Abstract

Adversarial attacks and anomaly detection are closely related, both focusing on identifying irregularities that deviate from normal patterns across various data types, including graph-structured data. Adversarial attacks on graphs pose a significant threat to graph convolutional networks (GCNs), involving intentional manipulation of graph data to mislead GCNs into making incorrect predictions. Standard GCNs, while powerful, often exhibit vulnerabilities to adversarial attacks that can significantly degrade their performance in anomaly detection tasks. These networks also have inherent limitations, such as their inability to effectively consider higher-order neighbour information, restricting their capacity to capture the full context of a node within the graph. To address these challenges, this thesis introduces an iterative graph filtering framework, which builds upon the graph signal processing concept of iteratively solving graph filtering using the fixed-point iterative method. The proposed framework is designed to enhance resilience against adversarial attacks while improving anomaly detection capabilities. The thesis makes two main contributions: a flexible spectral modulation filter that selectively attenuates high-frequency components of graph signals; and a robust aggregation mechanism that efficiently captures information from higher-order node neighbors, expanding the networks receptive field without increasing computational complexity. Extensive experiments are conducted on benchmark datasets to evaluate the effectiveness of the proposed methods. The results demonstrate significant improvements in anomaly detection accuracy and adversarial robustness compared to strong baselines. This highlights the potential of the proposed framework for reliable graph-based downstream tasks, paving the way for robust GCNs that can handle the complexities and adversarial threats inherent in real-world applications.