COMMENTS ON MULTILINEAR PLS

Recently, Bro published a paper on multilinear PLS (J. Chemometrics, 1 0, 47-61 (1996)) in which he proposed a generalization of PLS to multi way situations, called multilinear PLS, which is a mixture of a trilin ear model (PARAFAC) and PLS. However, Bro does not give the equations for the prediction step. In this paper these prediction equations are given in both their full and closed forms. The least squares propertie s of the proposed multilinear PLS are established and a more comprehen sive notation is given. Using this notation, it is clear that some oth er multiway analysis methods such as PARAFAC and Tucker1 models can be combined with PLS. Multiway methods such as Tucker2 and Tucker3 need a different approach. A framework is given for general two-block multi way models. (C) 1997 John Wiley & Sons, Ltd.