Multi-way analysis of outer product arrays using PARAFAC

PARAFAC was developed in order to deal with datasets presented in more than two-dimensional arrays. These data are intrinsically multi-way, i.e., for each sample, the measured array has at least two dimensions. PARAFAC has been extensively used in chemometrics to decompose 3D-fluorescence spectroscopy data or data from coupled techniques such as HPLC-DAD or GC-MS. In this article, several 1D-measurements (e.g., spectra) on samples are combined by computing the outer product of the two (or more) spectrum-vectors, resulting in a matrix (or a higher-order array) for each sample. The data set obtained when all the samples are grouped together is a multi-way array, which can then be analysed by PARAFAC. Application of this method to several real data sets yields interesting, easily interpreted results.