This chapter shows the usefulness of n-way techniques when there are legal requirements to meet the performance characteristics of analytical methods for the determination of residues of pharmacologically active substances, pesticides, migrants, or additives in food. Specifically, parallel factor analysis (PARAFAC) and PARAFAC2 n-way techniques are used, both can handle data cubes to extract the information underlying the chemical signals. This methodology allows solving different analytical problems, such as the coelution of interferents that have an absorbance spectrum similar to the target analyte (HPLC-DAD) or interferents that share m/z ions (GC–MS, LC–MS–MS) or solving overlapping spectra in the case of fluorescence spectroscopy. The most important novelty is the use of the “second-order advantage” to unequivocally identify and quantify analytes. In addition, the PARAFAC decomposition of trilinear arrays enables the optimization of several analytical procedures (derivatization reaction, microextraction optimization, etc.) that are previous (and necessary) to the chromatographic determination of complex samples.
Multiway data analysis holds high potential for the evaluation of spectroscopic data, in particular for information-rich mid-infrared spectra. This chapter provides an overview of recent applications of multiway data analysis in (laser-based) infrared spectroscopy of proteins. Correlation-optimized warping and wavelet transform are presented as useful techniques to alleviate instrument imperfections and improve noise levels of experimentally recorded data with optical setups. Multivariate curve resolution-alternating least squares was found to be an excellent tool to predict percentages of individual secondary structures in static protein spectra and to reveal profiles of spectral components and display their progression when monitoring dynamic changes in protein secondary structure. Finally, the outlined examples demonstrate that (laser-based) IR spectroscopy paired with multiway analysis is a powerful combination for monitoring and in-depth interpreting of protein folding.
Comprehensive two-dimensional gas chromatography coupled with mass spectrometry (GC × GC–MS) is now an integral analytical technique for the characterization of volatile and semivolatile compounds. With the rise of this technique in various application fields, the size and complexity of data sets have also grown, making manual interpretation of GC × GC–MS data sets cumbersome and tedious. However, for these comparative analysis studies, chemometric methods can efficiently discover chemical differences between samples. This chapter discusses the recent developments in chemometric analysis of GC × GC–MS data. As the application of these computational approaches is dependent on the quality of the data, instrumentation and data preprocessing methods are outlined. Key principles of both unsupervised and supervised nontargeted methods and their application in a pixel-based, peak table-based, and tile-based fashion are also reviewed. Finally, this chapter explores the application of targeted methods during a comparative analysis workflow to improve analyte identification and quantification.
This chapter focuses on the recent advances in theoretical and experimental procedures on third-order/four-way and fourth-order/five-way analytical methods. For higher-order data generation, most of the published works report the use of excitation–emission luminescence matrices technique coupled to some experimental variable as the third mode, e.g., kinetics, chromatographic resolution, pH gradient, luminescence lifetime, or other physical–chemical treatment. The success of these protocols has been demonstrated for a wide range of applications in the environmental, bioanalytical, and food fields, and is described here. In addition, the analytical benefits achieved by performing third- and fourth-order data modeling for the quantitative/qualitative/descriptive analysis of complex samples are detailed throughout this chapter.
Process analysis applies analytical science to the monitoring and control of industrial process; in this line, process analytical chemistry (PAC) has been largely used especially for quality assurance in analytical field. Most of the application relies on the use of first-order spectroscopic data, once the instrumentation is simpler to be implemented, on in-line or on-line process, which is interesting due to the possibility of an automatic feedback. However, multiway data analysis evolves in such a way that makes it possible to reduce the time dedicated to sample preparation and instrumental analysis, which enable the use of techniques, generally used with off-line approach, as at-line or even in an on-line process. In addition, it reduces the requirement of a high number of samples to be analyzed due to the amount of information present in the multiway data, which significantly impact even on sampling step or on the model update. This chapter presents the history of PAC and how this approach evolves together with the development of the analytical instrumentation and chemometrics.
The pH gradient modeling instrumental data, such as spectroscopic signals, represent a simple alternative to introduce an additional mode to obtain high-order data. This approach can be especially useful for the quantitation of pH-dependent compounds in environmental, biological, and food samples. Through some real examples, this chapter discusses how to deal with the analysis of this type of data, which poses special challenges to multivariate calibration algorithms.
This chapter outlines some of the challenging aspects when applying multiway data modeling in classification issues. The theoretical basis and applicative guidelines are detailed. The main analytical platforms and the utilization of the generated data used for classification are briefly discussed from the application point of view. A critical discussion of the advantages concerning the general features of the available algorithms and their underlying models is performed. To illustrate the high potentiality of multiway data modeling in the classification field, a literature example is presented and discussed. Furthermore, the demanded advances in remarkable data fusion strategies about optimally combining multiple data sources in an assortment of fields are revealed.
Hyperspectral image analysis offers many contexts where the treatment of second-order data is mandatory. To mention a few examples, working with sets of related images for quantitative analysis purposes, process monitoring, or fusing images acquired on the same sample with different spectroscopic platforms requires the use of data analysis tools that may handle simultaneously related blocks of information. Unmixing analysis in hyperspectral imaging is one of the most common tasks performed, as a complete spatial and chemical characterization of the compounds in a scanned sample needs retrieving their pure distribution maps and spectral signatures. Among the different algorithms, multivariate curve resolution-alternating least squares (MCR-ALS) offers a particularly flexible framework that allows combining images that may present significant differences in spatial and spectroscopic properties. Through challenging data configurations and the combined use of bilinear and multilinear models, a large diversity of image fusion scenarios can be properly addressed. This chapter gradually shows the image requirements and the chemometric solutions available for every problem.
Nowadays, miniaturized spectrometers have emerged as new technologies with many applications. Unlike a uniform design of mature benchtop spectrometers, miniaturized instruments employ diverse technological solutions, which impact their operational characteristics. Continuous progress leads to new instruments appearing on the market, which can be used for rapid, reliable, nondestructive, user-friendly, and on-site analysis in analytical chemistry. On the other side, miniaturized instruments suffer from different challenges such as scattering effects and instrumental/ambient noise, making robust chemometric methods crucial to extract the relevant information from the spectra. The focus of this chapter is to summarize miniaturized technologies, commercially available devices, multiway chemometric data analysis methods, and applications in analytical chemistry.
Datasets obtained from a factorial experimental design can be folded into N-way multidimensional arrays according to the levels and factors encoded in their design matrices. A method for designed experiments that incorporates statistical inference and visualization—parallel factor analysis ANOVA simultaneous component analysis (PARAFASCA)—makes it possible to obtain evidence of statistical significance for each experimental factor and their interactions while maintaining the benefits of PARAFAC for ease-of-interpretation. In this chapter, we present a use case of multiway decomposition in a metabolomics experiment to investigate the effect of deoxynivalenol on different cultivars of wheat and consider the similarities in interpretation with the original study. Rather than treating replicate samples as an additional mode in PARAFAC, we introduce a modeling solution that is more consistent with the ultimate goal of a designed experiment, where replicates are used to model the uncertainty associated with each of the loadings’ entries.
This chapter reviews relevant applications of multiway data analysis to electrochemical data. Four main strategies to get the second-order advantage are considered: (i) integration of electrochemical sensors into arrays; (ii) changing electrochemical parameters; (iii) using nonelectrochemical variables; and (iv) through spectroelectrochemical measurements. The multiway data obtained can be analyzed for different purposes and in many ways: (i) discrimination of samples by principal component analysis, linear discriminant analysis, partial least squares–discriminant analysis, and support vector machine–discriminant analysis; (ii) multivariate calibration using partial least-squares calibration (PLS), artificial neural network, and multivariate curve resolution–alternating least squares (MCR-ALS); (iii) multivariate curve resolution, mostly with MCR-ALS; and (iv) application of three-way methods such as parallel factor analysis and multilinear PLS. Examples, mostly from the fields of environmental analysis and food analysis, are discussed.
This chapter focuses on classical quantitative applications of the trilinear decomposition (TLD) model in chemistry and its related fields since 2015. Firstly, some basic theories, methods and rules in the use of trilinear decomposition models are briefly introduced, such as nomenclature in three-way data analysis, data types, model and algorithms, data preprocessing. Then, we sorted out the latest application examples of the TLD model in the two major categories of data (including the data of excitation-emission matrix fluorescence and chromatography with multichannel detector), and introduced the details of some typical cases. These examples will clearly show how the second-order calibration method based on the TLD model makes quantitative analysis simple, fast, green, and antiinterference.
This chapter presents improvements for the nondestructive fluorescence analysis of forensic evidence. Nondestructive techniques that can either discriminate between similar fibers or match a known to a questioned fiber—and still preserve the physical integrity of the fibers for further court examination—are highly valuable in forensic science. Differences in cross-sectional shape, type of fiber material (natural or synthetic), weave, and color usually make possible to rule out a common source for the known and questioned fiber. Previous to our research, most fluorescence articles reported fiber measurements made with excitation and emission band-pass filters, i.e., an approach that took no advantage of the information content that exists in the spectral signatures of fluorescence samples textile fibers. Research efforts in our group developed instrumentation and experimentation for the collection of excitation and emission spectra and excitation–emission matrices from single textile fibers. When combined with chemometric approaches, these data formats are able to discriminate among visually indistinguishable fibers, identify exogeneous substances on textile fibers that may prove useful in matching a trace fiber to its bulk specimen of origin, and provide information on the weathering history of the fiber.
This chapter discloses the joint use of second-order techniques and fluorescence spectroscopy in the study of aquatic environments. Focus is given on the use of parallel factor analysis (PARAFAC), the most employed technique, in the analysis of surface waters (fresh, marine, and estuarine), the most common application. An overview is provided on how to obtain good-quality fluorescence excitation–emission matrices (EEMs) and synchronic fluorescence matrices, covering the most used strategies for dealing with light scattering and missing values. Similarly, an analytical sequence for performing EEM–PARAFAC in the context of environmental analysis is presented, followed by a practical example based on the identification of organic contaminants in water. Finally, the use of EEM–PARAFAC as a fingerprint strategy for oil spills investigation is discussed, following a study analyzing the oil spill that occurred on the Brazilian coast in 2019.
Hyphenated chromatographic techniques are increasingly used for monitoring chemical pollutants in environmental samples. Multiway calibration methods have also become valuable tools for processing complicated environmental matrices because of the particular “second-order advantage,” which makes it possible to quantify a targeted group of pollutants even in the presence of unknown and uncalibrated matrix interferences. Moreover, global screening, including nontargeted analysis, is considered to be a powerful strategy for a more holistic evaluation of environmental samples. This chapter reviews recent progress and applications of multiway data processing methods in targeted/nontargeted scenarios. In each section, the principles of initial data generation based on GC/LC-multivariate spectral detection, high-dimensional data arrangement, the selected multiway data processing protocol, and the challenges are described.
Hard modeling is the branch of chemometrics that is most intimately associated with the actual chemistry of the process investigated. The goal is to analyze process data in terms of a chemical model, usually based on the law of mass action. The results include rate and or equilibrium constants that allow the quantitative understanding of chemical processes. In this chapter, the principles of hard modeling are described, in addition to an example of the successful conversion of hard-modeling results into an improved chemical process.
In pursuing the success of multiway data analysis, while the selection of the proper chemometric protocol plays an important role in the data resolution, equally noteworthy is the experimental and instrumental procedure that is implemented for the data acquisition. As increasing the dimensionality of the data, more tedious and sophisticated experimental procedures must be employed in an attempt to better fulfill the mathematical characteristics of the data to be modeled. In this way, performing experiments in dynamic mode (kinetics, time-dependent, temperature gradient) with higher-order data acquisition is a challenge for chemometricians. The main inconvenience often relies on the recording rate of the detectors, which is generally slower than or comparable with the variation rate of the observable measure. Despite linear or fast scanning detectors being available for the immediate acquisition of vectorial signals (e.g., spectrum), multidimensional signal registering (e.g., excitation–emission matrix) in continuous-flow systems seems to be a troublesome task with the available commercial instrumentation. This chapter focuses on the novel custom devices built for the high-throughput acquisition of multidimensional signals in dynamic systems that fulfill the criteria of multilinearity to further chemometric applications.
In this chapter, advances that have taken place since the first edition of this book are reviewed concerning the estimation of analytical figures of merit. They include (1) the introduction of instrumental noise structures other than the independent and identically distributed noise in the calculation of the figures of merit, leading to the proposal of new figures and modifications of the classical ones, both in multivariate (first-order) and multiway (higher-order) calibration, (2) the development of figures of merit for nonlinear multivariate models based on artificial neural networks applied to first-order data, but with potential application in the multiway field, and (3) the estimation of the impact of the phenomenon of rotational ambiguity in the prediction uncertainty when multiway calibration models are based on bilinear decomposition procedures, which also led to the suggestion of new figures of merit. Although the theory behind the estimation of multiway figures of merit is fairly complete, some specific issues still need further research, as discussed in this chapter.
