  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.
