PLS1 Algorithm Research Articles

Dual-sPLS: A family of Dual Sparse Partial Least Squares regressions for feature selection and prediction with tunable sparsity; evaluation on simulated and near-infrared (NIR) data

Relating a set of variables X to a response y is crucial in chemometrics. A quantitative prediction objective can be enriched by qualitative data interpretation, for instance by locating the most influential features. When high-dimensional problems arise, dimension reduction techniques can be used. Most notable are projections (e.g. Partial Least Squares or PLS ) or variable selections (e.g. lasso). Sparse partial least squares combine both strategies, by blending variable selection into PLS. The variant presented in this paper, Dual-sPLS, generalizes the classical PLS1 algorithm. It provides balance between accurate prediction and efficient interpretation. It is based on penalizations inspired by classical regression methods (lasso, group lasso, least squares, ridge) and uses the dual norm notion. The resulting sparsity is enforced by an intuitive shrinking ratio parameter. Dual-sPLS favorably compares to similar regression methods, on simulated and real chemical data.

Adaptive Reweighted Minimum Vector Variance Estimator of Covariance Used for as a New Robust Approach to Partial Least Squares Regression

Partial Least Squares Regression (PLSR), which is developed as partial type of the least squares estimator of regression in case of multicollinearity existence among independent variables, is a linear regression method. If there are outliers in data set, robust methods can be applied for diminishing or getting rid of the negative impacts of them. Past studies have shown that if the covariance matrix is appropriately robustified, PLS1 algorithm (PLSR for one dependent variable) becomes robust against outliers. In this study, an adaptive reweighted estimator of covariance based on Minimum Vector Variance as the first estimator is used and a new robust PLSR method: “PLS-ARWMVV“ is introduced. PLS-ARWMVV is compared with ordinary PLSR and four popular robust PLSR methods. The simulation and real data application are revealed that if there are contaminated observations, proposed robust PLS-ARWMVV is robust and efficient. It generally performs better than robust PRM and good alternative for other robust PLS-KurSD, RSIMPLS and PLS-SD methods.

Identification and Quantification of Adulterants in Coffee (Coffea arabica L.) Using FT-MIR Spectroscopy Coupled with Chemometrics.

Food adulteration is an illegal practice performed to elicit economic benefits. In the context of roasted and ground coffee, legumes, cereals, nuts and other vegetables are often used to augment the production volume; however, these adulterants lack the most important coffee compound, caffeine, which has health benefits. In this study, the mid-infrared Fourier transform spectroscopy (FT-MIR) technique coupled with chemometrics was used to identify and quantify adulterants in coffee (Coffea arabica L.). Coffee samples were adulterated with corn, barley, soy, oat, rice and coffee husks, in proportions ranging from 1–30%. A discrimination model was developed using the soft independent modeling of class analogy (SIMCA) framework, and quantitative models were developed using such algorithms as the partial least squares algorithms with one variable (PLS1) and multiple variables (PLS2) and principal component regression (PCR). The SIMCA model exhibited an accuracy of 100% and could discriminate among all the classes. The quantitative model with the highest performance corresponded to the PLS1 algorithm. The model exhibited an R2c: ≥ 0.99, standard error of calibration (SEC) of 0.39–0.82, and standard error of prediction (SEP) of 0.45–0.94. The developed models could identify and quantify the coffee adulterants, and it was considered that the proposed methodology can be applied to identify and quantify the adulterants used in the coffee industry.

Prediction of coumarin and ethyl vanillin in pure vanilla extracts using MID-FTIR spectroscopy and chemometrics

Fourier transform mid-infrared (MID-FTIR) spectroscopy coupled with chemometric analysis was used to identify and quantify coumarin (CMR) and ethyl vanillin (EVA) adulterations in pure vanilla extracts. Forty samples adulterated with CMR (0.25–10 ppm) and forty with EVA (0.25–10%) were prepared from pure vanilla extracts and characterized by MID-FTIR spectroscopy to develop chemometric models. Additionally, six commercial vanilla samples were analyzed. A soft independent modeling of class analogy (SIMCA) model was developed to identify and classify the purity from EVA-adulterated or CMR-adulterated samples. Prediction models for CMR or EVA content were developed using the principal component regression (PCR), partial least squares with single y-variables (PLS1), and with multiple y-variables (PLS2) algorithms. Moreover, the predictions of the best quantification chemometric model were compared with the results of a high-performance liquid chromatography-diode array detector (HPLC-DAD) method to evaluate the accuracy of the prediction. The PLS1 algorithm had better performance using 3 and 8 factors for EVA and CMR, respectively. The SIMCA model showed 100% recognition and rejections rates. The results demonstrate that adulteration of pure vanilla with EVA and CMR could be successfully predicted by the developed technique.

Chemical composition and antioxidant capacity in strawberry cultivars (Fragaria x ananassa Duch.) by FT-MIR spectroscopy and chemometrics

ABSTRACTFT-MIR spectroscopy coupled to chemometrics can be an alternative technique to conventional methods to determine the chemical composition of berries such as strawberry. This study developed chemometric models based on FT-MIR spectroscopy to identify strawberry cultivars at seven stages of ripening and quantify the main attributes involved in sensory quality of strawberry fruits (total soluble solids, total acidity, reducing sugars, pH) and the main bioactive compounds involved in antioxidant capacities (ascorbic acid, phenolics, flavonoids, anthocyanins). PCR, PLS1 and PLS2 algorithms were used to develop the prediction models. PLS1 algorithm developed excellent predictions with Rc2 -greater than 0.90. SIMCA model identified the cultivars with 99% confidence. Unlike conventional methods, FT-MIR allowed us to analyze simultaneously the attributes of quality, bioactive compounds, and antioxidant capacity of strawberries fruits in a fast and reliable way without the use of reagents and/or solvents, which considerably reduces the time and cost of the analyzes.

Development of an electrochemical biosensor for the determination of triglycerides in serum samples based on a lipase/magnetite-chitosan/copper oxide nanoparticles/multiwalled carbon nanotubes/pectin composite

A very sensitive electrochemical biosensor to determine totals triglycerides (TGs) in serum samples has been developed. It is based on the electrochemical oxidation of glycerol at glassy carbon electrodes modified with magnetic nanoparticles bonded to lipase enzyme and copper oxide nanoparticles, both supported on a multiwalled carbon nanotubes/pectin dispersion. Glycerol is produced by enzymatic reaction between the TGs present in samples and the lipase immobilized. The quantification of triglycerides was performed by amperometric measurements. The proposed electrochemical biosensor improves the performance of others methods developed for the TGs quantification. The determination of TGs does not need a pretreatment of serum samples. The PLS-1 algorithm was used for the quantification of TGs. According to this algorithm, the of detection and quantification limits were from 3.2 × 10−3 g L−1 to 3.6 × 10−3 g L−1, and from 9.6 × 10−3 to 1.1 × 10−2 g L−1, respectively. The sensitivity was 1.64 × 10−6 A L g−1. The proposed electrochemical biosensor exhibited a very good performance, a stability of 20 days, very good reproducibility and repeatability, and it is presented as a very good alternative for the determination of TGs in human serum clinical samples.

Generalization of Powered–Partial-Least-Squares

Indahl originally proposed a variant to Wold's PLS1 algorithm in which weight coefficients were all modified by an exponent coefficient. This led to Powered-PLS (P-PLS). The aim of this paper is to revisit Indahl's P-PLS algorithm in order to make a robust and fast regression methodology calculating easy to interpret models. We first demonstrate that P-PLS is in fact a regression based on correlation maximization, but constrained by weight coefficients originally calculated in standard PLS1. From that, we propose a generalization of P-PLS by replacing the power transformation function by β Cumulative Density Functions (β-CDFs), leading to our proposed regression methodology called β-PLS. With two public datasets, we demonstrate that P-PLS and even more β-PLS regressions outperform standard PLS1 in terms of cross-validation performances in the case where the number of calibration observations is largely lower than the number of variables in X.

Quantitative Analysis of Hexahydro-1,3,5-trinitro-1,3,5, Triazine/Pentaerythritol Tetranitrate (RDX-PETN) Mixtures by Terahertz Time Domain Spectroscopy.

Absorption spectra of explosives such as hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX), pentaerythritol tetranitrate (PETN), and mixtures of both were measured by terahertz time domain spectroscopy (THz-TDS). Chemometrics was applied to quantitative analysis of terahertz absorbance spectra obtained in transmission mode to predict the relative amounts of RDX and PETN in samples containing pure components or their mixtures. This analysis was challenging because significant spectral overlap prevented identification of each product fingerprint. Partial least squares (PLS) regression models were thus applied to the terahertz spectra. A comparison between the so-called PLS1 and PLS2 algorithms was performed to predict the PETN concentrations in mixture samples. PLS2 demonstrated better predictive ability than PLS1 with RMSE value lower than 3.5 mg for 400 mg total weight pellets. Moreover, the influence of the highly overlapping spectral frequency band was investigated by reducing the original 0.2-3 THz (6-100 cm(-1)) spectral band to 1.8-3 THz (60-100 cm(-1)). The predictive ability was quite similar in both cases, highlighting the excellent ability of chemometrics to perform quantitative analysis when applied to THz-TDS data, even in the case of highly overlapping spectra.

Application of MIR-FTIR spectroscopy and chemometrics to the rapid prediction of fish fillet quality

Fourier transform mid-infrared spectroscopy (MIR-FTIR) and a partial least square algorithm (PLS-1) were used to predict the deterioration indices, pH, and chemical composition of Atlantic bluefin tuna, crevalle jack, and Atlantic Spanish mackerel chilled fillets. To build calibration models, 90 samples from the 3 fish species were analysed to different seasons and were stored for various times. The performance of the regression models was evaluated based on the coefficients of determination (R2), residual predictive deviation of cross-validation (RPDcv), and percentage relative difference (% RD). Chemometric models provided good reliability in the prediction of the chemical composition (R2 between 0.969 and 0.992, RPDcv between 5.01 and 5.59%), the pH (R2 = 0.987, RPDcv = 7.18), and can be used for screening of deterioration indices (R2 between 0.944 and 0.969, RPDcv between 3.21 and 3.67%). The results demonstrated that the MIR-FTIR coupled with the PLS-1 algorithm could be simultaneously applied to predict the chemical parameters of chilled fillets of three fish species.

Genetic algorithm based multi-objective least square support vector machine for simultaneous determination of multiple components by near infrared spectroscopy

The near infrared (NIR) spectrum contains a global signature of composition, and enables to predict different proper ties of the material. In the present paper, a genetic algorithm and an adaptive modeling technique were applied to build a multiobjective least square support vector machine (MLS-SVM), which was intended to simultaneously determine the concentrations of multiple components by NIR spectroscopy. Both the benchmark corn dataset and self-made Forsythia suspense dataset were used to test the proposed approach. Results show that a genetic algorithm combined with adaptive modeling allows to efficiently search the LS-SVM hyperparameter space. For the corn data, the performance of multi-objective LS-SVM was significantly better than models built with PLS1 and PLS2 algorithms. As for the Forsythia suspense data, the performance of multi-objective LS-SVM was equivalent to PLS1 and PLS2 models. In both datasets, the over-fitting phenomena were observed on RBFNN models. The single objective LS-SVM and MLS-SVM didn't show much difference, but the one-time modeling convenience al lows the potential application of MLS-SVM to multicomponent NIR analysis.

The geometry of PLS1 explained properly: 10 key notes on mathematical properties of and some alternative algorithmic approaches to PLS1 modelling

The insight from, and conclusions of this paper motivate efficient and numerically robust ‘new’ variants of algorithms for solving the single response partial least squares regression (PLS1) problem. Prototype MATLAB code for these variants are included in the Appendix. The analysis of and conclusions regarding PLS1 modelling are based on a rich and nontrivial application of numerous key concepts from elementary linear algebra. The investigation starts with a simple analysis of the nonlinear iterative partial least squares (NIPALS) PLS1 algorithm variant computing orthonormal scores and weights.A rigorous interpretation of the squared P‐loadings as the variable‐wise explained sum of squares is presented. We show that the orthonormal row‐subspace basis of W‐weights can be found from a recurrence equation. Consequently, the NIPALS deflation steps of the centered predictor matrix can be replaced by a corresponding sequence of Gram–Schmidt steps that compute the orthonormal column‐subspace basis of T‐scores from the associated non‐orthogonal scores.The transitions between the non‐orthogonal and orthonormal scores and weights (illustrated by an easy‐to‐grasp commutative diagram), respectively, are both given by QR factorizations of the non‐orthogonal matrices. The properties of singular value decomposition combined with the mappings between the alternative representations of the PLS1 ‘truncated’ X data (including PtW) are taken to justify an invariance principle to distinguish between the PLS1 truncation alternatives. The fundamental orthogonal truncation of PLS1 is illustrated by a Lanczos bidiagonalization type of algorithm where the predictor matrix deflation is required to be different from the standard NIPALS deflation.A mathematical argument concluding the PLS1 inconsistency debate (published in 2009 in this journal) is also presented. Copyright © 2014 John Wiley & Sons, Ltd.

Potentiometric Sensor Array for Analysis of Complex Rare Earth Mixtures

AbstractAn approach for simultaneous quantification of several rare earth elements (RE) in complex mixtures, using an array of cross‐sensitive potentiometric sensors with plasticized polymeric membranes, is reported. 14 different ligands suggested in liquid extraction systems for separation of lanthanides/actinides were employed as membrane active compounds in the polymeric sensors. The sensors of the array were found to have high potentiometric sensitivity towards lanthanide ions in acidic solutions with pH 1.5. The array of 28 sensors was applied for simultaneous determination of three RE metals in four sets of model mixtures simulating technological solutions of spent nuclear fuel reprocessing process. Multivariate calibration models calculated with PLS1 algorithm revealed that analysis of Y, La and Gd in mixtures with uranyl nitrate is possible with RMSEP values 0.29, 0.17 and 0.28 logCMe correspondingly (confirmed by independent test set). Determination of Nd, Sm and Gd in mixtures with uranyl (RMSEP=0.25–0.26 logCMe) and with thorium (RMSEP=0.28–0.37 logCMe) is also possible.

Mixture quantification using PLS in plastic scintillation measurements

This article reports the capability of plastic scintillation (PS) combined with multivariate calibration (Partial least squares; PLS) to detect and quantify alpha and beta emitters in mixtures. While several attempts have been made with this purpose in mind using liquid scintillation (LS), no attempt was done using PS that has the great advantage of not producing mixed waste after the measurements are performed. Following this objective, ternary mixtures of alpha and beta emitters ((241)Am, (137)Cs and (90)Sr/(90)Y) have been quantified. Procedure optimisation has evaluated the use of the net spectra or the sample spectra, the inclusion of different spectra obtained at different values of the Pulse Shape Analysis parameter and the application of the PLS1 or PLS2 algorithms. The conclusions show that the use of PS+PLS2 applied to the sample spectra, without the use of any pulse shape discrimination, allows quantification of the activities with relative errors less than 10% in most of the cases. This procedure not only allows quantification of mixtures but also reduces measurement time (no blanks are required) and the application of this procedure does not require detectors that include the pulse shape analysis parameter.

Simultaneous voltammetric determination of levodopa, carbidopa and benserazide in pharmaceuticals using multivariate calibration

An analytical methodology based on differential pulse voltammetry (DPV) on a glassy carbon electrode and the partial least-squares (PLS-1) algorithm for the simultaneous determination of levodopa, carbidopa and benserazide in pharmaceutical formulations was developed and validated. Some sources of bi-linearity deviation for electrochemical data are discussed and analyzed. The multivariate model was developed as a ternary calibration model and it was built and validated with an independent set of drug mixtures in presence of excipients, according with manufacturer specifications. The proposed method was applied to both the assay and the uniformity content of two commercial formulations containing mixtures of levodopa–carbidopa (10:1) and levodopa–benserazide (4:1). The results were satisfactory and statistically comparable to those obtained by applying the reference Pharmacopoeia method based on high performance liquid chromatography. In conclusion, the methodology proposed based on DPV data processed with the PLS-1 algorithm was able to quantify simultaneously levodopa, carbidopa and benserazide in its pharmaceuticals formulations using a ternary calibration model for these drugs in presence of excipients. Furthermore, the model appears to be successful even in the presence of slight potential shifts in the processed data, which have been taken into account by the flexible chemometric PLS-1 approach.

Laser-Induced Breakdown Spectroscopy of Steel: A Comparison of Univariate and Multivariate Calibration Methods

Laser-induced breakdown spectroscopy (LIBS) was carried out on twenty-three low to high alloy steel samples to quantify their concentrations of chromium, nickel, and manganese. LIBS spectral data were correlated to known concentrations of the samples and three calibration methods were compared. A standard LIBS calibration technique using peak area integration normalized by an internal standard was compared to peak area integration normalized by total light and the multivariate statistical technique of partial least squares. For the partial least squares analysis, the PLS-1 algorithm was used, where a predictive model is generated for each element separately. Partial least squares regression coefficients show that the algorithm correctly identifies the atomic emission peaks of interest for each of the elements. Predictive capabilities of each calibration approach were quantified by calculating the standard and relative errors of prediction. The performance of partial least squares is on par with using iron as an internal standard but has the key advantage that it can be applied to samples where the concentrations of all elements are unknown.

A comparison of nine PLS1 algorithms

AbstractNine PLS1 algorithms were evaluated, primarily in terms of their numerical stability, and secondarily their speed. There were six existing algorithms: (a) NIPALS by Wold; (b) the non‐orthogonalized scores algorithm by Martens; (c) Bidiag2 by Golub and Kahan; (d) SIMPLS by de Jong; (e) improved kernel PLS by Dayal; and (f) PLSF by Manne. Three new algorithms were created: (g) direct‐scores PLS1 based on a new recurrent formula for the calculation of basis vectors yielding scores directly from X and y; (h) Krylov PLS1 with its regression vector defined explicitly, using only the original X and y; (i) PLSPLS1 with its regression vector recursively defined from X and the regression vectors of its previous recursions. Data from IR and NIR spectrometers applied to food, agricultural, and pharmaceutical products were used to demonstrate the numerical stability. It was found that three methods (c, f, h) create regression vectors that do not well resemble the corresponding precise PLS1 regression vectors. Because of this, their loading and score vectors were also concluded to be deviating, and their models of X and the corresponding residuals could be shown to be numerically suboptimal in a least squares sense. Methods (a, b, e, g) were the most stable. Two of them (e, g) were not only numerically stable but also much faster than methods (a, b). The fast method (d) and the moderately fast method (i) showed a tendency to become unstable at high numbers of PLS factors. Copyright © 2009 John Wiley & Sons, Ltd.

Preliminary studies about thermal degradation of edible oils through attenuated total reflectance mid-infrared spectrometry

Degradation of edible oils during their heating process has been evaluated through the determination of cis-unsaturation and trans-fatty acids together with free fatty acids as a function of time and temperature heating. Two types of cooking oils, sunflower and seed (mixture of different seeds non-detailed), were heated at three different temperatures (147, 171 and 189 °C) during a total time of 1920 min (32 h) shared out in four sessions of 8 h each one, and samples were studied from their spectra obtained by Fourier transform infrared spectrometry using attenuated total reflectance measurements. A critical comparison between different multivariate calibration models built based on full spectra or selected wavenumbers, using both PLS1 and PLS2 algorithms, was carried out for a preliminary evaluation of the heating conditions (temperature and time) of oil samples.

A twist to partial least squares regression

AbstractA modification of the PLS1 algorithm is presented. Stepwise optimization over a set of candidate loading weights obtained by taking powers of the y–X correlations and X standard deviations generalizes the classical PLS1 based on y–X covariances and hence adds flexibility to the modelling. When good linear predictions can be obtained, the suggested approach often finds models with fewer and more interpretable components. Good performance is demonstrated when compared with the classical PLS1 on calibration benchmark data sets. An important part of the comparisons is managed by a novel model selection strategy. The selection is based on choosing the simplest model among those with a cross‐validation error smaller than the pre‐specified significance limit of a χ2‐statistic. Copyright © 2005 John Wiley & Sons, Ltd.

Partial least-squares regression for the simultaneous determination of aluminum and beryllium in geochemical samples using xylenol orange

A partial least-squares regression (PLS) was developed for the simultaneous spectrophotometric determination of aluminum and beryllium in geochemical samples by xylenol orange as the chromogenic reagent in water media and in micellar media. The effects of pH, xylenol orange concentration and surfactant concentration on the complexes formation reactions were studied. In the absence of surfactant the complex color development takes place at 2 h after mixing the reagents. By using CTAB as micellar media the complexes formation was improved and the rate of the complexation reactions increased. By using PLS-1 algorithm satisfactory results were obtained. The proposed procedure showed to be useful for prediction of Al and Be values from 0.1 to 1.0 mg L −1.

Simultaneous Determination of Hydrocortisone and Zn-Bacitracin by Spectrophotometric Derivative and Multivariate Methods

Four spectrophotometric methods are described and applied to resolve binary mixtures of the corticosteroid hydrocortisone and the antibacterial polypeptide Zn-Bacitracin. The simultaneous determination of the two compounds was accomplished by means of derivative methods, which were satisfactory used to determine synthetic mixtures of these compounds in different ratios and in pharmaceutical preparations (only for hydrocortisone). Direct absorption spectra of compounds were used to optimise the spectral data set performs the calibration by PLS-1, PLS-2 and PCR algorithms. These calibration models were evaluated through internal validation (prediction of compounds in its own designed training set of calibration), cross-validation (obtaining statistical parameters that show the efficiency for a calibration fit model) and external validation over synthetic and pharmaceutical mixtures. The four described procedures do not require any separation step. Precision studies were achieved over two series of ten standards for each compound showing no significant differences at 95% confidence level in the two spectrophotometric methods. The results found in commercial products were compared with those obtained by means of MEKC method and similar values were found.