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Multiset Data Analysis: Extended Multivariate Curve Resolution

R. Tauler,M. Maeder,A. Juan

Published 2020 in Comprehensive Chemometrics

ABSTRACT

In this chapter, the extension of the multivariate curve resolution-alternating least squares (MCR-ALS) method to the simultaneous analysis of multiple data sets bearing information in common is presented. The basic assumption in this extension of multivariate curve resolution (MCR) methods is the fulfillment of a common bilinear model for the simultaneously analyzed data sets, which implies that they share at least some parts of their data variance, e.g.,. some chemical components or species are common among them. Different data arrangements are possible in this approach, depending on the common information shared among the different simultaneously analyzed data sets. If the common information is shared in the variables or column space, a column-wise data matrix augmentation scheme will be adequate to improve MCR analysis and results. On the contrary, if the common information is shared in the samples or row space, a row-wise data matrix augmentation scheme will be more adequate to improve MCR analysis and results. Finally, when these two possibilities are present, a row- and column-wise data matrix augmentation will give the optimal data arrangement for optimal MCR analysis and results. Using these different data matrix augmentation schemes, MCR analysis of multiset arrangements and of more structured multiway data sets is possible. Implementation of constraints during the alternating least squares (ALS) optimization can be tailored according to the specific features of each data matrix and higher order structures, allowing also for the fulfillment of trilinear and multilinear models. Apart from improved resolution capabilities, extended MCR via matrix augmentation is also a powerful tool to break chemical rank deficiencies that often plague chemical reaction-based systems and to perform accurate quantitative estimations deduced from the relative comparison of some parameters of the resolved concentration profiles (height, area) of the common components in the different data sets. A further extension of MCR methods is the inclusion of a priori fundamental knowledge or laws about the nature or behavior of some (or all) of the components in the system. This implies the inclusion of physical or deterministic (hard) modeling in the general frame of the MCR soft bilinear modeling. Kinetics and thermodynamics are the key disciplines of chemistry and are fundamental to all aspects of reaction analysis, where either equilibria mass action laws or kinetic rate laws govern the shape of the concentration profiles of the chemical species linked by multiple equilibria or by kinetics. The possibility of hybridizing these two types of modeling, also called hybrid hard–soft modeling (or gray modeling, considering hard-modeling as white modeling and soft-modeling as black modeling), opens the door to the use of extended MCR in fundamental studies in physical sciences in general and allows for the analysis of complex natural systems where the estimation of parameters (thermodynamic, kinetic) governing these systems is also of relevance and should be performed in the presence of interference contributions. This hybrid approach is especially interesting in cases where the strictly controlled conditions of a laboratory environment cannot be achieved and/or where unknown phenomena disturb the measured signals. Using extended MCR hybrid hard–soft models allows modeling a part of the data variance fulfilling strictly the requirements of physical laws and modeling another part of it freely by a bilinear type of soft model.

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