest coefficients of determination in cross-validation (R(val)(2)) and the lowest errors of cross-validation (SECV) were obtained for Ca (0.90 and 9.80mgL(-1)), Fe (0.86 and 0.65mgL(-1)) and for K (0.89 and 147.6mgL(-1)). Intermediate R(val)(2) (<0.80) and SECV were obtained for the other minerals analysed. The results showed that some macro- and microelements present in wine might be measured by VIS-NIRS spectroscopy.     

Incorporating interactions in multi‐block sequential and orthogonalised partial least squares regression

This paper is about how to incorporate interaction effects in multi‐block methodologies. The method proposed is inspired by polynomial regression modelling in the case with only a few independent variables but extends/generalises the idea to situations where the blocks are potentially very large with respect to the number of variables. The method follows a so‐called type I sums of squares strategy where the linear effects (main effects) are incorporated sequentially and before the interactions. The sequential and orthogonalised partial least squares (SO‐PLS) technique is used as a basis for the proposal. The SO‐PLS method is based on sequential estimation of each new block by the PLS regression method after orthogonalisation with respect to blocks already fitted. The new method preserves the invariance already established for SO‐PLS and can be used for blocks with different dimensionality. The method is tested on one real data set with two independent blocks with different complexity and on a simulated data set with a large number of variables in each block. Copyright © 2011 John Wiley & Sons, Ltd.     

Comparison between ordinary least squares regression and weighted least squares regression in the calibration of metals present in human milk determined by ICP-OES

In this study we compared the use of ordinary least squares and weighted least squares in the calibration of the method for analyzing essential and toxic metals present in human milk by ICP-OES, in order to avoid systematic errors in the measurements used. Human milk samples were provided by maternity clinic Odete Valadares and digested by means of a high-performance microwave (MW) oven. Evaluation of plasma short and long-term stability was made using a solution of digested milk (1:50) with 2.0 mg L⁻¹ Mg in HNO₃ 2% (v/v). The detection power resulted to be at or below the μg L⁻¹ level, whilst the precision expressed as relative standard deviation R.S.D. was almost always equal to or better than 3.3%. Certified reference material Infant Formula (NIST SRM 1846) was used to assess the accuracy of the proposed method, which proved to be accurate and precise. Recovery rates were in the range of 83-117%. Aqueous calibration was carried out for each element under study.     

Quantitative determination of polyphosphate in sediments using Attenuated Total Reflectance-Fourier Transform Infrared (ATR-FTIR) spectroscopy and partial least squares regression

Phosphorus (P) is a major cause of eutrophication and subsequent loss of water quality in freshwater ecosystems. A major part of the flux of P to eutrophic lake sediments is organically bound or of biogenic origin. Despite the broad relevance of polyphosphate (Poly-P) in bioremediation and P release processes in the environment, its quantification is not yet well developed for sediment samples. Current methods possess significant disadvantages because of the difficulties associated with using a single extractant to extract a specific P compound without altering others. A fast and reliable method to estimate the quantitative contribution of microorganisms to sediment P release processes is needed, especially when an excessive P accumulation in the form of polyphosphate (Poly-P) occurs. Development of novel approaches for application of emerging spectroscopic techniques to complex environmental matrices such as sediments significantly contributes to the speciation models of P mobilization, biogeochemical nutrient cycling and development of nutrient models. In this study, for the first time Attenuated Total Reflectance-Fourier Transform Infrared (ATR-FTIR) spectroscopy in combination with partial least squares (PLS) was used to quantify Poly-P in sediments. To reduce the high absorption matrix components in sediments such as silica, a physical extraction method was developed to separate sediment biological materials from abiotic particles. The aim was to achieve optimal separation of the biological materials from sediment abiotic particles with minimum chemical change in the sample matrix prior to ATR-FTIR analysis. Using a calibration set of 60 samples for the PLS prediction models in the Poly-P concentration range of 0-1 mg g(-1) d.w. (dry weight of sediment) (R(2) = 0.984 and root mean square error of prediction RMSEP = 0.041 at Factor-1) Poly-P could be detected at less than 50 μg g(-l) d.w. Using this technique, there is no solvent extraction or chemical treatment required, sample preparation is minimal and simple, and the analysis time is greatly reduced. The results from this study demonstrated the potential of ATR FT-IR spectroscopy as an alternative method to study Poly-P in sediments.