Riemannian representation learning for multi-source domain adaptation

•For the MSDA problem we show that the target error is bounded by the average source error and the average Hellinger distance.•We introduce the RRL approach that aligns distributions in the representation space under the average empirical Hellinger distance.•We derive the average empirical Hellinger distance by constructing and solving unconstrained convex optimization problems.•We conduct comprehensive experiments on several image datasets to demonstrate the superior adaptation performance of the RRL approach.