# HLSAD: Hodge Laplacian-based Simplicial Anomaly Detection

arXiv: https://arxiv.org/abs/2505.24534 · HTML: https://mlsanity.com/paper/2505.24534/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 36 references that are in the map.
- First posted on arXiv 30 May 2025.

## Builds on (most cited first, 12 of 12)

- [Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks](https://mlsanity.com/paper/2103.03212/) (2021)
- [Graph-based Anomaly Detection and Description: A Survey](https://mlsanity.com/paper/1404.4679/) (2014)
- [Laplacian Change Point Detection for Dynamic Graphs](https://mlsanity.com/paper/2007.01229/) (2020)
- [TopoX: A Suite of Python Packages for Machine Learning on Topological Domains](https://mlsanity.com/paper/2402.02441/) (2024)
- [Graph Anomaly Detection in Time Series: A Survey](https://mlsanity.com/paper/2302.00058/) (2023)
- [A Survey on Social Media Anomaly Detection](https://mlsanity.com/paper/1601.01102/) (2016)
- [Detecting change points in the large-scale structure of evolving networks](https://mlsanity.com/paper/1403.0989/) (2014)
- [Fast Change Point Detection on Dynamic Social Networks](https://mlsanity.com/paper/1705.07325/) (2017)
- [Laplacian Change Point Detection for Single and Multi-view Dynamic Graphs](https://mlsanity.com/paper/2302.01204/) (2023)
- [Graph similarity learning for change-point detection in dynamic networks](https://mlsanity.com/paper/2203.15470/) (2022)
- [Change Detection in a Dynamic Stream of Attributed Networks](https://mlsanity.com/paper/1711.04441/) (2017)
- [Latent Evolution Model for Change Point Detection in Time-varying Networks](https://mlsanity.com/paper/2212.08818/) (2022)

## Built on by (most cited first, 2 of 2)

- [Colored Markov Random Fields for Probabilistic Topological Modeling](https://mlsanity.com/paper/2512.03727/) (2025)
- [Geometry-Informed Parameter-Efficient Fine-Tuning of Pre-trained Molecular GNNs for Blood-Brain Barrier Permeability Prediction](https://mlsanity.com/paper/2608.04257/) (2026)

## Abstract (arXiv)

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.