HLSAD: Hodge Laplacian-based Simplicial Anomaly Detection

• URL: http://arxiv.org/abs/2505.24534v1
• Date: Fri, 30 May 2025 12:41:08 GMT
• Title: HLSAD: Hodge Laplacian-based Simplicial Anomaly Detection
• Authors: Florian Frantzen, Michael T. Schaub,
• Abstract summary: We propose HLSAD, a novel method for detecting anomalies in time-evolving simplicial complexes.<n>Our approach leverages the spectral properties of Hodge Laplacians of simplicial complexes to effectively model multi-way interactions among data points.
• Score: 6.629765271909503
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

Related papers

• Trivial Graph Features and Classical Learning are Enough to Detect Random Anomalies [0.0]
  We show here that trivial graph features and classical learning techniques are sufficient to detect such anomalies extremely well.<n>This basic approach has very low computational costs and it leads to easily interpretable results.
  arXiv  Detail & Related papers  (2026-03-02T13:19:29Z)
• Improving Deepfake Detection with Reinforcement Learning-Based Adaptive Data Augmentation [60.04281435591454]
  CRDA (Curriculum Reinforcement-Learning Data Augmentation) is a novel framework guiding detectors to progressively master multi-domain forgery features.<n>Central to our approach is integrating reinforcement learning and causal inference.<n>Our method significantly improves detector generalizability, outperforming SOTA methods across multiple cross-domain datasets.
  arXiv  Detail & Related papers  (2025-11-10T12:45:52Z)
• Transformers Provably Learn Directed Acyclic Graphs via Kernel-Guided Mutual Information [91.66597637613263]
  transformer-based models leveraging the attention mechanism have demonstrated strong empirical success in capturing complex dependencies within graphs.<n>We introduce a novel information-theoretic metric: the kernel-guided mutual information (KG-MI) based on the $f$-divergence.<n>We prove that, given sequences generated by a $K$-parent DAG, training a single-layer, multi-head transformer via a gradient ascent converges to the global optimum time.
  arXiv  Detail & Related papers  (2025-10-29T14:07:12Z)
• CLIP Meets Diffusion: A Synergistic Approach to Anomaly Detection [54.85000884785013]
  Anomaly detection is a complex problem due to the ambiguity in defining anomalies, the diversity of anomaly types, and the scarcity of training data.<n>We propose CLIPfusion, a method that leverages both discriminative and generative foundation models.<n>We believe that our method underscores the effectiveness of multi-modal and multi-model fusion in tackling the multifaceted challenges of anomaly detection.
  arXiv  Detail & Related papers  (2025-06-13T13:30:15Z)
• Mapping correlations and coherence: adjacency-based approach to data visualization and regularity discovery [0.0]
  Correlation is a most commonly-used and effective approach to describe regularities in data.<n>We present an algorithm to derive maps representing the type and degree of correlations.<n>The method should facilitate the development of new computational approaches to regularity discovery.
  arXiv  Detail & Related papers  (2025-06-06T05:31:16Z)
• ComplexVAD: Detecting Interaction Anomalies in Video [45.08126325125808]
  We introduce a new large-scale anomaly detection dataset: ComplexVAD.<n>In addition, we propose a method to detect complex anomalies via modeling interactions between objects using a scene graph with video attributes.<n>With our proposed method and two other state-of-the-art video anomaly detection methods, we obtain baseline scores on ComplexVAD and demonstrate that our new method outperforms existing works.
  arXiv  Detail & Related papers  (2025-01-16T18:35:45Z)
• A Generalizable Anomaly Detection Method in Dynamic Graphs [7.48376611870513]
  GeneralDyG is a method that samples temporal ego-graphs and sequentially extracts structural and temporal features.<n>Our proposed GeneralDyG significantly outperforms state-of-the-art methods on four real-world datasets.
  arXiv  Detail & Related papers  (2024-12-21T02:38:48Z)
• Simultaneous Dimensionality Reduction for Extracting Useful Representations of Large Empirical Multimodal Datasets [0.0]
  We focus on the sciences of dimensionality reduction as a means to obtain low-dimensional descriptions from high-dimensional data. We address the challenges posed by real-world data that defy conventional assumptions, such as complex interactions within systems or high-dimensional dynamical systems.
  arXiv  Detail & Related papers  (2024-10-23T21:27:40Z)
• Discovering physical laws with parallel combinatorial tree search [57.05912962368898]
  Symbolic regression plays a crucial role in scientific research thanks to its capability of discovering concise and interpretable mathematical expressions from data.<n>Existing algorithms have faced a critical bottleneck of accuracy and efficiency over a decade.<n>We introduce a parallel tree search (PCTS) model to efficiently distill generic mathematical expressions from limited data.
  arXiv  Detail & Related papers  (2024-07-05T10:41:15Z)
• Gradient-Based Feature Learning under Structured Data [57.76552698981579]
  In the anisotropic setting, the commonly used spherical gradient dynamics may fail to recover the true direction. We show that appropriate weight normalization that is reminiscent of batch normalization can alleviate this issue. In particular, under the spiked model with a suitably large spike, the sample complexity of gradient-based training can be made independent of the information exponent.
  arXiv  Detail & Related papers  (2023-09-07T16:55:50Z)
• Nonparametric Embeddings of Sparse High-Order Interaction Events [21.758306786651772]
  High-order interaction events are common in real-world applications. We propose Non Embeddings of Sparse High-order interaction events. We develop an efficient, scalable model inference algorithm.
  arXiv  Detail & Related papers  (2022-07-08T01:25:34Z)
• Amortized Inference for Causal Structure Learning [72.84105256353801]
  Learning causal structure poses a search problem that typically involves evaluating structures using a score or independence test. We train a variational inference model to predict the causal structure from observational/interventional data. Our models exhibit robust generalization capabilities under substantial distribution shift.
  arXiv  Detail & Related papers  (2022-05-25T17:37:08Z)
• Heterogeneous Graph Neural Networks using Self-supervised Reciprocally Contrastive Learning [102.9138736545956]
  Heterogeneous graph neural network (HGNN) is a very popular technique for the modeling and analysis of heterogeneous graphs. We develop for the first time a novel and robust heterogeneous graph contrastive learning approach, namely HGCL, which introduces two views on respective guidance of node attributes and graph topologies. In this new approach, we adopt distinct but most suitable attribute and topology fusion mechanisms in the two views, which are conducive to mining relevant information in attributes and topologies separately.
  arXiv  Detail & Related papers  (2022-04-30T12:57:02Z)
• Learning Neural Causal Models with Active Interventions [83.44636110899742]
  We introduce an active intervention-targeting mechanism which enables a quick identification of the underlying causal structure of the data-generating process. Our method significantly reduces the required number of interactions compared with random intervention targeting. We demonstrate superior performance on multiple benchmarks from simulated to real-world data.
  arXiv  Detail & Related papers  (2021-09-06T13:10:37Z)
• Graph Neural Network-Based Anomaly Detection in Multivariate Time Series [17.414474298706416]
  We develop a new way to detect anomalies in high-dimensional time series data. Our approach combines a structure learning approach with graph neural networks. We show that our method detects anomalies more accurately than baseline approaches.
  arXiv  Detail & Related papers  (2021-06-13T09:07:30Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.