用高阶拓扑结构提升动态数据异常检测精度
HLSAD: Hodge Laplacian-based Simplicial Anomaly Detection
- 基于霍奇拉普拉斯谱特性建模多体交互关系
- 在合成与真实数据上优于传统图方法
- 适合处理复杂结构变化的异常检测任务
本文提出HLSAD，一种用于检测时变单纯复形中异常的新方法。尽管传统图异常检测技术已广泛研究，但往往难以捕捉对识别复杂结构异常至关重要的高阶交互变化。这些高阶交互可能直接来自底层数据，或通过图提升技术产生。我们的方法利用单纯复形的霍奇拉普拉斯谱特性，有效建模数据点间的多维交互关系。通过引入高维单纯结构，该方法提升了检测准确率与计算效率。在合成与真实世界数据集上的全面实验表明，本方法在检测事件和变化点方面均优于现有图方法。
原文摘要 · Abstract (English)
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.
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