The continuity of sample complexity and its relationship to multivariate calibration: A general perspective on first-order calibration of spectral data in analytical chemistry

Classical calibration and inverse calibration represent two different scenarios in multivariate calibration in chemical modeling. A large amount of literature has been devoted to these two areas, yet the intrinsic differences and what kind of analytical systems they can be applied to, still remain not fully understood. In this tutorial, with the introduction of sample complexity of analytical systems, we present a systematic look at classical calibration and inverse calibration with their differences substantiated, internal links understood and the characteristics of analytical systems that they can model clarified. We first point out that a classical calibration model is established in Component Spectral Space, where a calibration model can generalize well only if it includes all components that may exist in test samples, whereas an inverse calibration model is built in Measured Variable Space, where variable selection is often necessary to improve predictive performances through the removal of interfering variables. Of particular importance, we argue that the explanation for PLS by simply using net analyte signal theory is questionable in the case of inverse calibration such as near-infrared spectral analysis. We verified our perspectives using carefully designed datasets.

► We related sample complexity to the selection of multivariate calibration methods.
► We explored the relationship between direct calibration and indirect calibration.
► We showed the power of variable selection for analyzing samples of high complexity.