GADPN: Graph Adaptive Denoising and Perturbation Networks via Singular Value Decomposition

While Graph Neural Networks (GNNs) excel on graph-structured data, their performance is fundamentally limited by the quality of the observed graph, which often contains noise, missing links, or structural properties misaligned with GNNs' underlying assumptions. To address this, graph structure learning aims to infer a more optimal topology. Existing methods, however, often incur high computational costs due to complex generative models and iterative joint optimization, limiting their practical utility. In this paper, we propose GADPN, a simple yet effective graph structure learning framework that adaptively refines graph topology via low-rank denoising and generalized structural perturbation. Our approach makes two key contributions: (1) we introduce Bayesian optimization to adaptively determine the optimal denoising strength, tailoring the process to each graph's homophily level; and (2) we extend the structural perturbation method to arbitrary graphs via Singular Value Decomposition (SVD), overcoming its original limitation to symmetric structures. Extensive experiments on benchmark datasets demonstrate that GADPN not only achieves state-of-the-art performance but does so with significantly improved efficiency. It shows particularly strong gains on challenging disassortative graphs, validating its ability to robustly learn enhanced graph structures across diverse network types.