Modeling Hierarchical Structural Distance for Unsupervised Domain Adaptation

Unsupervised domain adaptation (UDA) aims to estimate a transferable model for unlabeled target domains by exploiting labeled source data. Optimal Transport (OT) based methods have recently been proven to be a promising solution for UDA with a solid theoretical foundation and competitive performance. However, most of these methods solely focus on domain-level OT alignment by leveraging the geometry of domains for domain-invariant features based on the global embeddings of images. However, global representations of images may destroy image structure, leading to the loss of local details that offer category-discriminative information. This study proposes an end-to-end Deep Hierarchical Optimal Transport method (DeepHOT), which aims to learn both domain-invariant and category-discriminative representations by mining hierarchical structural relations among domains. The main idea is to incorporate a domain-level OT and image-level OT into a unified OT framework, hierarchical optimal transport, to model the underlying geometry in both domain space and image space. In DeepHOT framework, an image-level OT serves as the ground distance metric for the domain-level OT, leading to the hierarchical structural distance. Compared with the ground distance of the conventional domain-level OT, the image-level OT captures structural associations among local regions of images that are beneficial to classification. In this way, DeepHOT, a unified OT framework, not only aligns domains by domain-level OT, but also enhances the discriminative power through image-level OT. Moreover, to overcome the limitation of high computational complexity, we propose a robust and efficient implementation of DeepHOT by approximating origin OT with sliced Wasserstein distance in image-level OT and accomplishing the mini-batch unbalanced domain-level OT.