Revamping information entropy: A tailored metric for pre-evaluating quality of 2D analytical signal – A tutorial

Abstract

The information flow and its interpretation define today's analytical chemistry. The critical requirement for analytical methods development is to have an analytical signal containing the maximum information about the material system under study. To date, this has been evaluated ex-post, i.e., once the analytical method has been fully developed and validated. However, it would be useful to have a suitable tool allowing to know a priori the informative quality, and even compare signals from different analytical techniques or acquired under different instrumental conditions. This tutorial proposes a way to perform this ex-ante evaluation. For this purpose, information theory, scarcely applied in recent years in analytical chemistry, is rescued. It is based on the entropy calculation as an indirect measurement of the amount of information embedded in an instrumental signal. Applying this approach enabled to propose several information indices, normalised between 0 and 1 and thus easily interpretable, to assess the information present in an analytical signal. Some analytical signal modifications that can affect its informative quality are highlighted by applying the metrics to simulated signals. Finally, the same metrics are calculated and interpreted on real analytical signals (Raman, NMR and chromatographic ones) to exemplify the advantages of this new approach.