A comparison of several trilinear second-order calibration algorithms

A comprehensive and systematic strategy for evaluating the performances of several trilinear second-order calibration algorithms is presented in this paper, in particular with a view of practical applications. Several trilinear second-order calibration methods such as PARAFAC, ATLD, SWATLD and APTLD, which have the “second-order advantage” and are gaining widespread acceptance in the field of chemometrics, were compared. Based on different input parameters including noise level, initial value, number of estimated components and collinearity in simulated and real data, the performances of these methods were evaluated in terms of predicting ability, consistency of resolved and real profiles, fitness obtained by selected components and speed of convergence. The obtained results give a reevaluation of the position and role of these trilinear second-order calibration methods in chemometrics and provide a guidance in practical applications for solving complicated quantitative analysis problems in analytical chemistry. It is useful and helpful to choose, for example, which algorithm would be more suitable for predicting the concentration of the analyte(s) of interest even in the presence of unknown interferents in complex systems.