  Domain adaptation is a popular paradigm in modern machine learning which aims
at tackling the problem of divergence (or shift) between the labeled training
and validation datasets (source domain) and a potentially large unlabeled
dataset (target domain). The task is to embed both datasets red into a common
space in which the source dataset is informative for training while the
divergence between source and target is minimized. The most popular domain
adaptation solutions are based on training neural networks that combine
classification and adversarial learning modules, frequently making them both
data-hungry and difficult to train. We present a method called Domain
Adaptation Principal Component Analysis (DAPCA) that identifies a linear
reduced data representation useful for solving the domain adaptation task.
DAPCA algorithm introduces positive and negative weights between pairs of data
points, and generalizes the supervised extension of principal component
analysis. DAPCA is an iterative algorithm that solves a simple quadratic
optimization problem at each iteration. The convergence of the algorithm is
guaranteed, and the number of iterations is small in practice. We validate the
suggested algorithm on previously proposed benchmarks for solving the domain
adaptation task. We also show the benefit of using DAPCA in analyzing the
single-cell omics datasets in biomedical applications. Overall, DAPCA can serve
as a practical preprocessing step in many machine learning applications leading
to reduced dataset representations, taking into account possible divergence
between source and target domains.

Machine Learning