Discussion on the superiority of third-order advantage: Analytical application for four-way data in complex system

In this paper, the ‘third-order advantage’ was explored through comparing the performance of PARAFAC and four-way PARAFAC using simulated and experimental data sets. The results demonstrated that the third-order calibration method could extract more inherent information from the data, and easily solve the problems of serious collinearity, high-intensity noise and strong background interference. As an example, a real experimental data set has been processed for the quantitative analysis of three phenolic acids in cosmetic samples. However, PARAFAC is disappointing due to serious collinearity and high-intensity noise of the experimental data in this report. In contrast, the satisfactory results (average recovery, 99.96–101.49%, average relative error, 6.26–13.48%) are provided by four-way PARAFAC.