Flexible Trilinearity Alignment (FTA) and Shift Invariant Transformation (SIT) Constraints in Three-Way Multivariate Curve Resolution Data Analysis

In this work, two alternative ways of analyzing three-way data with multivariate curve resolution alternating least squares (MCR-ALS) using the trilinearity constraint are described and compared. Different synthetic datasets and experimental three-way datasets covering different scenarios are analyzed, and the results obtained are compared. The two new different ways of applying the trilinearity constraint are named flexible trilinearity alignment (FTA) and shift invariant transformation (SIT). The effects of noise in the application of both types of constraints are investigated in detail. Results show that both approaches are particularly adequate for those cases like in gas chromatography and especially in liquid chromatography where the elution profiles of the same chemical component in different chromatographic runs are not totally reproducible because they are time shifted, although they preserve their shape. When strong time shifts and co-elution occur, then the “standard” trilinear model does not work, and alternative approaches should be used, such as the MCR extended bilinear model to multiset (multirun) data, or the proposed relaxation of the trilinearity constraint in the FTA and SIT methods to capture the time drift changes produced in the elution profiles of the resolved components.