Data-Driven Version of Multiway Soft Independent Modeling of Class Analogy (N-Way DD-SIMCA): Theory and Application.

One-class classification (OCC) is discussed in the framework of the measurement and processing of multiway data. Data-driven soft independent modeling of class analogy (DD-SIMCA) is applied in the following formats: (1) multiblock and (2) Tucker 3 N-way SIMCA, which are shown to be useful tools for solving classification tasks. A new decision rule for N-way DD-SIMCA is adopted based on the conventional two-way DD-SIMCA model. Multiblock SIMCA is shown to be useful for variable selection, and Tucker 3 SIMCA to select the optimal model complexity when applying multiway data decomposition and to assess the role of individual samples in the classification model. Both approaches, together with the two-way DD-SIMCA version applied to the unfolded data, are compared regarding the analysis of an experimental data set including genuine and adulterated blueberry extract samples. The latter were employed to produce matrix spectral-time data matrices per sample within a flow injection system, taking advantage of the spectral changes in the sample constituents as a function of the pH of the carrier phase. The need to employ the Tucker 3 model instead of a trilinear decomposition is supported by a discussion on the lack of the trilinearity property of the studied data.

Unraveling surface-enhanced Raman spectroscopy results through chemometrics and machine learning: principles, progress, and trends.

Surface-enhanced Raman spectroscopy (SERS) has gained increasing attention because it provides rich chemical information and high sensitivity, being applicable in many scientific fields including medical diagnosis, forensic analysis, food control, and microbiology. Although SERS is often limited by the lack of selectivity in the analysis of samples with complex matrices, the use of multivariate statistics and mathematical tools has been demonstrated to be an efficient strategy to circumvent this issue. Importantly, since the rapid development of artificial intelligence has been promoting the implementation of a wide variety of advanced multivariate methods in SERS, a discussion about the extent of their synergy and possible standardization becomes necessary. This critical review comprises the principles, advantages, and limitations of coupling SERS with chemometrics and machine learning for both qualitative and quantitative analytical applications. Recent advances and trends in combining SERS with uncommonly used but powerful data analysis tools are also discussed. Finally, a section on benchmarking and tips for selecting the suitable chemometric/machine learning method is included. We believe this will help to move SERS from an alternative detection strategy to a general analytical technique for real-life applications.

Chromatographic Applications in the Multi-Way Calibration Field.

In this review, recent advances and applications using multi-way calibration protocols based on the processing of multi-dimensional chromatographic data are discussed. We first describe the various modes in which multi-way chromatographic data sets can be generated, including some important characteristics that should be taken into account for the selection of an adequate data processing model. We then discuss the different manners in which the collected instrumental data can be arranged, and the most usually applied models and algorithms for the decomposition of the data arrays. The latter activity leads to the estimation of surrogate variables (scores), useful for analyte quantitation in the presence of uncalibrated interferences, achieving the second-order advantage. Recent experimental reports based on multi-way liquid and gas chromatographic data are then reviewed. Finally, analytical figures of merit that should always accompany quantitative calibration reports are described.

A New Parameter for Measuring the Prediction Uncertainty Produced by Rotational Ambiguity in Second-Order Calibration with Multivariate Curve Resolution.

Multivariate curve resolution-alternating least-squares (MCR-ALS) is the model of choice when dealing with matrix data that cannot be arranged into a trilinear three-way array, that is, mostly from chromatographic origin with spectral detection. A range of feasible solutions may be found in MCR studies, due to the phenomenon of rotational ambiguity associated with bilinear decompositions of matrices. The application of chemically driven constraints is vital to achieving an adequate solution and minimizing the degree of rotational ambiguity present in the system. However, when studying complex samples, it may not be possible to recover unique solutions, even under the application of proper constraints. In such cases, it is important to be able to assess the propagation of rotation uncertainty to the estimated analyte concentrations, which stems from the existence of a finite range of feasible solutions. In this work, we present a new analytical parameter to estimate the potential uncertainty in analyte prediction brought about by rotational ambiguity, in the form of an associated root-mean-square error, named RMSERA. The proposed parameter comes in the form of a range of values, whose limits are δRA/(12)1/2 and δRA/(3)1/2, with δRA being defined as the difference between the maximum and minimum values of the analyte concentration that would be predicted by the MCR model from its concentration profiles lying in the range of feasible solutions, and corresponding to maximum and minimum area, respectively. We support our proposal on extensive simulations for systems of varying composition, and demonstrate its application on experimental data aimed at the determination of four pollutants in environmental water samples.

Sensitivity for Multivariate Calibration Based on Multilayer Perceptron Artificial Neural Networks.

The use of machine learning for multivariate spectroscopic data analysis in applications related to process monitoring has become very popular since non-linearities in the relationship between signal and predicted variables are commonly observed. In this regard, the use of artificial neural networks (ANN) to develop calibration models has demonstrated to be more appropriate and flexible than classical multivariate linear methods. The most frequently reported type of ANN is the so-called multilayer perceptron (MLP). Nevertheless, the latter models still lack a complete statistical characterization in terms of prediction uncertainty, which is an advantage of the parametric counterparts. In the field of analytical calibration, developments regarding the estimation of prediction errors would derive in the calculation of other analytical figures of merit (AFOMs), such as sensitivity, analytical sensitivity, and limits of detection and quantitation. In this work, equations to estimate the sensitivity in MLP-based calibrations were deduced and are here reported for the first time. The reliability of the derived sensitivity parameter was assessed through a set of simulated and experimental data. The results were also applied to a previously reported MLP fluorescence calibration methodology for the biopharmaceutical industry, yielding a value of sensitivity ca. 30 times larger than for the univariate reference method.

Strategy To Obtain Accurate Analytical Solutions in Second-Order Multivariate Calibration with Curve Resolution Methods.

A novel procedure is described for processing the second-order data matrices with multivariate curve resolution-alternating least-squares; while the data set is nontrilinear and severe profile overlapping occurs in the instrumental data modes. The area of feasible solutions can be reduced to a unique solution by including/considering the area correlation constraint, besides the traditional constraints (i.e., non-negativity, unimodality, species correspondence, etc.). The latter is implemented not only for the unknown samples but also for all calibration samples, regardless of their interferent content. The area of correlation constraint was specially designed to remove rotational ambiguity in the chemical data sets when information about calibration samples is at hand. In this contribution a comprehensive strategy is developed to uniquely unravel nontrilinear data sets or data sets with severely overlapped profiles in the instrumental data modes. The approach is illustrated with simulated and experimental data sets. Borgen plots are employed to adequately visualize the extent of rotational ambiguity under non-negativity constraint.

Quantifying the Prediction Error in Analytical Multivariate Curve Resolution Studies of Multicomponent Systems.

In multivariate curve resolution (MCR) analysis, a range of feasible solutions is often encountered, because of the rotational ambiguities associated with the bilinear decomposition of data matrices. For quantitative purposes, the analysis is usually applied to a carefully designed set of calibration and test samples having uncalibrated interferents. Under the usual minimal constraints (non-negativity, unimodality, species correspondence, etc.), concentration and spectral profiles of the analyte in the test samples are not univocally recovered, unlike those in the calibration samples, especially when profile overlapping with the interferents is significant and selective regions do not exist for the analyte. In this report, a quantitative measure of the prediction errors due to rotational ambiguities is discussed, based on the calculation of the differences between the maximum and minimum area under the analyte concentration profiles calculated by the MCR-BANDS procedure. This methodology can be applied in different analytical scenarios with any number of analytes and interferents. Both absolute and relative quantitative errors due to rotation ambiguities are estimated and discussed in both simulated and experimental examples derived from liquid chromatography with diode array detection. The proposed procedure can be generalized to most of the analytical situations where every instrumentally measured sample produces a data table or data matrix.

A road map for multi-way calibration models.

A large number of experimental applications of multi-way calibration are known, and a variety of chemometric models are available for the processing of multi-way data. While the main focus has been directed towards three-way data, due to the availability of various instrumental matrix measurements, a growing number of reports are being produced on order signals of increasing complexity. The purpose of this review is to present a general scheme for selecting the appropriate data processing model, according to the properties exhibited by the multi-way data. In spite of the complexity of the multi-way instrumental measurements, simple criteria can be proposed for model selection, based on the presence and number of the so-called multi-linearity breaking modes (instrumental modes that break the low-rank multi-linearity of the multi-way arrays), and also on the existence of mutually dependent instrumental modes. Recent literature reports on multi-way calibration are reviewed, with emphasis on the models that were selected for data processing.

Sensitivity, Prediction Uncertainty, and Detection Limit for Artificial Neural Network Calibrations.

With the proliferation of multivariate calibration methods based on artificial neural networks, expressions for the estimation of figures of merit such as sensitivity, prediction uncertainty, and detection limit are urgently needed. This would bring nonlinear multivariate calibration methodologies to the same status as the linear counterparts in terms of comparability. Currently only the average prediction error or the ratio of performance to deviation for a test sample set is employed to characterize and promote neural network calibrations. It is clear that additional information is required. We report for the first time expressions that easily allow one to compute three relevant figures: (1) the sensitivity, which turns out to be sample-dependent, as expected, (2) the prediction uncertainty, and (3) the detection limit. The approach resembles that employed for linear multivariate calibration, i.e., partial least-squares regression, specifically adapted to neural network calibration scenarios. As usual, both simulated and real (near-infrared) spectral data sets serve to illustrate the proposal.

A new modeling strategy for third-order fast high-performance liquid chromatographic data with fluorescence detection. Quantitation of fluoroquinolones in water samples.

Matrix augmentation is regularly employed in extended multivariate curve resolution-alternating least-squares (MCR-ALS), as applied to analytical calibration based on second- and third-order data. However, this highly useful concept has almost no correspondence in parallel factor analysis (PARAFAC) of third-order data. In the present work, we propose a strategy to process third-order chromatographic data with matrix fluorescence detection, based on an Augmented PARAFAC model. The latter involves decomposition of a three-way data array augmented along the elution time mode with data for the calibration samples and for each of the test samples. A set of excitation-emission fluorescence matrices, measured at different chromatographic elution times for drinking water samples, containing three fluoroquinolones and uncalibrated interferences, were evaluated using this approach. Augmented PARAFAC exploits the second-order advantage, even in the presence of significant changes in chromatographic profiles from run to run. The obtained relative errors of prediction were ca. 10 % for ofloxacin, ciprofloxacin, and danofloxacin, with a significant enhancement in analytical figures of merit in comparison with previous reports. The results are compared with those furnished by MCR-ALS.

Scope of partial least-squares regression applied to the enantiomeric composition determination of ketoprofen from strongly overlapped chromatographic profiles.

Valuable quantitative information could be obtained from strongly overlapped chromatographic profiles of two enantiomers by using proper chemometric methods. Complete separation profiles where the peaks are fully resolved are difficult to achieve in chiral separation methods, and this becomes a particularly severe problem in case that the analyst needs to measure the chiral purity, i.e., when one of the enantiomers is present in the sample in very low concentrations. In this report, we explore the scope of a multivariate chemometric technique based on unfolded partial least-squares regression, as a mathematical tool to solve this quite frequent difficulty. This technique was applied to obtain quantitative results from partially overlapped chromatographic profiles of R- and S-ketoprofen, with different values of enantioresolution factors (from 0.81 down to less than 0.2 resolution units), and also at several different S:R enantiomeric ratios. Enantiomeric purity below 1% was determined with excellent precision even from almost completely overlapped signals. All these assays were tested on the most demanding condition, i.e., when the minor peak elutes immediately after the main peak. The results were validated using univariate calibration of completely resolved profiles and the method applied to the determination of enantiomeric purity of commercial pharmaceuticals.

Spray drying formulation of albendazole microspheres by experimental design. In vitro-in vivo studies.

Both an experimental design and optimization techniques were carried out for the development of chitosan-pectin-carboxymethylcellulose microspheres to improve the oral absorption of albendazole as a model drug. The effect of three different factors (chitosan, pectin and carboxy methyl cellulose concentrations) was studied on five responses: yield, morphology, dissolution rate at 30 and 60 min, and encapsulation efficiency of the microspheres. During the screening phase, the factors were evaluated in order to identify those which exert a significant effect. Simultaneous multiple response optimizations were then used to find out experimental conditions where the system shows the most adequate results. The optimal conditions were found to be: chitosan concentration, 1.00% w/v, pectin concentration 0.10% w/v and carboxymethylcellulose concentration 0.20% w/v. The bioavailability of the loaded drug in the optimized microspheres was evaluated in Wistar rats which showed an area under curve (AUC) almost 10 times higher than the pure drug.

IUPAC-consistent approach to the limit of detection in partial least-squares calibration.

There is currently no well-defined procedure for providing the limit of detection (LOD) in multivariate calibration. Defining an estimator for the LOD in this scenario has shown to be more complex than intuitively extending the traditional univariate definition. For these reasons, although many attempts have been made to arrive at a reasonable convention, additional effort is required to achieve full agreement between the univariate and multivariate LOD definitions. In this work, a novel approach is presented to estimate the LOD in partial least-squares (PLS) calibration. Instead of a single LOD value, an interval of LODs is provided, which depends on the variation of the background composition in the calibration space. This is in contrast with previously proposed univariate extensions of the LOD concept. With the present definition, the LOD interval becomes a parameter characterizing the overall PLS calibration model, and not each test sample in particular, as has been proposed in the past. The new approach takes into account IUPAC official recommendations, and also the latest developments in error-in-variables theory for PLS calibration. Both simulated and real analytical systems have been studied for illustrating the properties of the new LOD concept.

Recent applications of first- and second-order multivariate calibration to analytical chemistry.

This report reviews recent literature on the application of multivariate calibration techniques to both first- and second-order data, aimed at the analytical determination of analytes of interest or sample properties in a variety of industrial, pharmaceutical, food, and environmental samples, including examples of process control. The most used data processing tools are briefly described, with emphasis on the advantages that can be obtained by applying specific combinations of multivariate data and algorithms. The main focus is on works devoted to first-order data (i.e., spectra, chromatograms, etc.) combined with partial least-squares regression, which has become the standard for this type of analytical research. A brief discussion on recent work on second-order data and algorithms is also included, as this field is rapidly growing, although at present it does not show, the general applicability of the first-order counterparts.

An exhaustive analysis of the use of image moments for second-order calibration. A comparison with multivariate curve resolution-alternating least-squares.

BACKGROUND: the chemometric processing of second-order chromatographic-spectral data is usually carried out with the aid of multivariate curve resolution-alternating least-squares (MCR-ALS). Recently, an alternative procedure was described based on the estimation of image moments for each data matrix and subsequent application of multiple linear regression after suitable variable selection. RESULTS: The analysis of both simulated and experimental data leads to the conclusion that the image moment method, although can cope with chromatographic lack of reproducibility across injections, it only performs well in the absence of uncalibrated interferents. MCR-ALS, on the other hand, provides good analytical results in all studied situations, whether the test samples contain uncalibrated interferents or not. SIGNIFICANCE: The results are useful to assess the real usefulness of newly proposed methodologies for second-order calibration in the case of chromatographic-spectral data sets, especially when samples contain unexpected chemical constituents.

Electronic waste analysis using laser-induced breakdown spectroscopy (LIBS) and X-ray fluorescence (XRF): Critical evaluation of data fusion for the determination of Al, Cu and Fe.

BACKGROUND: Electronic waste (e-waste) proliferation and its implications underscore the imperative for advanced analytical methods to mitigate its environmental impact. It is estimated that e-waste production stands at a staggering 20-50 million tons yearly, of which merely 20-25% undergo formal recycling. The e-waste samples evaluated contain computers, laptops, smartphones, and tablets. RESULTS: Forty-one samples were processed, involving the disassembly and separation of components. Subsequently, two analytical techniques, laser-induced breakdown spectroscopy (LIBS) and energy dispersive X-ray fluorescence (ED-XRF), were applied to quantify aluminum (Al), copper (Cu), and iron (Fe) in the e-waste samples. The samples were then analyzed after acid mineralization with 50% v v-1 aqua regia in a digester block and finally by ICP OES. A solid residue composed of Si and Ti was observed after the digestion of the samples. Multivariate calibration strategies such as partial least-squares regression (PLS), principal component regression (PCR), maximum likelihood principal component regression (MLPCR), and error covariance penalized regression (ECPR) were used for calibration. Finally, the figures of merit were calculated to verify the most suitable models. The results revealed robust models with notable sensitivity, varying from 8.98 to 35.04 Signal (a.u.)(% w w-1) -1, low Limits of Detection (LoD) within the range of 0.001-0.2 % w w-1, and remarkable relative errors ranging from 2% to 33%, particularly for Cu and Fe. SIGNIFICANCE: Notably, the models for Al faced inherent challenges, thus highlighting the complexities associated with its quantification in e-waste samples. In conclusion, this research represents an important step toward a more sustainable and efficient future for electronic waste recycling, signifying its relevance to global environmental welfare and resource conservation.

Design, characterization, and in vitro evaluation of antifungal polymeric films.

The objective of the present paper was the development and the full characterization of antifungal films. Econazole nitrate (ECN) was loaded in a polymeric matrix formed by chitosan (CH) and carbopol 971NF (CB). Polyethylene glycol 400 and sorbitol were used as plasticizing agents. The mechanical properties of films were poorer when the drug was loaded, probably because crystals of ENC produces network outages and therefore reduces the polymeric interactions between the polymers. Polymers-ECN and CH-CB interactions were analyzed by Fourier-transform infrared spectroscopy (FTIR), thermal gravimetry analysis, and differential thermal analysis (DTA-TGA). ECN did not show structure alterations when loaded into the films. In scanning electron microphotographs and atomic force microscopy analysis, films prepared with CB showed an evident wrinkle pattern probably due to the strong interactions between the polymers, which were observed by FTIR and DTA-TGA. The in vitro activity of the formulations against Candida krusei and Candida parapsilosis was twice as greater as the commercial cream, probably as a result of the antifungal combination of the drug with the CH activity. All these results suggest that these polymeric films containing ECN are potential candidates in view of alternatives dosages forms for the treatment of the yeast assayed.

A new constraint to model background signals when processing chromatographic-spectral second-order data with multivariate curve resolution.

BACKGROUND: the chemometric processing of second-order chromatographic-spectral data is usually carried out with the aid of multivariate curve resolution-alternating least-squares (MCR-ALS). When baseline contributions occur in the data, the background profile retrieved with MCR-ALS may show abnormal lumps or negative dips at the position of the remaining component peaks. RESULTS: The phenomenon is shown to be due to remaining rotational ambiguity in the obtained profiles, as confirmed by the estimation of the boundaries of the range of feasible bilinear profiles. To avoid the abnormal features in the retrieved profile, a new background interpolation constraint is proposed and described in detail. Both simulated and experimental data are employed to support the need of the new MCR-ALS constraint. In the latter case, the estimated analyte concentrations agreed with those previously reported. SIGNIFICANCE: The developed procedure helps to reduce the extent of rotational ambiguity in the solution and to better interpret the results on physicochemical grounds.

Analytical figures of merit for partial least-squares coupled to residual multilinearization.

A new expression is developed which allows estimating the sensitivity for the whole family of multivariate calibration algorithms based on partial least-squares regression combined with residual multilinearization. The sensitivity can be employed to compute other relevant figures of merit such as analytical sensitivity, limit of detection, limit of quantitation, and uncertainty in predicted concentration. The results are substantiated by extensive Monte Carlo noise addition simulations for a variety of systems with a different number of analytes and interfering agents, different degrees of overlapping in component profiles, and different numbers of instrumental data modes per sample, all requiring the achievement of the second-order advantage. The connection between the present approach and the intuitive concept of net analyte signal is discussed. An experimental example for which second-, third-, and fourth-order data are available is also studied, concerning the improvement in figures of merit on increasing the data order, which is consistent with the decrease in average prediction error.

New developments for the sensitivity estimation in four-way calibration with the quadrilinear parallel factor model.

Appropriate closed-form expressions are known for estimating analyte sensitivities when calibrating with one-, two-, and three-way data (vectors, matrices, and three-dimensional arrays, respectively, built with data for a group of samples). In this report, sensitivities are estimated for calibration with four-way data using the quadrilinear parallel factor (PARAFAC) model, making it possible to assess important figures of merit for method comparison or optimization. The strategy is based on the computation of the uncertainty in the fitted PARAFAC parameters through the Jacobian matrix. Extensive Monte Carlo noise addition simulations in four-way data systems having widely different overlapping situations are helpful in supporting the present approach, which was also applied to two experimental analytical systems. With this proposal, the estimation of the PARAFAC sensitivity for calibration scenarios involving three- and four-way data may be considered complete.