Homeomorphism Alignment for Unsupervised Domain Adaptation

Existing unsupervised domain adaptation (UDA) methods rely on aligning the features from the source and target domains explicitly or implicitly in a common space (i.e., the domain invariant space). Explicit distribution matching ignores the discriminability of learned features, while the implicit counterpart such as self-supervised learning suffers from pseudo-label noises. With distribution alignment, it is challenging to acquire a common space which maintains fully the discriminative structure of both domains. In this work, we propose a novel HomeomorphisM Alignment (HMA) approach characterized by aligning the source and target data in two separate spaces. Specifically, an invertible neural network based homeomorphism is constructed. Distribution matching is then used as a sewing up tool for connecting this homeomorphism mapping between the source and target feature spaces. Theoretically, we show that this mapping can preserve the data topological structure (e.g., the cluster/group structure). This property allows for more discriminative model adaptation by leveraging both the original and transformed features of source data in a supervised manner, and those of target domain in an unsupervised manner (e.g., prediction consistency). Extensive experiments demonstrate that our method can achieve the state-of-the-art results. Code is released at https://github.com/buerzlh/HMA.