2.21 - Multiway Data Analysis: Eigenvector-Based Methods

Abstract

A variety of analytical techniques generate a matrix of instrumental responses for each analyzed sample. A large number of multivariate (multiway) methods of analysis can provide qualitative and quantitative information from such data. In this section we discuss those methods that are based on solving an eigenvalue problem, basically rank annihilation factor analysis (RAFA), generalized rank annihilation method (GRAM), direct trilinear decomposition (DTD), and direct exponential curve resolution algorithm (DECRA), along with some variations and related methods. The theoretical background of the methods, the necessary structure of the data and model assumptions, and the position of these methods among alternatives that can be applied to this type of data (especially those methods based on least squares) are discussed. The practical aspects that must be taken into account are also discussed along with a list of applications. Finally, derivations of the equations and source code for the core computations are given in the appendices.