Abstract Domain shift, which occurs when there is a mismatch between the distributions of training (source) and testing (target) datasets, usually results in poor performance of the trained model on the target domain. Existing algorithms typically solve this issue by reducing the distribution discrepancy in the input spaces. However, for kernel-based learning machines, performance highly depends on the statistical properties of data in reproducing kernel Hilbert spaces (RKHS). Motivated by these considerations, we propose a novel strategy for matching distributions in RKHS, which is done by aligning the RKHS covariance matrices (descriptors) across domains. This strategy is a generalization of the correlation alignment problem in Euclidean spaces to (potentially) infinite-dimensional feature spaces. In this paper, we provide two alignment approaches, for both of which we obtain closed-form expressions via kernel matrices. Furthermore, our approaches are scalable to large datasets since they can naturally handle outof-sample instances. We conduct extensive experiments (248 domain adaptation tasks) to evaluate our approaches. Experiment results show that our approaches outperform other state-of-the-art methods in both accuracy and computationally efficiency