  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.
