标题： 基于霍奇拉普拉斯算子的单纯形异常检测 显示英文标题

标题： HLSAD: Hodge Laplacian-based Simplicial Anomaly Detection

摘要： 本文提出了一种名为HLSAD的新方法，用于检测随时间演化的单纯复形中的异常。 尽管传统的图异常检测技术已被广泛研究，但它们往往无法捕捉到更高阶交互的变化，而这些变化对于识别复杂的结构异常至关重要。 这些更高阶的交互可能直接来自底层数据本身，也可能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算子的谱特性，有效地对数据点之间的多向交互进行建模。 通过将高维单纯结构融入我们的方法中，我们的方法提高了检测准确性和计算效率。 通过在合成数据集和真实数据集上的综合实验，我们证明了我们的方法在检测事件和变化点方面优于现有的图方法。 显示英文摘要

摘要： 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.