An alternating coupled two-unequal residual functions algorithm for second-order calibration

Abstract

In this paper, a novel algorithm, alternating coupled two-unequal residual functions (ACTUF), has been presented to deal with three-way data for second-order calibration and it is able to achieve the important second-order advantage. This new algorithm resolves the parameter matrices by minimizing the two functions of measurement residuals and parameter residuals. Compared with two widely used algorithms, i.e., PARAFAC and SWATLD, the performance of the new algorithm is evaluated by using two simulation and two real data arrays in some aspects, such as noise, collinearity, analysis speed and solution. The results reveal that ACTUF can not only retain the second-order advantage, but also be insensitive to excessive component numbers and hold strong anti-noise tolerance. Besides, compared to the other two algorithms, ACTUF can successfully deal with the problems due to severe collinearity.