Multiway calibration. Multilinear PLS

A new multiway regression method called N ‐way partial least squares (N‐PLS) is presented. The emphasis is on the three‐way PLS version (tri‐PLS), but it is shown how to extend the algorithm to higher orders. The developed algorithm is superior to unfolding methods, primarily owing to a stabilization of the decomposition. This stabilization potentially gives increased interpretability and better predictions. The algorithm is fast compared with e.g. PARAFAC, because it consists of solving eigenvalue problems. An example of the developed algorithm taken from the sugar industry is shown and compared with unfold‐PLS. Fluorescence excitation—emission matrices (EEMs) are measured on white sugar solutions and used to predict the ash content of the sugar. The predictions are comparable by the two methods, but there is a clear difference in the interpretability of the two solutions. Also shown is a simulated example of EEMs with very noisy measurements and a low relative signal from the analyte of interest. The predictions from unfold‐PLS are almost twice as bad as from tri‐PLS despite the large number of samples (125) used in the calibration. The algorithms are available from World Wide Web: hhtp:\\newton.foodsci.kvl.dk\foodtech.