Hazards of using multivariate curve resolution for processing first-order spectral data. A rotational ambiguity analysis.

Background: A growing number of reports are discussing the use of multivariate curve resolution - alternating least-squares (MCR-ALS) to process matrices built with first-order data, e.g., spectra.

How does sensor-wise N-BANDS relate to the of area of feasible solutions?

Background: The method of sensor-wise N-BANDS aims to compute the envelope of the range of the feasible concentration profiles and the envelope of the range of the feasible spectral profiles. These envelopes are obtained by a sensor-wise maximization and minimization for each chemical species. They describe the rotational ambiguity which can also be explored by the area of feasible solutions.

Feasible band boundaries computation in bilinear matrix decomposition using essential data.

Background: Multivariate curve resolution methods are usually confronted with non-unique pure component factors. This rotational ambiguity can be represented by ranges of feasible profiles, which are equally compatible with the imposed constraints. Sensor-wise N-BANDS is an effective algorithm for the calculation of the bounds of feasible profiles in the presence of noise, but suffers from high computational cost.

Novel Data Fusion Strategy for Second-Order Data: Multivariate Curve Resolution for the Determination of Pharmaceuticals by Means of Fluorimetric Measurements.

A new strategy is proposed for second-order data fusion based on the simultaneous modeling of two data sets using the multivariate curve resolution-alternating least-squares (MCR-ALS) model, applying a new constraint during the ALS stage, called "Proportionality of Scores". This approach allows for the fusion of data from different sources, without requiring common dimensionality, and enables the application of specific constraints to each data set. This strategy was applied to the determination of five pharmaceutical contaminants (naproxen, danofloxacin, ofloxacin, sarafloxacin, and enoxacin) in environmental water samples, by fusing two sets of excitation-emission fluorescence matrices, measured before and after photochemical derivatization.

Cement classification and characterization using Non-Invasive techniques.

Cement is one of the most widely used materials in the global construction industry, serving as an adhesive and binder in projects that require strength and durability. Additionally, cement production indicates a country's development and economic activity, with global production reaching approximately 4 billion tons annually. It is a fine powder composed mainly of lime, silica, iron oxide, and alumina.

Contribution of multiway calibration to White Analytical Chemistry.

In this article, the compatibility between second- and third-order calibration and White Analytical Chemistry (WAC) is exposed and discussed. The WAC concept and the principles on which it is based are briefly presented. Multiway calibration methods, which consist of performing analyte(s) quantification by processing second- or higher-order instrumental data using chemometric models, are analyzed in light of their contribution to the whiteness of an analytical method.

Authentication of Argentinean extra-virgin olive oils using three-way fluorescence and two-way near-infrared data fused with multi-block DD-SIMCA.

A trending problem of Extra Virgin Olive Oil (EVOO) adulteration is investigated using two analytical platforms, involving: (1) Near Infrared (NIR) spectroscopy, resulting in a two-way data set, and (2) Fluorescence Excitation-Emission Matrix (EEFM) spectroscopy, producing three-way data. The related instruments were employed to study genuine and adulterated samples. Each data set was first separately analyzed using the Data Driven-Soft Independent Modeling of Class Analogies (DD-SIMCA) method, based on Principal Component Analysis (for the two-way NIR data) and PARallel FACtor analysis (for the three-way EEFM data).

Area of Feasible Figures of Merit (AF-FOMs) for second-order multivariate calibrations in Multivariate Curve Resolution (MCR).

Background: The significance and necessity of using powerful multivariate curve resolution (MCR) techniques in the study and investigation of chemical systems are clear and obvious. It has long been recognized the importance of using second-order data to extract both quantitative and qualitative information in analytical chemistry through multivariate calibration instead of univariate calibration. Although the calculation of analytical figures of merit (AFOMs) in multivariate calibrations seems to be complicated, in recent years these parameters have been reported for each developed analytical method based on multivariate calibrations.

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.

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.

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.

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.

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.

A Critical Review on the Development of Optical Sensors for the Determination of Heavy Metals in Water Samples. The Case of Mercury(II) Ion.

Recent publications are reviewed concerning the development of sensors for the determination of mercury in drinking water, based on spectroscopic methodologies. A critical analysis is made of the specific details and figures of merit of the developed protocols. Special emphasis is directed to the validation and applicability to real samples in the usual concentration range of mercury, considering the maximum allowed limits in drinking water established by international regulations.

Linear or non-linear multivariate calibration models? That is the question.

Concepts from data science, machine learning, deep learning and artificial neural networks are spreading in many disciplines. The general idea is to exploit the power of statistical tools to interpret complex and, in many cases, non-linear data. Specifically in analytical chemistry, many chemometrics tools are being developed.

Sensitivity and generalized analytical sensitivity expressions for quantitative analysis using convolutional neural networks.

In recent years, convolutional neural networks and deep neural networks have been used extensively in various fields of analytical chemistry. The use of these models for calibration tasks has been highly effective; however, few reports have been published on their properties and characteristics of analytical figures of merit. Currently, most performance measures for these types of networks only incorporate some function of prediction error.

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.

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.

Interference-free calibration with first-order instrumental data and multivariate curve resolution. When and why?

The possibility of building an interference-free calibration with first-order instrumental data with multivariate curve resolution-alternating least-squares (MCR-ALS) has been a recent topic of interest. When the protocols were successful, MCR-ALS proved to be suitable for the extraction of chemically meaningful information from first-order calibration datasets, even in the presence of unexpected species, i.e.

A down-to-earth analyst view of rotational ambiguity in second-order calibration with multivariate curve resolution - a tutorial.

Rotational ambiguity is a phenomenon with the potential of generating an uncertainty in the estimation of analyte concentrations in protocols based on matrix instrumental data processed by multivariate curve resolution - alternating least-squares (MCR-ALS). This is particularly relevant when the second-order advantage is to be achieved, i.e.

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).

Initialization effects in two-component second-order multivariate calibration with the extended bilinear model.

Bilinear decomposition of an augmented data matrix is usually complicated by the phenomenon of rotational ambiguity. If the latter is significant, quantitative and qualitative information of the recovered profiles may be less useful. Although constraints can reduce the extent of feasible regions and the degree of rotational ambiguity, the estimation of initial parameters to start the decomposition is an important phase in multivariate curve resolution-alternating least-squares (MCR-ALS) studies.

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.

On second-order calibration based on multivariate curve resolution in the presence of highly overlapped profiles.

Multivariate curve resolution has been applied to both simulated and experimental data sets where high or even complete overlapping occurs between component profiles in one data mode. It is shown that rotational ambiguity exists in the bilinear decomposition of the augmented data matrices built with second-order data for pure analyte standards and test samples containing uncalibrated interferents. However, even in the presence of rotational ambiguity, initialization based on the so-called purest variables in one of the data modes may allow one to develop analytical protocols with reasonable statistical indicators for the prediction of the analyte of interest.