Principal component analysis is one of the most important and powerful methods in chemometrics as well as in a wealth of other areas.

A sub‐fraction of dissolved organic matter fluoresces when excited with ultraviolet light. This property is used to quantify and characterize changes in dissolved organic matter (DOM) in aquatic environments. Detailed mapping of the fluorescence properties of DOM produces excitation emission matrices (EEM), which are well suited to multi‐way data analysis techniques (chemometrics). Techniques such as parallel factor analysis (PARAFAC) are increasingly being applied to characterize DOM fluorescence properties. Here, an introduction to the technique and description of the advantages and pitfalls of its application to DOM fluorescence is presented. Additionally a MATLAB based tutorial and toolbox specific to PARAFAC analysis of DOM fluorescence is presented.

PARAllel FACtor analysis (PARAFAC) is increasingly used to decompose fluorescence excitation emission matrices (EEMs) into their underlying chemical components. In the ideal case where fluorescence conforms to Beers Law, this process can lead to the mathematical identification and quantification of independently varying fluorophores. However, many practical and analytical hurdles stand between EEM datasets and their chemical interpretation. This article provides a tutorial in the practical application of PARAFAC to fluorescence datasets, demonstrated using a dissolved organic matter (DOM) fluorescence dataset. A new toolbox for MATLAB is presented to support improved visualisation and sensitivity analyses of PARAFAC models in fluorescence spectroscopy.

A new diagnostic called the core consistency diagnostic (CORCONDIA) is suggested for determining the proper number of components for multiway models. It applies especially to the parallel factor analysis (PARAFAC) model, but also to other models that can be considered as restricted Tucker3 models. It is based on scrutinizing the ‘appropriateness’ of the structural model based on the data and the estimated parameters of gradually augmented models. A PARAFAC model (employing dimension‐wise combinations of components for all modes) is called appropriate if adding other combinations of the same components does not improve the fit considerably. It is proposed to choose the largest model that is still sufficiently appropriate. Using examples from a range of different types of data, it is shown that the core consistency diagnostic is an effective tool for determining the appropriate number of components in e.g. PARAFAC models. However, it is also shown, using simulated data, that the theoretical understanding of CORCONDIA is not yet complete. Copyright © 2003 John Wiley & Sons, Ltd.