Locally differentially private graph learning on decentralized social graph

In recent years, decentralized social networks have gained increasing attention, where each client maintains a local view of a social graph. To provide services based on graph learning in such networks, the server commonly needs to collect the local views of the graph structure, which raises privacy issues. In this paper, we focus on learning graph neural networks (GNNs) on decentralized social graphs while satisfying local differential privacy (LDP). Most existing methods collect high-dimensional local views under LDP through Randomized Response, which introduces a large amount of noise and significantly decreases the usability of the collected graph structure for training GNNs. To address this problem, we present Structure Learning-based Locally Private Graph Learning (SL-LPGL). Its main idea is to first collect low-dimensional encoded structural information called cluster degree vectors to reduce the amount of LDP noise, then learn a high-dimensional graph structure from the cluster degree vectors via graph structure learning (GSL) to train GNNs. In SL-LPGL, we propose a Homophily-aware Graph StructurE Initialization (HAGEI) method to provide a low-noise initial graph structure as learning guidance for GSL. We then introduce an Estimated Average Degree Vector Enhanced Graph Structure Learning (EADEGSL) method to further mitigate the negative impact of LDP noise in GSL. We conduct experiments on four real-world graph datasets. The experimental results demonstrate that SL-LPGL outperforms the baselines.