Low-Rank Few-Shot Node Classification by Node-Level Graph Diffusion

In this paper, we propose a novel node-level graph diffusion method with low-rank feature learning for few-shot node classification (FSNC), termed Low-Rank Few-Shot Graph Diffusion Model or LR-FGDM. LR-FGDM first employs a novel Few-Shot Graph Diffusion Model (FGDM) as a node-level graph generative method to generate an augmented graph with an enlarged support set, then performs low-rank transductive classification to obtain the few-shot node classification results. Our graph diffusion model, FGDM, comprises two components, the Hierarchical Graph Autoencoder (HGAE) with an efficient hierarchical edge reconstruction method and a new prototypical regularization, and the Latent Diffusion Model (LDM). The low-rank regularization is robust to the noise inherently introduced by the diffusion model and empirically inspired by the Low Frequency Property. We also provide a strong theoretical guarantee justifying the low-rank regularization for the transductive classification in few-shot learning. To further enhance the performance of LR-FGDM, we introduce LRA-LR-FGDM with a novel efficient LR-Attention layer, or the LRA layer, which applies self-attention to the output of the LR-FGDM encoder. The LRA layer further reduces the kernel complexity of LR-FGDM and contributes to a tighter generalization bound, leading to improved performance. Extensive experimental results evidence the effectiveness of LR-FGDM for few-shot node classification, which outperforms the current state-of-the-art. The code of the LR-FGDM is available at \url{https://github.com/Statistical-Deep-Learning/LR-FGDM}.