New Graph Learning Techniques for Networked Knowledge Inference and Protection
- Publication Type:
- Thesis
- Issue Date:
- 2024
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Graph topologies have been detected in data captured in social networks, biological networks, traffic networks, smart grids, and ecological networks. Graphs provide effective means to represent the statistical dependence or similarity among signals observed at different vertices. A critical challenge is to excavate graphs underlying observed signals, because of non-convex problem structure and associated high computational requirements. On the other hand, latent graph structure and stimulus of graph 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.
In this thesis, a new alternating optimization (AO) based graph learning technique is investigated to solve the challenge. However, the fidelity of the topologies inferred from the graph signals was penalized due to the use of the AO-based approximation. To surpass the limitations of the AO-based approximation, we propose a new graph learning technique that is able to efficiently infer the graph structure underlying observed graph signals by deriving a new closed-form analytic expression for the graph Fourier transform (GFT) basis, which depends deterministically on the observed signals. The new graph learning technique is applied to accurately infer the graph structure of COVID-19 data, helping to reveal the correlation of pandemic dynamics among different countries and identify influential countries for pandemic response analysis.
To protect the latent privacy of the latent graph structures and stimuli of graph-structured data, a novel approach has been proposed to obfuscate the latent information and maximize its utility. We first analyze the 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.
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