Geometry-Aware Unsupervised Domain Adaptation

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.