Title: Low-Rank Few-Shot Node Classification by Node-Level Graph Diffusion
Primary area: learning on graphs and other geometries & topologies
Keywords: Few-Shot Node Classification, Low-Rank Few-Shot Graph Diffusion Model, Low-Rank Learning

Abstract: 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. 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://anonymous.4open.science/r/LR-FGDM/}.

TL;DR: We propose a novel node-level graph diffusion method with low-rank feature learning for few-shot node classification, termed Low-Rank Few-Shot Graph Diffusion Model  (LR-FGDM), with strong theoretical guarantee and extensive empirical results.