Chapter 3 - Multiway Calibration Based on Alternating Multilinear Decomposition

Abstract

Abstract With the increasing number of analytical instruments capable of generating multidimensional arrays of experimental data per sample, multiway data analysis has attracted more and more attention and gained widespread acceptance in many scientific fields. The uniqueness property of trilinear or multilinear decomposition solution implies that the data following the trilinear or multilinear model can be uniquely decomposed into individual contributions holding physical significance. Especially, trilinear data analysis possesses “second-order advantage,” e.g., several components of interest can be quantified even in the presence of unknown interferents by using such calibration methodology. In this chapter, some aspects of multiway calibration mainly based on alternating multilinear decomposition, such as multilinear component (factor) models, multiway cyclic symmetry property, algorithms for multiway calibration, estimation of the chemical rank, toolbox, and other fundamental issues, will be briefly described. Finally, the way of obtaining solutions and MATLAB programs for some multiway calibration methods are shown in Appendixes.