Is independent component analysis appropriate for multivariate resolution in analytical chemistry?

Abstract

In this article, we examine Independent Component Analysis (ICA) and the concept of Mutual information (MI) as a quantitative measure of independence from the point of view of analytical chemistry. We compare results obtained by different ICA methods with results obtained by Multivariate Curve Resolution Alternating Least Squares (MCR-ALS). These results have shown that, when non-negativity constraints are applied, values of MI increase considerably and the resolved components cannot anymore be considered to be independent (i.e. they can only be considered to be the “least dependent” components). MI values of profiles resolved by MCR-ALS and ICA did not differ significantly when non-negativity constraints were applied. In addition, since data-fitting values were also practically the same in both cases, the solutions provided by them should be considered equivalent from a mathematical point of view and within the region of feasible solutions for the particular set of applied constraints. We therefore conclude that the solutions based only on the independence concept are not necessarily better from the point of view of analytical chemistry than those obtained by other proposed MCR methods. Results obtained in this work also show that ICA can be considered an alternative tool for resolving mixed signals only in a limited number of cases.