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Domain adaptation is a popular paradigm in modern machine learning which aimsat tackling the problem of divergence (or shift) between the labeled trainingand validation datasets (source domain) and a potentially large unlabeleddataset (target domain). The task is to embed both datasets red into a commonspace in which the source dataset is informative for training while thedivergence between source and target is minimized. The most popular domainadaptation solutions are based on training neural networks that combineclassification and adversarial learning modules, frequently making them bothdata-hungry and difficult to train. We present a method called DomainAdaptation Principal Component Analysis (DAPCA) that identifies a linearreduced data representation useful for solving the domain adaptation task.DAPCA algorithm introduces positive and negative weights between pairs of datapoints, and generalizes the supervised extension of principal componentanalysis. DAPCA is an iterative algorithm that solves a simple quadraticoptimization problem at each iteration. The convergence of the algorithm isguaranteed, and the number of iterations is small in practice. We validate thesuggested algorithm on previously proposed benchmarks for solving the domainadaptation task. We also show the benefit of using DAPCA in analyzing thesingle-cell omics datasets in biomedical applications. Overall, DAPCA can serveas a practical preprocessing step in many machine learning applications leadingto reduced dataset representations, taking into account possible divergencebetween source and target domains.

Domain Adaptation Principal Component Analysis: base linear method for learning with out-of-distribution data