Comparison of three-way resolution methods for non-trilinear chemical data sets

Resolution of three-way chemical data sets can be tackled using two families of chemometric methods: those assuming trilinear structure in the data set, such as direct trilinear decomposition (DTD) or parallel factor analysis (PARAFAC); and those which decompose the three-way data set according to a model lacking this structure, such as TUCKER3 or multivariate curve resolution-alternating least squares (MCR-ALS). The first group of methods provides unique solutions, whereas the second group gives solutions subject to rotational ambiguities. DTD and PARAFAC are thus the choice to deal with chemical data sets with trilinear structure. However, in the analysis of chemical data with non-trilinear structure, which is most commonly found in practice, the more ambiguous solutions given by TUCKER3 and MCR-ALS could be balanced by the major flexibility in the modelling of profiles. To assess this possibility, three-way resolution methods from the two mentioned families are applied to simulated and real data sets designed to show typical non-trilinear chemical situations, caused by shifts and shape changes in profiles. Copyright (C) 2001 John Wiley Sons, Ltd.