Local rank exploratory analysis of evolving rank-deficient systems

Abstract

The information related to the local rank plays a key role in the resolution of dynamic multicomponent systems. Methods based on Principal Component Analysis, such as Evolving Factor Analysis (EFA), are perfectly designed to obtain this information as long as the processes under study are described by full rank two-way data sets, i.e., single matrices where all process contributions are linearly independent and can be mathematically distinguished from each other. Two-way rank-deficient systems do not fulfil the requirements needed by classical local rank analysis methods. On one hand, the structure of the single data matrix as such does not allow for the distinction of all the real process contributions; on the other hand, the condition of full rank can only be achieved by matrix augmentation and, then, a three-way data set is obtained. The aim of this work is the design of a local rank exploratory method adapted to work with full rank three-way data sets obtained by matrix augmentation of rank-deficient systems. The method will be tested on several real examples, where the rank-deficiency derives from the presence of coexisting evolving systems. Chemometric aspects, such as the way to obtain local rank information and to build initial estimates, and chemical aspects, such as the use of the method to gather knowledge about unknown interferent systems or about main contributions affected by strong evolving backgrounds, will be commented from the results obtained.