A chemometrics toolbox based on projections and latent variables

TLDR

Projection methods such as PCA, PLS, and related techniques have evolved since the 1970s, driven by the recognition that multidimensional spectroscopic and chromatographic data contain richer information than single‑variable analyses, leading to a data‑driven approach in chemometrics. The toolbox builds on PCA as a foundation for more complex models—including soft independent modeling of class analogy, partial least squares, hierarchical PCA/PLS, PLS‑discriminant analysis, orthogonal projection to latent structures, and their discriminant variants. These projection‑based approaches, when combined with PCA and PLS, have proven highly effective for analyzing chemical data, as illustrated by several examples and anecdotes. © 2014 John Wiley & Sons, Ltd.

Abstract

A personal view is given about the gradual development of projection methods—also called bilinear, latent variable, and more—and their use in chemometrics. We start with the principal components analysis (PCA) being the basis for more elaborate methods for more complex problems such as soft independent modeling of class analogy, partial least squares (PLS), hierarchical PCA and PLS, PLS‐discriminant analysis, Orthogonal projection to latent structures (OPLS), OPLS‐discriminant analysis and more. From its start around 1970, this development was strongly influenced by Bruce Kowalski and his group in Seattle, and his realization that the multidimensional data profiles emerging from spectrometers, chromatographs, and other electronic instruments, contained interesting information that was not recognized by the current one variable at a time approaches to chemical data analysis. This led to the adoption of what in statistics is called the data analytical approach, often called also the data driven approach, soft modeling, and more. This approach combined with PCA and later PLS, turned out to work very well in the analysis of chemical data. This because of the close correspondence between, on the one hand, the matrix decomposition at the heart of PCA and PLS and, on the other hand, the analogy concept on which so much of chemical theory and experimentation are based. This extends to numerical and conceptual stability and good approximation properties of these models. The development is informally summarized and described and illustrated by a few examples and anecdotes. Copyright © 2014 John Wiley & Sons, Ltd.