Trilinear least-squares and unfolded-PLS coupled to residual trilinearization: New chemometric tools for the analysis of four-way instrumental data

A new chemometric algorithm, trilinear least-squares (TLLS) coupled to residual trilinearization (RTL), developed as an extension of one of the variants of bilinear least-squares (BLLS), the so-called singular value decomposition-least-squares (SVD-LS) coupled to residual bilinearization (RBL), is described for the analysis of four-way data. Monte Carlo numerical simulations are employed to compare its performance with that of the well-known parallel factor analysis (PARAFAC) model, and also with the combination of unfolded partial least-squares (PLS) with RTL. This latter method has been developed as an extension of unfolded-PLS coupled to RBL. An experimental system based on the kinetic measurement of the evolution of the excitation-emission fluorescence matrices with time for mixtures of two anticancer drugs is also studied. The kinetic reaction is based on the oxidation of leucovorin and metotrexate with potassium permanganate to give highly fluorescent compounds. Both chemometric methodologies exploit the second-order advantage of the employed multi-way data, allowing analyte concentrations to be estimated even in the presence of uncalibrated components in the samples. The new methods herein described constitute new competitors of PARAFAC for this type of analyses, in which four-way instrumental data are used.