Unlearning on Spatio-Temporal Graphs through Subgraph Virtual Edge Reconstruction

Spatiotemporal graphs underpin applications such as traffic forecasting, weather forecasting, and healthcare monitoring. Privacy regulations such as the GDPR and the CCPA require the complete removal of unauthorized data from trained models, but achieving this on a spatiotemporal graph is difficult: because information propagates globally through both spatial and temporal message passing, fully erasing a node's influence forces costly full-graph retraining. ST-graph unlearning requires both exactness and efficiency. We propose IsleNet, which uses spatial-entropy-guided partitioning to create balanced, locally coherent subgraphs and reconnects them with lightweight virtual edges. Upon an unlearning request, only the affected subgraph encoder and virtual-edge layer are retrained, ensuring exact removal with low cost. Experiments on four real-world benchmarks show that IsleNet attains up to 94% of full-graph accuracy while reducing unlearning time by up to an order of magnitude. Our code is publicly available at https://github.com/wenlu-lab/STGraphUnlearning.

Graph unlearning removes the influence of designated training data from a trained graph model without retraining from scratch. However, existing methods suffer a sharp drop in model utility under large deletion ratios (mass deletion), a phenomenon we refer to as catastrophic unlearning. We find that a key cause is the uniform treatment of all deleted samples, which is particularly damaging in graph learning: structural dependencies cause different nodes to play vastly different roles in the learned model, yet existing methods apply the same forgetting operation to the entire forget set. Based on this insight, we propose CUNO, a curriculum-based graph unlearning framework that removes the forget set progressively, ordering samples by their estimated unlearning difficulty across multiple stages. CUNO further employs a distribution-level negative preference optimization (NPO) objective at each curriculum stage that steers the model away from its original behavior on the current forget subset while preserving retained performance. Our theoretical analysis shows that the curriculum design is most beneficial when the forget set spans a wide range of unlearning difficulty, a condition naturally satisfied under mass deletion. Comprehensive experiments confirm that CUNO consistently mitigates catastrophic unlearning: at 20% deletion, it retains 74% of the original utility compared to 26-53% for existing methods, and maintains more than half the original utility even at 50% deletion. Our code is publicly available at https://anonymous.4open.science/r/cuno-D4FF.

We propose a novel framework for learning time-varying graphs from spatiotemporal measurements. Given an appropriate prior on the temporal behavior of signals, our proposed method can estimate time-varying graphs from a small number of available measurements. To achieve this, we introduce three regularization terms in convex optimization problems that constrain the sparseness of temporal variations of the time-varying networks. Moreover, a computationally scalable algorithm is introduced to solve the optimization problem efficiently. The experimental results with synthetic and real datasets (point cloud, temperature, and EEG data) demonstrate that our proposed method outperforms state-of-the-art methods.