Semi-supervised covariate shift modelling of spectroscopic data

Utilizing the full potential of spectroscopic calibrations in changing environments typically requires large amounts of maintenance and/or model updates as the presence of new sources of variation makes the calibration insufficient. In this paper, we propose the use of unlabelled data in order to automize such maintenance. We extend the Linear Joint Trained Framework by Ryan and Culp such that the shifts in mean value and covariance structure are modelled explicitly. The extension yields a more flexible framework, and thus we are able to regularize the final calibration in a more desirable manner. The proposed framework is tested on a simulated dataset where we simulate three different realistic scenarios that are either challenging for classic multivariate calibrations or challenging when adding unlabelled data. Furthermore, we test our framework on two real datasets across multiple data splits. We find that our framework not only achieves the same (and in some instances lower) error level as that of the baseline model (NARE), it also yields better calibration models than the Linear Joint Trained Framework.