A robust PARAFAC method
Sanne M.E. Engelen, Mia Hubert · 2005
Modelling higher order arrays of data has gained importance in chemometrics (see e.g. Andersen et al. (2003), Smilde et al. (2004), Tomasi et al. (2005)). Different models exist for this purpose among which PARAFAC (parallel factor analysis) is one of the most important ones. PARAFAC helps understanding the underlying structure of three-way data if these data are approximately trilinear. The algorithm to compute the PARAFAC parameters (see Bro (1998), Smilde et al. (2004)) is based on an alternating least squares procedure, which can not withstand the presence of outliers. Because outliers are frequently common in chemometrics, a robust alternative is necessary. In the literature (see Pravdova et al. (1999), Riu et al. (2003)) some methods have already been investigated, but they can not cope with groups of outliers or with high-dimensional data. We propose a robust PARAFAC version starting with unfolding the three-way array and applying a method for robust principal components analysis.