Alternating asymmetric trilinear decomposition for three-way data arrays analysis

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. (c) 2005 Elsevier B.V. All rights reserved.