Mitigating Homophily Disparity in Graph Anomaly Detection: A Scalable and Adaptive Approach

TL;DR

This paper introduces SAGAD, a scalable and adaptive graph anomaly detection framework that effectively handles homophily disparity and improves efficiency on large graphs through multi-hop embeddings and frequency-guided loss.

Contribution

SAGAD is a novel GAD method that combines multi-hop embeddings, adaptive fusion, and frequency guidance to address homophily disparity and scalability issues.

Findings

SAGAD achieves superior accuracy on 10 benchmarks.

It supports mini-batch training with linear complexity.

It drastically reduces memory usage on large graphs.

Abstract

Graph anomaly detection (GAD) aims to identify nodes that deviate from normal patterns in structure or features. While recent GNN-based approaches have advanced this task, they struggle with two major challenges: 1) homophily disparity, where nodes exhibit varying homophily at both class and node levels; and 2) limited scalability, as many methods rely on costly whole-graph operations. To address them, we propose SAGAD, a Scalable and Adaptive framework for GAD. SAGAD precomputes multi-hop embeddings and applies reparameterized Chebyshev filters to extract low- and high-frequency information, enabling efficient training and capturing both homophilic and heterophilic patterns. To mitigate node-level homophily disparity, we introduce an Anomaly Context-Aware Adaptive Fusion, which adaptively fuses low- and high-pass embeddings using fusion coefficients conditioned on Rayleigh Quotient-guided anomalous subgraph structures for each node. To alleviate class-level disparity, we design a Frequency Preference Guidance Loss, which encourages anomalies to preserve more high-frequency information than normal nodes. SAGAD supports mini-batch training, achieves linear time and space complexity, and drastically reduces memory usage on large-scale graphs. Theoretically, SAGAD ensures asymptotic linear separability between normal and abnormal nodes under mild conditions. Extensive experiments on 10 benchmarks confirm SAGAD's superior accuracy and scalability over state-of-the-art methods.