Graph Neural Network for Local Corruption Recovery

Graph neural networks (GNNs) have seen a surge of development for exploiting the relational information of input graphs. Nevertheless, messages propagating through a graph contain both interpretable patterns and small perturbations. Despite global noise could be distributed over the entire graph data, it is not uncommon that corruptions appear well-concealed and merely pollute local regions while still having a vital influence on the GNN learning and prediction performance. This work tackles the graph recovery problem from local poisons by a robustness representation learning. Our developed strategy identifies regional graph perturbations and formulates a robust hidden feature representation for GNNs. A mask function pinpointed the anomalies without prior knowledge, and an $\ell_{p,q}$ regularizer defends local poisonings through pursuing sparsity in the framelet domain while maintaining a conditional closeness between the observation and new representation. The proposed robust computational unit alleviates the inertial alternating direction method of multipliers to achieve an efficient solution. Extensive experiments show that our new model recovers graph representations from local pollution and achieves excellent performance.