# PhoGAD: Graph-based Anomaly Behavior Detection with Persistent Homology Optimization

arXiv: https://arxiv.org/abs/2401.10547 · HTML: https://mlsanity.com/paper/2401.10547/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 46 references that are in the map.
- First posted on arXiv 19 Jan 2024.

## Builds on (most cited first, 17 of 17)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [LSTM: A Search Space Odyssey](https://mlsanity.com/paper/1503.04069/) (2015)
- [AnomalyDAE: Dual autoencoder for anomaly detection on attributed networks](https://mlsanity.com/paper/2002.03665/) (2020)
- [Graph Structure Learning with Variational Information Bottleneck](https://mlsanity.com/paper/2112.08903/) (2021)
- [SUGAR: Subgraph Neural Network with Reinforcement Pooling and Self-Supervised Mutual Information Mechanism](https://mlsanity.com/paper/2101.08170/) (2021)
- [Position-aware Structure Learning for Graph Topology-imbalance by Relieving Under-reaching and Over-squashing](https://mlsanity.com/paper/2208.08302/) (2022)
- [Anomal-E: A Self-Supervised Network Intrusion Detection System based on Graph Neural Networks](https://mlsanity.com/paper/2207.06819/) (2022)
- [Semi-supervised Anomaly Detection on Attributed Graphs](https://mlsanity.com/paper/2002.12011/) (2020)
- [Persistent Homology of Complex Networks for Dynamic State Detection](https://mlsanity.com/paper/1904.07403/) (2019)
- [Unveiling the potential of Graph Neural Networks for robust Intrusion Detection](https://mlsanity.com/paper/2107.14756/) (2021)
- [HP-GMN: Graph Memory Networks for Heterophilous Graphs](https://mlsanity.com/paper/2210.08195/) (2022)
- [Entity Embedding-based Anomaly Detection for Heterogeneous Categorical Events](https://mlsanity.com/paper/1608.07502/) (2016)
- [The Devil is in the Conflict: Disentangled Information Graph Neural Networks for Fraud Detection](https://mlsanity.com/paper/2210.12384/) (2022)
- [LogLG: Weakly Supervised Log Anomaly Detection via Log-Event Graph Construction](https://mlsanity.com/paper/2208.10833/) (2022)

## Built on by (most cited first, 3 of 3)

- [Multivariate Time-Series Anomaly Detection based on Enhancing Graph Attention Networks with Topological Analysis](https://mlsanity.com/paper/2408.13082/) (2024)
- [Decompose to Understand, Fuse to Detect: Frequency-Decoupled Anomaly Detection for Encrypted Network Traffic](https://mlsanity.com/paper/2605.02970/) (2026)
- [Quantum Topological Graph Neural Networks for Detecting Complex Fraud Patterns](https://mlsanity.com/paper/2512.03696/) (2025)

## Abstract (arXiv)

A multitude of toxic online behaviors, ranging from network attacks to anonymous traffic and spam, have severely disrupted the smooth operation of networks. Due to the inherent sender-receiver nature of network behaviors, graph-based frameworks are commonly used for detecting anomalous behaviors. However, in real-world scenarios, the boundary between normal and anomalous behaviors tends to be ambiguous. The local heterophily of graphs interferes with the detection, and existing methods based on nodes or edges introduce unwanted noise into representation results, thereby impacting the effectiveness of detection. To address these issues, we propose PhoGAD, a graph-based anomaly detection framework. PhoGAD leverages persistent homology optimization to clarify behavioral boundaries. Building upon this, the weights of adjacent edges are designed to mitigate the effects of local heterophily. Subsequently, to tackle the noise problem, we conduct a formal analysis and propose a disentangled representation-based explicit embedding method, ultimately achieving anomaly behavior detection. Experiments on intrusion, traffic, and spam datasets verify that PhoGAD has surpassed the performance of state-of-the-art (SOTA) frameworks in detection efficacy. Notably, PhoGAD demonstrates robust detection even with diminished anomaly proportions, highlighting its applicability to real-world scenarios. The analysis of persistent homology demonstrates its effectiveness in capturing the topological structure formed by normal edge features. Additionally, ablation experiments validate the effectiveness of the innovative mechanisms integrated within PhoGAD.