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

TL;DR

GADPN tackles the challenge of noisy and incomplete graphs in graph neural networks by introducing a two-stage refinement: Bayesian-optimized adaptive denoising via randomized SVD to select a data-driven rank $k^*$, and a generalized singular value perturbation framework that extends the Structural Perturbation Method to arbitrary graphs. The recovered edges are selectively reintegrated with a controllable weight $\alpha$, producing a final refined adjacency $\mathbf{A}_E$ that feeds standard GNN backbones. The approach achieves state-of-the-art results across six benchmarks, with notable improvements on disassortative graphs, while maintaining computational efficiency. These results demonstrate robust graph structure learning that generalizes across homophily regimes and offers practical gains for real-world network analysis. The work opens avenues for dynamic graph extensions and integration with causal reasoning to further enhance robustness.

Abstract

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 achieves state-of-the-art performance while significantly improving efficiency. It shows particularly strong gains on challenging disassortative graphs, validating its ability to robustly learn enhanced graph structures across diverse network types.

Figures (6)

• Figure 1: The framework of GADPN.
• Figure 2: Performance comparison (%) of GADPN and its variants across all datasets.
• Figure 3: Visualization of the learned node embeddings on the Chameleon dataset.
• Figure 4: Performance sensitivity analysis with respect to the base perturbation ratio $p$.
• Figure 5: Performance sensitivity analysis with respect to the recovery adjustment parameter $q$.