Alternating asymmetric trilinear decomposition for three-way data arrays analysis

Abstract

An alternating asymmetric trilinear decomposition for three-way data arrays analysis (AATLD) method was introduced. The new proposed algorithm combines the merit of Three-way Alternating Least Squares (Tri-ALS) and Alternating Trilinear Decomposition (ATLD). It retains the second-order advantage of quantification for analyte(s) of interest even in the presence of potentially unknown interferents. As an asymmetric trilinear decomposition, AATLD can perform well when three-way data arrays possess serious collinearity problem. Simulated and real high-performance liquid chromatography data arrays were used to demonstrate these advantages of the algorithm. In contrast with traditional PARAFAC, ATLD and Tri-ALS, the new proposed algorithm performs better when the data are high collinear, e.g., the large condition number of the loading matrices A, B and C. Even with heavily collinear simulated data set, it was also found that the AATLD algorithm is faster than others on obtaining solutions with chemical meaning.