Graph Neural Networks (GNNs) have been shown to possess strong representation abilities over graph data. However, GNNs are vulnerable to adversarial attacks, and even minor perturbations to the graph structure can significantly degrade their performance. Existing methods either are ineffective against sophisticated attacks or require the optimization of dense adjacency matrices, which is time-consuming and prone to local minima. To remedy this problem, we propose an Efficient Low-Rank Graph Neural Network (ELR-GNN) defense method, which aims to learn low-rank and sparse graph structures for defending against adversarial attacks, ensuring effective defense with greater efficiency. Specifically, ELR-GNN consists of two modules: a Coarse Low-Rank Estimation Module and a Fine-Grained Estimation Module. The first module adopts the truncated Singular Value Decomposition (SVD) to initialize the low-rank adjacency matrix estimation, which serves as a starting point for optimizing the low-rank matrix. In the second module, the initial estimate is refined by jointly learning a low-rank sparse graph structure with the GNN model. Sparsity is incorporated into the learned low-rank adjacency matrix by pruning weak connections, which can reduce redundant data while maintaining valuable information. As a result, instead of using the dense adjacency matrix directly, ELR-GNN can learn a low-rank and sparse estimate of it in a simple, efficient and easy to optimize manner. The experimental results demonstrate that ELR-GNN outperforms the state-of-the-art GNN defense methods in the literature, in addition to being very efficient and easy to train.

提出了一种高效的低秩图神经网络防御方法(ELR-GNN)，通过学习低秩和稀疏的图结构来抵御对抗性攻击，并在保证有效防御的同时提高效率。实验结果表明，ELR-GNN在文献中超过了现有技术的图神经网络防御方法，而且非常高效易用。

高效低秩图神经网络防御结构性攻击