  Unsupervised Domain Adaptation (UDA) aims to transfer the knowledge from the
labeled source domain to the unlabeled target domain in the presence of dataset
shift. Most existing methods cannot address the domain alignment and class
discrimination well, which may distort the intrinsic data structure for
downstream tasks (e.g., classification). To this end, we propose a novel
geometry-aware model to learn the transferability and discriminability
simultaneously via nuclear norm optimization. We introduce the domain coherence
and class orthogonality for UDA from the perspective of subspace geometry. The
domain coherence will ensure the model has a larger capacity for learning
separable representations, and class orthogonality will minimize the
correlation between clusters to alleviate the misalignment. So, they are
consistent and can benefit from each other. Besides, we provide a theoretical
insight into the norm-based learning literature in UDA, which ensures the
interpretability of our model. We show that the norms of domains and clusters
are expected to be larger and smaller to enhance the transferability and
discriminability, respectively. Extensive experimental results on standard UDA
datasets demonstrate the effectiveness of our theory and model.
