Novel augmented parallel factor model for four-way calibration of high-performance liquid chromatography–fluorescence excitation–emission data

• A novel augmented parallel factor analysis model is presented.
• It allows calibration of four-way chromatographic-excitation–emission data.
• Simulated and experimental systems are analyzed with the new model.
• Experimental data concerning olive oil samples are studied.
• Comparison is made with multivariate curve resolution and partial least-squares.

A new augmented parallel factor analysis model (Augmented PARAFAC) is presented, inspired by the useful augmentation concept employed in multivariate curve resolution-alternating least-squares (MCR-ALS), applicable to calibration based on non-quadrilinear four-way data, such as those produced by high-performance liquid chromatography with matrix excitation–emission fluorescence detection. The new model involves creating an augmented three-way array in the elution time direction, containing data for the calibration sample set and for each of the test samples, subsequently analyzed with an Augmented PARAFAC version. To test the properties of this approach, chromatographic data were simulated with different degrees of overlapping and misalignment among the chromatographic peaks. Additionally, experimental data from olive oil samples were tested with the new model, aimed at the quantitation of the level of chlorophylls and pheophytins. The results were compared with those obtained by data processing with MCR-ALS. Relative prediction errors (%) were: Augmented PARAFAC, 9.7, 21.0, 14.7 and 9.3, and MCR-ALS, 5.9, 14.5, 20.0 and 14.7 for Chl a, Chl b, Phe a Phe b, respectively, for concentrations in the range 0.00–1.00 μg mL− 1. Both MCR-ALS and Augmented PARAFAC allow one to obtain a detailed and realistic description of the analyzed samples, in terms of pure elution time, excitation and emission spectral profiles, which can be independently retrieved for every component.