  In this paper, we propose a novel approach for unsupervised domain
adaptation, that relates notions of optimal transport, learning probability
measures and unsupervised learning. The proposed approach, HOT-DA, is based on
a hierarchical formulation of optimal transport, that leverages beyond the
geometrical information captured by the ground metric, richer structural
information in the source and target domains. The additional information in the
labeled source domain is formed instinctively by grouping samples into
structures according to their class labels. While exploring hidden structures
in the unlabeled target domain is reduced to the problem of learning
probability measures through Wasserstein barycenter, which we prove to be
equivalent to spectral clustering. Experiments on a toy dataset with
controllable complexity and two challenging visual adaptation datasets show the
superiority of the proposed approach over the state-of-the-art.
