Alternating coupled matrices resolution method for three-way arrays analysis

An alternating coupled matrices resolution (ACOMAR) method is developed for decomposition of three-way data arrays. By utilizing alternating least squares algorithm to minimize the proposed coupled matrices resolution error, the intrinsic profiles are found. Moreover, it yields simultaneously a numerically exact solution for all analytes present in the samples. This method retains the second-order advantage of quantization for analyte(s) of interest in the presence of potentially unknown interferents. The performance of a simulated experiment and a real analytical example shows that the proposed method works well when the number of components is chosen to be equal to or greater than the actual model dimensionality. The insensitivity of the ACOMAR method to the estimated component number escapes the difficulty of determining a proper component number for the model, which is hard to handle for the PARAFAC algorithm. Furthermore, this method circumvents the two-factor degeneracy, which is intrinsic in the PARAFAC algorithm.