Partial least squares-discriminant analysis (PLS-DA) is a versatile algorithm that can be used for predictive and descriptive modelling as well as for discriminative variable selection. However, versatility is both a blessing and a curse and the user needs to optimize a wealth of parameters before reaching reliable and valid outcomes. Over the past two decades, PLS-DA has demonstrated great success in modelling high-dimensional datasets for diverse purposes, e.g. product authentication in food analysis, diseases classification in medical diagnosis, and evidence analysis in forensic science. Despite that, in practice, many users have yet to grasp the essence of constructing a valid and reliable PLS-DA model. As the technology progresses, across every discipline, datasets are evolving into a more complex form, i.e. multi-class, imbalanced and colossal. Indeed, the community is welcoming a new era called big data. In this context, the aim of the article is two-fold: (a) to review, outline and describe the contemporary PLS-DA modelling practice strategies, and (b) to critically discuss the respective knowledge gaps that have emerged in response to the present big data era. This work could complement other available reviews or tutorials on PLS-DA, to provide a timely and user-friendly guide to researchers, especially those working in applied research.

Partial least squares-discriminant analysis (PLS-DA) for classification of high-dimensional (HD) data: a review of contemporary practice strategies and knowledge gaps

Authenticating products and documents with security inks is vital to global commerce, security and health. Lanthanide complexes are widely used in luminescent security inks owing to their unique and robust photophysical properties. Lanthanide complexes can also be engineered to undergo circularly polarized luminescence (CPL), which encodes chiral molecular fingerprints in luminescence spectra that cannot be decoded by conventional optical measurements. However, chiral CPL signals have not yet been exploited as an extra security layer in advanced security inks. This Review introduces CPL and related concepts that are necessary to appreciate the challenges and potential of lanthanide-based, CPL-active security inks. We describe recent advances in CPL analysis and read-out technologies that have expedited CPL-active security ink applications. Further, we provide a systematic meta-analysis of strongly CPL-active Euiii, Tbiii, Smiii, Ybiii, Cmiii, Dyiii and Criii complexes, discussing the suitability of their photophysical properties and highlighting promising candidates. We conclude by providing key recommendations for the development and advancement of the field. Several transition-metal and lanthanide complexes undergo circularly polarized luminescence. This Review describes design principles for the complexes and instruments used to measure them, including in the context of security inks.

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Circularly polarized lanthanide luminescence for advanced security inks

Vibrational spectroscopy techniques, such as Fourier-transform infrared (FTIR) and Raman spectroscopy, have been successful methods for studying the interaction of light with biological materials and facilitating novel cell biology analysis. Spectrochemical analysis is very attractive in disease screening and diagnosis, microbiological studies and forensic and environmental investigations because of its low cost, minimal sample preparation, non-destructive nature and substantially accurate results. However, there is now an urgent need for multivariate classification protocols allowing one to analyze biologically derived spectrochemical data to obtain accurate and reliable results. Multivariate classification comprises discriminant analysis and class-modeling techniques where multiple spectral variables are analyzed in conjunction to distinguish and assign unknown samples to pre-defined groups. The requirement for such protocols is demonstrated by the fact that applications of deep-learning algorithms of complex datasets are being increasingly recognized as critical for extracting important information and visualizing it in a readily interpretable form. Hereby, we have provided a tutorial for multivariate classification analysis of vibrational spectroscopy data (FTIR, Raman and near-IR) highlighting a series of critical steps, such as preprocessing, data selection, feature extraction, classification and model validation. This is an essential aspect toward the construction of a practical spectrochemical analysis model for biological analysis in real-world applications, where fast, accurate and reliable classification models are fundamental.

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Tutorial: multivariate classification for vibrational spectroscopy in biological samples.

This review represents a detailed discussion of the multivariate methods used in the examination of forensic exhibits; their advantages, disadvantages, and efficiency are compared. The last decade has seen the application of the chemometric methods combined with analytical techniques for characterization and discrimination of samples, which leads to the informative and representative examinations of the samples. Many research articles with reference to the use of chemometrics in forensic science have been published. This review has been divided into various sections which include chemometrics, its history, multivariate methods, and the application of chemometrics in various disciplines of forensic science. It is suggested that these new techniques and mathematical/statistical methods should be utilized in forensic science casework to get statistical confidence in the results.

Francisco J.O. Scafi

Papers

Discrimination between authentic and counterfeit banknotes using Raman spectroscopy and PLS-DA with uncertainty estimation