Can Angle Measures Be Useful in MCR Analyses?

Abstract

In MCR analyses, the similarity of pairs of spectra or concentration profiles can be measured in terms of the acute angle that is enclosed by the representing vectors. Acute angles between vectors can be generalized to pairs of subspaces. So-called canonical angles, also called principal angles, measure the mutual orientation of a pair of subspaces. This work discusses how angles and canonical angles can support multivariate curve resolution analyses. A canonical angle analysis (CAA) can help to detect changes of the chemical composition during a chemical reaction in a way comparable, but different to the evolving factor analysis (EFA).