HLSAD: Hodge Laplacian-based Simplicial Anomaly Detection

TL;DR

HLSAD introduces a spectral method based on Hodge Laplacians for detecting anomalies in time-evolving simplicial complexes, capturing higher-order interactions for improved accuracy.

Contribution

It is the first to leverage Hodge Laplacian spectral properties for anomaly detection in simplicial complexes, enhancing detection of complex structural changes.

Findings

Outperforms existing graph anomaly detection methods.

Effectively captures higher-order interactions.

Improves detection accuracy and efficiency.

Abstract

In this paper, we propose HLSAD, a novel method for detecting anomalies in time-evolving simplicial complexes. While traditional graph anomaly detection techniques have been extensively studied, they often fail to capture changes in higher-order interactions that are crucial for identifying complex structural anomalies. These higher-order interactions can arise either directly from the underlying data itself or through graph lifting techniques. Our approach leverages the spectral properties of Hodge Laplacians of simplicial complexes to effectively model multi-way interactions among data points. By incorporating higher-dimensional simplicial structures into our method, our method enhances both detection accuracy and computational efficiency. Through comprehensive experiments on both synthetic and real-world datasets, we demonstrate that our approach outperforms existing graph methods in detecting both events and change points.