Comparison between the direct trilinear decomposition and the multivariate curve resolution-alternating least squares methods for the resolution of three-way data sets

Direct trilinear decomposition (DTD) and multivariate curve resolution-alternating least squares (MCR-ALS) methods are two of the most representative three-way resolution procedures. The former, non-iterative, is based on the resolution of the generalized eigenvector/eigenvalue problem and the latter, iterative, is focused on the optimization of initial estimates by using data structure and chemical constraints. DTD and MCR-ALS have been tested on a variety of three-way simulated data sets having common sources of variation in real response profiles, such as signal shift, broadening or shape distortions caused by noise. The effect of these factors on the resolution results has been evaluated through the analysis of several parameters related to the recovery of both qualitative and quantitative information and to the quality of the overall data description. Conclusions inferred from the simulated examples help to clarify the performance of both methods on a real example and to provide some general guidelines to understand better the potential of each method.