Domain adaptation for regression under Beer–Lambert’s law

We consider the problem of unsupervised domain adaptation (DA) in regression under the assumption of linear hypotheses (e.g. Beer–Lambert’s law) – a task recurrently encountered in analytical chemistry. Following the ideas from the non-linear iterative partial least squares (NIPALS) method, we propose a novel algorithm that identifies a low-dimensional subspace aiming at the following two objectives: (i) the projections of the source domain samples are informative w.r.t. the output variable and (ii) the projected domain-specific input samples have a small covariance difference. In particular, the latent variable vectors that span this subspace are derived in closed-form by solving a constrained optimization problem for each subspace dimension adding flexibility for balancing the two objectives. We demonstrate the superiority of our approach over several state-of-the-art (SoA) methods on different DA scenarios involving unsupervised adaptation of multivariate calibration models between different process lines in Melamine production and equality to SoA on two well-known benchmark datasets from analytical chemistry involving (unsupervised) model adaptation between different spectrometers. The former dataset is published with this work1 1https://github.com/RNL1/Melamine-Dataset.