Multivariate statistics: considerations and confidences in food authenticity problems

Modern analytical measurement technologies, such as infrared, NMR, mass spectrometry and chromatography, provide a wealth of information on the chemical composition of all kinds of samples. These instruments are invariably controlled by computers, and the data (spectrum, chromatogram) recorded in digital form. A measurement on a single sample typically comprises thousands of numbers. Usually, this is many more than the number of samples, meaning that the experiment overall is underdetermined. Furthermore, chemically different specimens often give rise to quite similar measurements, especially in some of the spectroscopy methods where there are large numbers of overlapped spectral bands. The task, then, is how to get the best out of these complex and unwieldy datasets. Fortunately, there is an assortment of computational methods that are especially suitable for dealing with this kind of data: these are the techniques of multivariate analysis. In this opinion paper, we present an overview of multivariate statistics for food authentication applications. We discuss the advantages of a multivariate strategy compared with univariate assessments and look at selected techniques that are now well established in analytical chemistry, such as the data compression methods of principal component analysis. We also consider predictive approaches suitable for authentication applications: discriminant and classification strategies, and class-modelling techniques. Critical to the proper application of multivariate techniques is the concept of validation. We conclude by discussing some wider aspects of experimental design, such as the importance of representative sampling. Illustrations are drawn from real-world examples of food authenticity problems.