An improved trilinear decomposition algorithm based on a Lagrange operator.

An improved trilinear decomposition algorithm based on a Lagrange operator (LO) is developed in this paper, which introduces a Lagrange operator and penalty terms in the loss function to improve the performance of the algorithm. Compared to the traditional parallel factor (PARAFAC) algorithm, the algorithm not only may converge much faster, but also overcome the sensibility to estimate the number of components. A set of simulated and measured excitation/emission fluorescence data were treated by both the proposed and traditional PARAFAC algorithm to compare their efficiencies. The analytical results obtained with real chemical system containing aspirin and its metabolic products show that the trilinear decomposition methodology is a promising tool to obtain spectral and composition information from mixtures without chemical separation.