Efficient Low-Rank GNN Defense Against Structural Attacks

by   Abdullah Alchihabi, et al.

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.


GARNET: Reduced-Rank Topology Learning for Robust and Scalable Graph Neural Networks

Graph neural networks (GNNs) have been increasingly deployed in various ...

Graph Structure Learning for Robust Graph Neural Networks

Graph Neural Networks (GNNs) are powerful tools in representation learni...

Rethinking Graph Lottery Tickets: Graph Sparsity Matters

Lottery Ticket Hypothesis (LTH) claims the existence of a winning ticket...

Structure-Preserving Progressive Low-rank Image Completion for Defending Adversarial Attacks

Deep neural networks recognize objects by analyzing local image details ...

Robust Adversarial Defense by Tensor Factorization

As machine learning techniques become increasingly prevalent in data ana...

Finding Dense Clusters via "Low Rank + Sparse" Decomposition

Finding "densely connected clusters" in a graph is in general an importa...

Law of Large Graphs

Estimating the mean of a population of graphs based on a sample is a cor...

Please sign up or login with your details

Forgot password? Click here to reset