Unfolded Partial Least-squares Research Articles

Enantiomeric purity determination of lactofen formulations through Chemometric Deconvolution of partially overlapped chromatographic profiles

Lactofen is a chiral restricted-use herbicide, classified as toxicity class I by the Environmental Protection Agency (EPA), commonly used to control broadleaved weeds. While the observed herbicidal activity mostly derives from the (S)-(+)-enantiomer, formulations have been manufactured as a mixture of both enantiomers. In this work, we present a quantitative method for the enantiomeric determination of lactofen in commercial formulations based on the development of a second-order calibration to assist the selectivity of chiral separation under reversed-phase liquid chromatographic mode coupled to diode array detection. Chromatographic conditions were aimed to minimize analysis time and solvent consumption. This approach is feasible because second-order calibration allows for the quantification of overlapping bands and analytes in the presence of interferences. Chromatographic-spectral matrices were processed by unfolded partial least-squares coupled to residual bilinearization. The proposed methodology was evaluated through validation samples, achieving relative errors of predictions of 2–4 %. Finally, commercial formulations were subjected to minimal sample treatment and analyzed, and figures of merit for real samples were determined. The described methodology results suitable for the determination of enantiomeric purity and quality control in commercial lactofen formulations.

Fiber optic fluorescence as non-invasive tool to monitor the ripening process of cheeses: Torta del casar and Queso de la Serena

In this work, the use of excitation-emission fluorescence matrices (EEMs) has been addressed to differentiate two kinds of cheeses with protected designations of origin (PDO), “Torta del Casar” and “Queso de la Serena”. The fluorescence signals were recorded directly on cheese samples during the ripening process, by using a fiber optic assembled to the fluorescence spectrometer, and the data were subjected to analysis by the multivariate algorithm parallel factor analysis (PARAFAC). PARAFAC analysis identified the presence of three fluorophores in both cheeses. The scores of the two first components, attributed to the presence of tryptophane, decreased as the ripening time increased. However, the third component, related to retinol (vitamin A), remains almost constant along the ripening period. EEMs of the samples of the two types of cheese were similar in the initial days of the maturation periods. However, when only the samples from day 36 onwards were considered, it was possible to differentiate them with high precision by PARAFAC in combination with linear discriminant analysis (LDA).In addition, a model was built for the quantification of vitamin A and α-tocopherol (vitamin E), by using the EEMs combined with the multivariate unfolded partial least squares (UPLS) algorithm.

A ratiometric carbon dots/AgInS2 quantum dots sensing probe for the kinetic determination of histamine resorting to N-PLS chemometric model

Biogenic amines are compounds that play several crucial roles in the human body but can also cause serious health problems when present at high concentrations in foodstuffs. Therefore, it is important to develop rapid, simple, cost-effective, and reliable analytical techniques for their monitoring, acting as indicators of food quality and preventing potential risks. In this sense, carbon dots and 3-mercaptopropionic acid (MPA)-capped AgInS2 (AIS) quantum dots were used as fluorescent probes to implement a ratiometric sensing platform, coupled to chemometrics, for the kinetic fluorometric determination of histamine in foodstuffs using second-order data. The obtained data were analysed through unfolded partial least squares (U-PLS) and N-way partial least squares (N-PLS). The model optimization revealed that the application of N-PLS yielded the best results and that a kinetic spectral acquisition for 5 minutes was enough to ensure reliable measurements. The developed method was evaluated using spiked samples of different complex matrices (tuna, tomato and hake fish), at different concentration levels, and the obtained results, in terms of figures of merit, confirmed its suitability, accuracy and effectiveness. In fact, a relative percentage error below 10%, with a coefficient of determination for the prediction higher than 0.9, was obtained, together with a LOD and LOQ of 1.26 and 3.80 mg L−1, respectively, which are much lower than the maximum threshold value established by European Union legislation for histamine in fishery products (200 mg kg−1). These results were obtained with samples containing uncalibrated species and without using toxic reagents, which attest the suitability of the procedure. Globally, the developed methodology proved to be accurate and much simpler and faster than the reference procedures.

Kinetic Determination of Acetylsalicylic Acid Using a CdTe/AgInS2 Photoluminescence Probe and Different Chemometric Models

The combination of multiple quantum dots (QDs) in a multi-emitter nanoprobe can be envisaged as a promising sensing scheme, as it enables obtaining a collective response of individual emitters towards a given analyte and allows for achieving specific analyte-response profiles. The processing of these profiles using adequate chemometric methods empowers a more sensitive, reliable and selective determination of the target analyte. In this work, we developed a kinetic fluorometric method consisting of a dual CdTe/AgInS2 quantum dots photoluminescence probe for the determination of acetylsalicylic acid (ASA). The fluorometric response was acquired as second-order time-based excitation/emission matrices that were subsequently processed using chemometric methods seeking to assure the second-order advantage. The data obtained in this work are considered second-order data as they have a three-dimensional size, I × J × K (where I represents the samples' number, J the fluorescence emission wavelength while K represents the time). In order to select the most adequate chemometric method regarding the obtained data structure, different chemometric models were tested, namely unfolded partial least squares (U-PLS), N-way partial least squares (N-PLS), multilayer feed-forward neural networks (MLF-NNs) and radial basis function neural networks (RBF-NNs).

Monitoring of Chlorophylls during the Maturation Stage of Plums by Multivariate Calibration of RGB Data from Digital Images

The methodology developed in this study was based on digital imaging processing of plums harvested in eight different weeks during their ripening process. Mean RGB data, histograms, and matrices of RGB data were used to characterise the ripening stage of the plums, in both qualitative and quantitative approaches, by using classification and quantification chemometric methods. An exploratory analysis of data was performed using principal component analysis (PCA) and parallel factor analysis (PARAFAC) in RGB histograms and matrices data, respectively, showing differences in the colour features since the fourth week of harvesting. In the case of the quantitative approach, high correlation was achieved between the histogram data, using partial least squares (PLS), and total chlorophyll content. In addition, between three-way matrixes and total chlorophyll content, good correlations were obtained applying unfolded-PLS (U-PLS) and N-way-PLS (N-PLS). The most accurate results were obtained on the green channel. Analytical parameters obtained were good, with determination coefficients (R2) higher than 0.91 for all models in the first and second-order multivariate analysis. In addition, relative errors of prediction (REPs) were lower than 12% in all models for the green channel. Therefore, the proposed method was a satisfactory alternative to destructive physiological and biochemical methods in the determination of total chlorophylls in plum samples. In the routine analysis, first-order multivariate calibration with PLS analysis is a good option due to the simplicity of data processing.

Fluorescence Monitoring Oxidation of Extra Virgin Olive Oil Packed in Different Containers.

'Picual' olive oil was stored in different types of containers for 10 months and monitored via quality parameters. In combination with the mentioned analysis, non-destructive fluorescence spectroscopy was performed combined with multivariate analysis to monitor and quantify oil quality levels. Excitation emission matrices (EMMs) were analyzed using parallel factor analysis (PARAFAC). According to the quality parameters, it was observed that Transparent Crystal (TC) and Opaque Crystal (OC) samples were the ones that deteriorated faster due to their higher exposure to light in comparison with Plastic (P) and Canned (C) samples. In a fast and non-destructive manner, the fluorescence spectroscopy-based prototype successfully monitored the oxidation changes in the EVOOs. Unfolded partial least squares (U-PLS) was used to generate a regression model to quantify quality parameters. Good correlation coefficients were found for the peroxide index, K232 and the oxidative stability index (r2 between 0.90 and 0.94 for cross-validation and validation). For all of that, the results obtained confirmed the ability of fluorescence spectroscopy to monitor the quality of olive oil and EEMs combined with U-PLS can be used to analyze these parameters, eluding the classical methods.

Tensor partial least squares for hyperspectral image classification

A hyperspectral image is classically a three-way (or tensor) block of data. In order to extract information from it, it has to be classified using image classifiers. Since classifiers are traditionally two-way classifiers, the hyperspectral data is unfolded into a two-way data. Processing the hyperspectral data as a two-way data often reduces the accuracy of the classification. This research explores the novel application of Tensor Partial Least Squares (TPLS) for hyperspectral image classification. TPLS has been proven to be more robust than the two-way PLS. Unlike the two-way classifiers, the TPLS utilises the hyperspectral data as a three-way (tensor) data. Two hyperspectral images of Indian Pines region in Northwest Indiana, USA and University of Pavia, Italy are used as test beds for the experiment. The results extracted by the model are the X loadings, Y loadings, X scores, and Y scores. The computed training mean r square values for Indian Pines and University of Pavia are 0.9061 ± 0.74 , and 0.9155 ± 0.63 respectively. The results of the experiment show that the TPLS performed better than the unfolded PLS, but fell short of the notable traditional classifiers.

Geographical discrimination of grapevine leaves using fibre optic fluorescence data and chemometrics. Determination of total polyphenols and chlorophylls along different vegetative stages

Auto fluorescence of grapevine leaves has been employed to discriminate vineyards from two different geographical regions and to quantify the amount of total polyphenols and chlorophylls. For that, fluorescence spectroscopy with an optical fibre was used on samples of grapevine leaves (previously freeze-dried) and excitation-emission matrices were collected. Two spectral regions were analysed independently: one with excitation wavelengths from 279 to 372 nm and emission wavelengths from 384 to 496 nm, and the second with excitation between 390 and 585 nm and the emission between 654 and 756 nm. Firstly, an exploratory analysis was performed with parallel factor analysis (PARAFAC) to extract useful information from the data (scores and loadings). The obtained scores were used to perform a linear discriminant analysis (LDA) model for the classification of samples according to its geographical region. A total of 95% of correct predictions were obtained in the validation samples. Moreover, the PARAFAC scores of the components used in each model were analysed along the vegetative stage and a clear evolution with time has been observed.The quantification of total polyphenols and chlorophylls was also carried out with unfolded partial least squares (U-PLS) and N-way partial least squares (N-PLS). Good correlation coefficients (for the validation set) were obtained for both parameters and similar results were achieved with both algorithms (0.82 (U-PLS) and 0.76 (N-PLS) for total polyphenol and 0.83 (U-PLS) and 0.82 (N-PLS) for total chlorophylls).

Chemometric-assisted kinetic determination of oxytetracycline using AgInS2 quantum dots as PL sensing platforms

In this work a kinetic fluorometric methodology relying on the time-based monitoring of the photoluminescence quenching of AgInS2 ternary quantum dots induced by oxytetracycline, was developed. The kinetic approach allowed not only to reduce the LOD and improve sensitivity and selectivity but also to collect second-order data that was explored for the quantification of the target analyte in the presence of uncalibrated interfering species.Upon processing the acquired second-order kinetic PL data by unfolded partial least-squares (U-PLS), oxytetracycline was quantified in commercially available pharmaceutical formulations. The obtained results, namely an R2P higher than 0.99 and RE lower than 8%, proved the suitability and accuracy of the developed approach.

Achieving the analytical second-order advantage with non-bilinear second-order data

Multi-way calibration based on second-order data constitutes a revolutionary milestone for analytical applications. However, most classical chemometric models assume that these data fulfil the property of low rank bilinearity, which cannot be accomplished by all instrumental methods. Indeed, various techniques are able to generate non-bilinear data, which are all potentially useful for the development of novel second-order calibration methodologies. However, the achievement of the second-order advantage in these cases may be severely limited, since methods for comprehensive modelling of non-bilinear second-order data remain only partially explored. In this research, the analytical performance of three well-known second-order models, namely non-bilinear rank annihilation (NBRA), unfolded partial least-squares with residual bilinearization (U-PLS-RBL) and multivariate curve resolution - alternating least-squares (MCR-ALS) is systematically assessed through sets of simulated and experimental non-bilinear second-order data, involving one analyte and one interferent. Although it is not possible to establish a single strategy to model any type of non-bilinear second-order data with the studied methods, each approach may lead to successful predictions under certain circumstances. It is shown that the prediction capacity is severely affected by data properties such as the level of instrumental noise, the rank of the response matrices and the signal selectivity pattern of the analyte.

Simultaneous measurement of phenols by three-way fluorescence spectroscopy: A comparison of N-PLS/RBL, U-PLS/RBL and PARAFAC.

Phenol, o-cresol, p-cresol, catechol and resorcinol are five phenolic compounds with extremely similar structure. Their fluorescence spectra are hard to be analyzed because of the serious spectral overlaps between any two of the five phenolic components in the mixture system. In this experiment, multi-dimensional partial least-squares (N-PLS), unfolded partial least-squares (U-PLS) with residual bilinearization (RBL) and parallel factor analysis (PARAFAC) are employed to analyze the three-way fluorescence spectra aiming to achieve quantitative results. Meanwhile, a contrast of these three methods is given. The experiment results show that N-PLS/RBL and U-PLS/RBL algorithms are superior to PARARFAC in terms of analysis of highly overlapping three-way fluorescence spectra for concentration determination.

Second-order calibration in combination with fluorescence fibre-optic data modelling as a novel approach for monitoring the maturation stage of plums

In this work, non-destructive autofluorescence of plums was employed to study the chlorophylls’ concentration evolution along the maturation process. For that, excitation-emission matrices (EEMs), containing full fluorescence information, were collected with a fibre-optic, assembled to a spectrofluorometer. Data analysis was performed with several second-order multi-way algorithms, such as parallel factor analysis (PARAFAC), multi-way partial least-squares (N-PLS), unfolded partial least-squares (U-PLS), and multivariate curve resolution-alternating least-squares (MCR-ALS). Firstly, the EEMs of each plum, collected each week along the maturation process, were processed with PARAFAC. Two components were used to model the data and the excitation and emission loadings were obtained. Score values for the first PARAFAC component showed a clear evolution with time, increasing during the first five weeks, and decreasing for the last weeks. Also, the chlorophyll concentrations obtained by HPLC analysis, in the skin and the whole fruit, were compared with those obtained with different algorithms mentioned before. Best results were obtained in the case of skin for all algorithms. Similar correlation coefficients (r) were obtained in all cases (0.899 (PARAFAC); 0.940 (U-PLS); 0.936 (N-PLS) and 0.958 (MCR-ALS)). When the elliptical joint confidence region (EJCR), for the slope and intercept, were calculated, the theoretically expected values of 1 and 0, for the slope and intercept, respectively, were included in all ellipses. However, it was observed that for the skin data and U-PLS and N-PLS algorithms, the EJCR confidence region was smaller than in the other cases.

Using chemometric tools to investigate the quality of three- and four-way liquid chromatographic data obtained with two different fluorescence detectors and applied to the determination of quinolone antibiotics in animal tissues

A comparison of two multi-way methodologies is presented regarding the simultaneous quantitation of several analytes in complex samples. Both protocols are based on liquid chromatography with fluorescence detection, in the following modes: (1) collecting second-order/three-way data by fluorescence emission detection at a fixed excitation wavelength, and (2) measuring third-order/four-way data through excitation-emission fluorescence matrix detection. Ten quinolone antibiotics were simultaneously analyzed in edible animal tissues such as chicken liver and bovine liver and kidney. Multivariate curve resolution - alternating least-squares (MCR-ALS) provided excellent results with the second-order strategy, with average relative prediction errors in the range 4–12% for real samples, at analyte concentrations which are compatible with the corresponding maximum residue levels. For third-order data, however, the overall MCR-ALS analytical results were worse than for second-order data (relative errors were in the range 9–23%), and one analyte was not resolved. As an alternative, unfolded partial least-squares with residual bi- and trilinearization (U-PLS/RBL and U-PLS/RTL) were applied to both second- and third-order data, with relative errors of 7–18% and 5–27% respectively. The latter errors were significantly larger than those for MCR-ALS/second-order data, although the U-PLS/RTL model permitted the detection of all analytes when processing the third-order data. Relative advantages and disadvantages of the applied procedures are discussed on the basis of the analytical performances and the specific details of the instrumental setups.

Non-destructive fluorescence spectroscopy combined with second-order calibration as a new strategy for the analysis of the illegal Sudan I dye in paprika powder

This paper presents a novel strategy for determination of the illegal dye Sudan I in paprika powder. The method is based on fluorescence spectroscopy combined with second-order calibration, which was employed for the first time for this purpose. The method is non-destructive and requires no sample preparation. It was probed that Sudan I exhibited fluorescence; however, the color of paprika samples affected the signal and it was not possible to quantify this adulterant by means of univariate and first-order calibration. To model the effect of variability of color in samples, a central composite experimental design was performed with varying ASTA (American Spices Trade Association) color values and Sudan I concentrations. Different second-order algorithms were tried for quantification. The best results for calibration and validation were obtained from Unfolded-Partial Least-Squares (U-PLS) and Multi-way Partial Least-Squares (N-PLS). The level of detection ranges were 0.4 – 3 mg/g and 0.5 – 3 mg/g for U-PLS and N-PLS, respectively. This was lower than other methods found in the literature.

Multi-attribute quality screening of immunoglobulin G using polarized Excitation Emission Matrix spectroscopy

Immunoglobulin G (IgG) is often used as a starting material for the production of functionalised antibodies, like Antibody Drug Conjugates (ADCs), PEGlyated-conjugates, or radioimmunoconjugates. The gross structural quality of the protein starting material is, therefore, an important factor in determining final product composition, purity, and quality. In terms of structural quality, one needs to know both the aggregation content and the tertiary structure of the protein. The measurement of structural quality in solution can thus be difficult, but the use of intrinsic fluorescence measurements might offer a solution because of its high sensitivity, ease of use, and when implemented in via multi-dimensional techniques like polarized Excitation Emission Matrix (pEEM) spectroscopy, its high information content.Here we demonstrate how pEEM measurements can be used as a multi-attribute screening method for protein quality using a polyclonal rabbit immunoglobulin (rIgG) model system. By using both Rayleigh scatter and fluorescence emission in combination with simple chemometric data analysis methods like Principal Component analysis (PCA) and unfolded partial least squares (U-PLS) one can simultaneously measure protein concentration, structural variance, and particle/aggregate composition. Furthermore, one can generate quantitative prediction models for non-reversible aggregation content as described by size exclusion chromatography (SEC) and obtain qualitative information about reversible aggregate content, which cannot be obtained from SEC measurements. In conclusion, the pEEM measurement approach is a potentially useful Process Analytical Technology (PAT) method for downstream processing operations in biopharmaceutical manufacturing.

Hierarchical batch-to-batch optimization of cobalt oxalate synthesis process based on data-driven model

The synthesis process has been widely used in cobalt hydrometallurgical industry. To better operate the cobalt oxalate synthesis process, a data-driven model based hierarchical batch-to-batch optimization method is presented in this work. In the upper level of hierarchy, the proposed response surface model based modifier-adaptation (MA) strategy is used to calculate the nominal control profile for the next level, and the design of dynamic experiment (DODE) method is also employed to symmetrically generate the dataset for response surface model building. In the lower level of hierarchy, the batch-wise unfolded PLS (BW-PLS) model based self-tuning batch-to-batch optimization method is utilized to further refine the control profile on the basis of the result of the upper level. The main advantages of the proposed method are: (i) the size of the dataset for data-driven model building are rather modest, (ii) the control profile can be discretized into a large number of intervals to further improve the optimization performances, and (iii) the unqualified batches is efficiently avoided during the evolution of batch-to-batch optimization. The superior performances for the cobalt oxalate synthesis process are verified through simulation study.

Classification of pre-dyed textile fibers exposed to weathering and photodegradation by non-destructive excitation-emission fluorescence spectroscopy paired with discriminant unfolded-partial least squares

Undyed textile fabrics such as Acrylic 864, Nylon 361 and Cotton 400 were pre-dyed with Basic Green 4 (BG4), Acid Yellow 17 (AY17) and Direct Blue 1 (DB1) dyes, respectively; and then exposed to two extremely diverse weather conditions in the United States: desert and humid environmental settings in Arizona (AZ) and Florida (FL) respectively, for different time intervals of exposure, which included 0, 3, 6, 9 and 12 months. After every interval of a 3 months period, ten fibers were uniformly sampled from each cloth piece, and fluorescence microscopy was employed to collect two-dimensional excitation and fluorescence spectra (2-D spectra) and three-dimensional (3D) excitation-emission matrices (EEMs). A significant loss of fluorescence intensity was observed upon fiber exposure to outdoor weathering conditions. For a comprehensive statistical data analysis and to be able to discriminate between any two single fibers weathered under different conditions, a multiway calibration algorithm known as discriminant unfolded partial least-squares (DU-PLS) method was applied to the exposed fibers. Results indicate that fluorescence spectroscopy combined with DU-PLS has the ability to appropriately classify and differentiate between any two pairs of dyed cotton or nylon fibers (acrylic in some cases) exposed to dry versus humid weather environments under different time intervals of exposure. These results provide the foundation for future studies towards a non-destructive approach capable to provide information on the weathering history of the fiber.

Spectrochromatographic determination of dorzolamide hydrochloride and timolol maleate in an ophthalmic solution using three-way analysis methods

In this study, the simultaneous spectrochromatographic determination of dorzolamide hydrochloride (DOR) and timolol maleate (TMM) in an ophthalmic formulation was performed by applying multiway resolution methods, parallel factor analysis (PARAFAC) and three way partial least squares (3W-PLS) models. In similar manner, unfolded partial least squares (U-PLS) approach was applied to the UPLC analysis of the related drugs. For the three-way resolutions, the ultra-performance liquid chromatography–photodiode array (UPLC-PDA) data array of the calibration samples and others (validation and commercial samples) containing the analyzed drugs (DOR and TMM) and thiamine hydrochloride as an internal standard (IS) was decomposed into triads or trilinear components. These three different calibration models were employed for the spectrochromatographic resolution of a commercial ophthalmic formulation of DOR and TMM and then successful quantitation results were obtained. Analysis results provided by applying three-way and two-way resolutions were statistically compared to those obtained by the newly developed standard UPLC approach. It was observed that the proposed methods gave comparable determination results for analysis of the DOR-TMM ophthalmic formulation.

Front-face fluorescence excitation-emission matrices in combination with three-way chemometrics for the discrimination and prediction of phenolic response to vineyard agronomic practices

Phenolic extracts from cv Tempranillo grapes subjected to water stress and irrigation treatment, both of them with high and low crop load, were analyzed by front-face fluorescence. Excitation-emission matrices (EEMs) were analyzed by means of unsupervised parallel factor analysis (PARAFAC), PARAFAC supervised by linear discriminant analysis, and discriminant unfolded partial least-squares. All algorithms allowed to differentiate between water stress and irrigation grape samples when the fluorescence maxima region of catechin and epicatechin, and resveratrol was considered. A central composite design was employed for the calibration of catechin, epicatechin and resveratrol. Resveratrol was quantified by U-PLS in both, irrigated and water stressed samples, and levels between 3.46 ± 0.22 and 4.67 ± 0.08 μg mL−1 and 2.43 ± 0.60 and 3.03 ± 0.10 μg mL−1, respectively, were found. PARAFAC only allowed the determination of the sum of catechin plus epicatechin (R2 = 0.9397). The determination of total catechin plus epicatechin by means of PARAFAC was successfully validated by liquid chromatography.

Fast Multiway Partial Least Squares Regression.

Multiway array decomposition has been successful in providing a better understanding of the structure underlying data and in discovering potentially hidden feature dependences serving high-performance decoder applications. However, the computational cost of multiway algorithms can become prohibitive, especially when considering large datasets, rendering them unsuitable for time-critical applications. We propose a multiway regression model for large-scale tensors with optimized performance in terms of time complexity, called fast higher order partial least squares (fHOPLS). We compare fHOPLS with its native version, higher order partial least squares (HOPLS), the state-of-the-art in multilinear regression, under different noise conditions and tensor dimensionalities using synthetic data. We also compare their performance when used for predicting scalp-recorded electroencephalography signals from invasively recorded electrocorticography signals in an oddball experiment. For the sake of exposition, we evaluated the performance of standard unfolded partial least squares (PLS) and linear regression. Our results show that fHOPLS is significantly faster than HOPLS, in particular for big data. In addition, the regression performances of fHOPLS and HOPLS are comparable and outperform both unfolded PLS and linear regression. Another interesting result is that multiway array decoding yields more accurate results than epoch-based averaging procedures traditionally used in the brain computer interfacing community.