Functional data analysis, a comprehensive framework for processing non-quadrilinear and low-selective data provided by four-way liquid chromatography analysis

Abstract

The chemometric treatment of higher-order chromatographic (LC) data often crashes due to two main effects: the chromatographic band shifts/warpings across samples and quasi-full overlaps between component signals, affecting their analytical selectivities. From a chemometric point of view, these phenomena have independent effects, although they can jointly contribute to the failure of the algorithms: 1) data multilinearity breaking, leading to the poor performance of multilinear decomposition algorithms, and 2) linear dependence between the analytes signals, causing the failure of folded models. Under this scenario, making chemometric processing feasible involves defining specific experimental conditions that minimize these effects or increasing the number of instrumental ways to deal with selectivity lost.

This work presents the Functional Aligned of Pure Vectors (FAPV) algorithm for restoring four-way chromatographic data multilinearity and bearing the spectral overlap trouble. Simulated and experimental four-way data were used to test the FAPV analytical efficiency, covering a wide range of chromatographic artifacts. Based on a multi-injection procedure, the experimental case implied the chromatographic determination of two analytes with uncalibrated interferents in aqueous samples. Both data systems were subjected to FAPV and then processed by PARAFAC. Therefore, a comprehensive comparison was made with the most widely used chemometric models for non-multilinear chromatographic data (MCR-ALS and PARAFAC2). Moreover, the performance of the FAPV approach was compared with commonly used alignment procedures, e.g., correlation-optimized warping. The results (c.a. REPs of 10 % in both analytes from the experimental case) show the efficiency of the FAPV algorithm in solving the troubles observed in chromatographic/spectral data.