Preserving the Privacy of Latent Information for Graph-Structured Data

Latent graph structure and stimulus of graph-structured data contain critical private information, such as brain disorders in functional magnetic resonance imaging data, and can be exploited to identify individuals. It is critical to perturb the latent information while maintaining the utility of the data, which, unfortunately, has never been addressed. This paper presents a novel approach to obfuscating the latent information and maximizing the utility. Specifically, we first analyze the graph Fourier transform (GFT) basis that captures the latent graph structures, and the latent stimuli that are the spectral-domain inputs to the latent graphs. Then, we formulate and decouple a new multi-objective problem to alternately obfuscate the GFT basis and stimuli. The difference-of-convex (DC) programming and Stiefel manifold gradient descent are orchestrated to obfuscate the GFT basis. The DC programming and gradient descent are employed to perturb the spectral-domain stimuli. Experiments conducted on an attention-deficit hyperactivity disorder dataset demonstrate that our approach can substantially outperform its differential privacy-based benchmark in the face of the latest graph inference attacks.