Multiway analysis through direct excitation-emission matrix imaging

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

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.

The advantages behind the efforts of performing higher-order calibration methods - A case study

BACKGROUND

Across numerous investigations delved into second- and higher-order data, an undoubted finding emerges: models based on such data can effectively exploit the second-order advantage. However, whether further benefits can be achieved by modeling data of higher dimensions remains a subject of inquiry. In this regard, a prevailing question emerges in third-order data-based applications regarding the fundamental need to increase the data dimension and, hence, the data analysis complexity. This study aims to provide meaningful evidence to support the advantages inherent in employing third-order calibration methods despite the associated efforts, such as instrumentation and data analysis complexity.

RESULTS

This study compares the analytical performance achieved using a third-order calibration method with those obtained from most of the possible second-order calibration approaches derived from the same dataset. This work delves into the structural properties of the data, modeling limitations, and analytical characteristics associated with each model. Additionally, it includes a comprehensive statistical comparison of the models based on their recovery performance. First, the outcomes demonstrate the importance of capitalizing on all available chemical information and harnessing the full potential of data to maximize its benefits. Moreover, the results provide evidence that asserts the fact that third-order calibration methods bring the opportunity to increase the number of analytes that can be simultaneously determined, notwithstanding the need for more tedious experimental protocols, specialized instrumentation (sometimes), and quite complex data analysis.

SIGNIFICANCE

this research marks the first extensive comparison of third-order data calibration models with possible second-order calibration methods. Moreover, this work pioneers the incorporation of highly challenging non-multilinear data. The advancements detailed in this study emphasize the advantages of third-order data acquisition, notwithstanding the need for more tedious experimental protocols, specialized instrumentation (sometimes), and quite complex data analysis.

Chromatographic Applications in the Multi-Way Calibration Field

In this review, recent advances and applications using multi-way calibration protocols based on the processing of multi-dimensional chromatographic data are discussed. We first describe the various modes in which multi-way chromatographic data sets can be generated, including some important characteristics that should be taken into account for the selection of an adequate data processing model. We then discuss the different manners in which the collected instrumental data can be arranged, and the most usually applied models and algorithms for the decomposition of the data arrays. The latter activity leads to the estimation of surrogate variables (scores), useful for analyte quantitation in the presence of uncalibrated interferences, achieving the second-order advantage. Recent experimental reports based on multi-way liquid and gas chromatographic data are then reviewed. Finally, analytical figures of merit that should always accompany quantitative calibration reports are described.

Four- and five-way excitation-emission luminescence-based data acquisition and modeling for analytical applications. A review

The latest advances in both theory and experimental procedures on third-order/four-way and fourth-order/five-way calibration methods are discussed. This report is focused on excitation-emission (fluorescence and phosphorescence) matrices generation, employing different variables as the third data mode (time retention in chromatography, pH gradient, fluorescence/phosphorescence lifetime, kinetics, or other chemical treatments). Fully capitalizing on the second-order advantage, it has been possible to develop appealing analytical applications in spite of the complexity of the data. Extraction of the significant chemical information about the system under study as well as the individual abundance of the contributing constituents after proper higher-order data decomposition has allowed to analytical researchers performing quantitative analysis of complex samples. The experimental works reported up to the present are introduced and discussed in order to illustrate concepts. Throughout this work, the analytical benefits achieved by modeling third- and fourth-order data are exposed, attempting to contribute to the ongoing debate in the chemometric community regarding the existence and the true nature of the third-order advantage.