用奇异值分解自适应优化图结构，提升GNN在噪声图上的表现。
GADPN: Graph Adaptive Denoising and Perturbation Networks via Singular Value Decomposition
- 基于SVD实现任意图的结构扰动，突破对称性限制。
- 引入贝叶斯优化自适应调节去噪强度，适配不同同质性图。
- 在异质图上显著提效，适合复杂网络结构学习场景。
图神经网络（GNN）在图结构数据上表现优异，但其性能受限于观测图的质量，常存在噪声、缺失边或结构特性与GNN假设不符等问题。为解决此问题，图结构学习旨在推断更优拓扑。然而现有方法因采用复杂生成模型和迭代联合优化，计算成本高，实用性受限。本文提出GADPN，一种简单高效的图结构学习框架，通过低秩去噪与广义结构扰动自适应优化图拓扑。核心贡献：(1) 引入贝叶斯优化，自适应确定最优去噪强度，适配各图的同质性水平；(2) 基于奇异值分解（SVD）将结构扰动扩展至任意图，突破原有对称结构限制。在基准数据集上的大量实验表明，GADPN达到当前最优性能且效率显著提升，尤其在挑战性的异质图上表现突出，验证了其在多种网络类型中鲁棒学习增强图结构的能力。
原文摘要 · Abstract (English)
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.
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