Graph neural networks (GNNs) tend to suffer from lower robustness and reduced prediction accuracy when trained under differential privacy (DP), especially when the graph data follow a non-uniform distribution or contain outliers. Traditional aggregation-based perturbation methods often fail to adapt to such complex data characteristics, and they struggle to find a proper balance between privacy protection and model performance. To tackle these problems, this paper introduces an adaptive normalization and aggregation perturbation approach named MVNAP, specifically designed for non-uniform data distributions. The proposed method consists of three main components: feature-wise personalized normalization using mean and variance, aggregation over sparse graph node matrices, and Gaussian differential privacy perturbation. This design removes scale deviations across different feature dimensions at the root level, ensures strict privacy protection, and retains the essential structural information of the graph. MVNAP has a decoupled, modular architecture, allowing it to be seamlessly integrated as a plug-and-play module into various DP-GNN frameworks without modifying the original network structure or training logic. We evaluate the method on benchmark datasets with power-law distributions and varying feature scales—Reddit, Amazon, and FB-100—under both edge-level and node-level DP scenarios. Experimental results show that the proposed DP-GNN method is well suited for complex, non-uniform data distributions and can serve as a key optimization module to facilitate the practical deployment of differentially private graph neural networks in privacy-sensitive applications.
Graph Neural Networks, Differential Privacy, Aggregation Perturbation, Non-Uniform Data Distribution, Model Robustness.
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