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

TL;DR

GADPN is a novel graph structure learning framework that adaptively denoises and perturbs graph topology using SVD and Bayesian optimization, improving GNN performance on noisy and diverse graphs.

Contribution

It introduces a simple, efficient method combining low-rank denoising and SVD-based structural perturbation with adaptive Bayesian optimization for graph topology refinement.

Findings

Achieves state-of-the-art results on benchmark datasets.

Significantly improves performance on disassortative graphs.

Enhances robustness and efficiency of graph structure learning.

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.