NAGG: Noised graph node feature aggregations for preserving privacy

Graph node feature aggregation is a very common basic operation in graph data query and graph neural networks. We design three noised aggregation methods to protect the node features of the graph and analyze the privacy of these methods from the perspective of differential privacy. NAGG1, our first method, adds Gaussian noise to the aggregation result, extending the classic Gaussian mechanism of differential privacy directly to the graph domain. Subsequently, we design NAGG2 which adds noise to the raw data of each sample and then performs the aggregation. This makes it possible to decouple the data owner and subsequent data users. We impose some restrictions on the original definition of differential privacy, and under these new assumptions, we demonstrate that the effects of Gaussian noise in NAGG2 can be achieved with any other type of noise that meets the requirements. We call this method NAGG3, which significantly enhances the flexibility of added noise in theory. For these methods, we instantiate them with mean aggregation and graph convolutional aggregation. We analyze their privacy protection using the framework of differential privacy and evaluate their utility through experiments.