Dual-Space Topological Isomorphism and Maximization of Predictive Diversity for Unsupervised Domain Adaptation

Most existing unsupervised domain adaptation methods rely on explicitly or implicitly aligning the features of source and target domains to construct a domain-invariant space, often using entropy minimization to reduce uncertainty and confusion. However, this approach faces two challenges: 1) Explicit alignment reduces discriminability, while implicit alignment risks pseudo-label noise, making it hard to balance structure preservation and alignment. 2) Sole reliance on entropy minimization can lead to trivial solutions in UDA, where all samples collapse into a single class. To address these issues, we propose Dual-Space Topological Isomorphism and Maximization of Predictive Diversity (DTI-MPD). Topological isomorphism is a continuous, bijective mapping that preserves the topological properties of two spaces, ensuring the global structure and relationships of data remain intact during alignment. Our method aligns source and target domain data in two independent spaces while balancing the effects of entropy minimization through predictive diversity maximization. The core of dual-space topological isomorphism lies in establishing a reversible correspondence between the source and target domains, avoiding information loss during alignment and preserving the global structural and topological characteristics of the data. Meanwhile, predictive diversity maximization mitigates the class collapse caused by entropy minimization, ensuring a more balanced predictive distribution across categories. This approach effectively overcomes the aforementioned issues, enabling better adaptation to new data. Extensive experiments demonstrate that our method achieves state-of-the-art performance on multiple benchmark datasets, validating its effectiveness.