Volume 1 (Statistics, Experimental Design, Optimization)
a) Statistics:
This section covers the more fundamental aspects of statistics used in chemical and biochemical labs and industries, with chapters covering the sampling theory, quality and proficiency testing and control, and the introduction of statistical resampling, Bayesian methodologies and robust statistical methods. Some of these last chapters of the section, for example Bayesian and robust approaches, should be updated and extended in the new edition of this section.
b) Experimental Design
This section gives a good coverage of the field of experimental design including methods for initial screening, quantitative study of the effects of the factors, response surface methodologies, mixture designs and non-classical strategies. These chapters help the experimenter in solving most of the situations encountered in practice. Either in this section or in others, there is the need of including more explicitly a discussion of multivariate extension of ANOVA for the study of the effects in well-designed experiments, an area of special importance nowadays, for instance in omics type of studies
c) Optimization
Many chemistry and chemometric data analysis problems can be formulated using numerical optimization strategies. Several chapters devoted to different optimization strategies are described in this section, including state of the art approaches for constrained and unconstrained optimization, sequential optimization, multi-criteria decision-making, and genetic algorithms. These methods could be complemented in the next edition of the work by including coverage of other methods such as particle swarm optimization and machine learning methods.
Volume 2 (Data preprocessing, Linear modeling, Unsupervised data mining)
d) Data preprocessing
Data preprocessing is a fundamental step in the chemometrics workflow which is increasingly recognized. In the last few years, special efforts have been dedicated to systematize and classify the different approaches available, including signal pretreatment, background elimination, shift and alignment, scaling and normalization methods. Especially important are preprocessing methods to handle size effects and their relation with compositional approaches. (These areas were insufficiently covered in the previous edition.)
e) Linear Soft-Modeling
Linear soft-modelling is at the core of many of the chemometric data analysis methods and this section gives full coverage of most of them, from bilinear-based methods such as principal component analysis (PCA), independent component analysis (ICA) and multivariate curve resolution (MCR), to trilinear (multilinear) based methods like PARAFAC- or Tucker3-based methods. Special topics to be extended in this section are simultaneous component analysis methods (along with their relation to extended ANOVA approaches in the experimental statistical design section) and very importantly maximum likelihood approaches which allow extending data analysis to more rigorous linear approaches where noise structure is included in the estimation of the parameters.
f) Unsupervised Learning and Data Mining
The most frequently used clustering methods used in unsupervised data analysis are described in this section. Classical methods (both linear and non-linear) and other data mapping techniques, density-based methods and tree-based methods are reviewed in detail with many examples of application in different fields. A relatively new field is Topological Data Analysis (TDA). The main goal of TDA is to study data shape, which may reveal important information about the studied systems or phenomena. It can be useful in data exploration, clustering of numerous samples, and comparison of different platforms
Volume 3 (Linear and Non-linear Regression, Classification, Feature selection and Robust methods)
g) Linear Regression Modeling
Multivariate linear regression modelling is another of the core elements of the chemometrics field and of its literature. Calibration strategies based on linear regression, such as PLS methods, including regression diagnostics, validation, variable selection methodology, handling missing data in regression, and adequate data preprocessing procedures are considered in detail in this section. In addition to these topics, more advanced robust regression approaches, transfer of calibration models, and three-way calibration regression methods are also presented.
h) Non-linear regression
Non-linear regression methods have been especially important for deterministic and hard modelling data fitting and parameter estimation type of problems. These methods have been extended to multivariate data. Non-linear, soft modelling approaches are especially useful when no physical model is available and the data structure is highly non-linear. Especially important are the so-called kernel methods (support vector machines, SVM, kernel PCA or kernel PLS) that extend the potential of linear soft-modelling methods to non-linear data and problems. Also, locally weighted regression and other extension of linear methods are discussed in detail in this section. Neural networks in their different facets are also summarized.
i) Classification
Classification (or supervised pattern recognition) methods are another family of frequently used chemometric methods to solve many problems of class membership in analytical data from chemical, biological and environmental fields. Statistical discriminant analysis (linear, quadratic and higher dimensional), decision tree modeling and neural networks (revisited in detail here for classification purposes) are each covered in separate chapters. A last chapter shows some examples of how validation of the classifiers is performed.
j) Feature Selection
This section will be restructured and it will include new approaches proposed for feature selection in different fields. Four different chapters will describe different techniques used for feature selection by means of PLS (elimination of non-informative variables), sparse methods, genetic algorithms and wavelets (described in detail).
k) Multivariate Robust Techniques
A final section and chapter on robust techniques summarize the concepts, approaches and methods used when normal distribution assumptions either do not hold, describe the experimental data rather poorly, or are violated by the presence of outliers. Robust alternatives to PLS regression and to linear discriminant analysis are described in detail and examples of their application, as well as uncertainty analysis of the obtained robust parameters using bootstrap permutation methods, are given.
Volume 4: Applications
A whole volume is dedicated to the description of the application of chemometrics to relevant problems in a variety of fields, including environmental chemistry, food, health, sensory analysis, QSAR, spectroscopic imaging, microarray DNA, genomics, systems biology, chemoinformatics, process analytical technologies and process control, smart sensors and electrochemistry. This list of applications is by no means exhaustive, and the list of topics given here may require updating with the possible incorporation of new chapters in the next edition. Our aim is to document the development and use of chemometric methods in these fields and in new, emerging ones (including transcriptomics, DNA-sequencing metabolomics, proteomics, flow cytometry and others).
