  Unsupervised domain adaptation (UDA) aims to transfer knowledge from a
labeled source domain to an unlabeled target domain. In this paper, we
introduce a novel approach called class-aware optimal transport (OT), which
measures the OT distance between a distribution over the source
class-conditional distributions and a mixture of source and target data
distribution. Our class-aware OT leverages a cost function that determines the
matching extent between a given data example and a source class-conditional
distribution. By optimizing this cost function, we find the optimal matching
between target examples and source class-conditional distributions, effectively
addressing the data and label shifts that occur between the two domains. To
handle the class-aware OT efficiently, we propose an amortization solution that
employs deep neural networks to formulate the transportation probabilities and
the cost function. Additionally, we propose minimizing class-aware Higher-order
Moment Matching (HMM) to align the corresponding class regions on the source
and target domains. The class-aware HMM component offers an economical
computational approach for accurately evaluating the HMM distance between the
two distributions. Extensive experiments on benchmark datasets demonstrate that
our proposed method significantly outperforms existing state-of-the-art
baselines.
