2.24 - Multiset Data Analysis: Extended Multivariate Curve Resolution

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.