Graph-based calibration transfer

Calibration transfer (CT), sometimes referred to as instrument standardization in chemometrics, is the process of transferring a calibration model from one instrument to another [1, 2, 3]. Ideally, CT preserves the accuracy and precision of a calibration model developed on a primary instrument, i.e. providing statistically identical analysis of the same samples measured on the secondary instrument. Historically, CT has been addressed by i) model updating, or ii) measuring a set of so-called calibration standards on both instruments in order to derive a correction for the difference in the instrumental response. The former can be considered more generic and copes with any type of change related to the measurement condition such as environmental influences, matrix effects or instrumental changes. Slope and bias correction [4], calibration set augmentation [5], model updating via Tihkonov regularization [6] or domain-invariant modelling [7, 8, 9] all belong to this category and have been applied with success to CT problems. However, these methods usually require a considerable amount of (additional) samples (and reference measurements) and deciding between maintenance and re-calibration is not always straightforward. Calibration transfer by means of calibration standards, on the other hand, solely requires a small set of samples that can be measured on both devices and does not require any additional reference values. In this second category, Direct- (DS) and piecewise direct standardization (PDS) can be considered the gold standard [10]. Both operate by learning a multivariate transformation (mapping) such that the instrumental response of the secondary instrument matches with the one of the primary instrument.