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 met
