HLSAD: Hodge Laplacian-based Simplicial Anomaly Detection
This addresses the problem of detecting complex structural anomalies in higher-order data for applications where traditional graph methods fail, representing a novel method for a known bottleneck.
The paper tackles anomaly detection in time-evolving simplicial complexes by proposing HLSAD, which leverages Hodge Laplacians to model higher-order interactions, outperforming existing graph methods in detecting events and change points.
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.