Unsupervised Domain Adaptation (UDA) is crucial for reducing the need for extensive manual data annotation when training deep networks on point cloud data. A significant challenge of UDA lies in effectively bridging the domain gap. To tackle this challenge, we propose \textbf{C}urvature \textbf{D}iversity-Driven \textbf{N}uclear-Norm Wasserstein \textbf{D}omain Alignment (CDND). Our approach first introduces a \textit{\textbf{Curv}ature Diversity-driven Deformation \textbf{Rec}onstruction (CurvRec)} task, which effectively mitigates the gap between the source and target domains by enabling the model to extract salient features from semantically rich regions of a given point cloud. We then propose \textit{\textbf{D}eformation-based \textbf{N}uclear-norm \textbf{W}asserstein \textbf{D}iscrepancy (D-NWD)}, which applies the Nuclear-norm Wasserstein Discrepancy to both \textit{deformed and original} data samples to align the source and target domains. Furthermore, we contribute a theoretical justification for the effectiveness of D-NWD in distribution alignment and demonstrate that it is \textit{generic} enough to be applied to \textbf{any} deformations. To validate our method, we conduct extensive experiments on two public domain adaptation datasets for point cloud classification and segmentation tasks. Empirical experiment results show that our CDND achieves state-of-the-art performance by a noticeable margin over existing approaches.

Graph-structured data can be found in numerous domains, yet the scarcity of labeled instances hinders its effective utilization of deep learning in many scenarios. Traditional unsupervised domain adaptation (UDA) strategies for graphs primarily hinge on adversarial learning and pseudo-labeling. These approaches fail to effectively leverage graph discriminative features, leading to class mismatching and unreliable label quality. To navigate these obstacles, we develop the Denoising and Nuclear-Norm Wasserstein Adaptation Network (DNAN). DNAN employs the Nuclear-norm Wasserstein discrepancy (NWD), which can simultaneously achieve domain alignment and class distinguishment. DANA also integrates a denoising mechanism via a variational graph autoencoder that mitigates data noise. This denoising mechanism helps capture essential features of both source and target domains, improving the robustness of the domain adaptation process. Our comprehensive experiments demonstrate that DNAN outperforms state-of-the-art methods on standard UDA benchmarks for graph classification.