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Stochastic Voronoi Ensembles for Anomaly Detection

Yang Cao

TL;DR

This work tackles anomaly detection in datasets with heterogeneous local densities by introducing SVEAD, a Stochastic Voronoi Ensembles Anomaly Detector. It builds an ensemble of random Voronoi partitions via anchor sampling and computes a dual-factor per-point score that combines normalized relative distance to an anchor with a local-density proxy, then averages scores across partitions to produce a final anomaly score. The authors prove that random anchor sampling provides density-adaptive partitioning, ensemble averaging reduces variance, and the dual-factor scoring yields a clear separation between anomalies and normal points. Empirically, SVEAD achieves state-of-the-art performance on 45 datasets against 12 baselines, with linear-time and constant-space complexity, and demonstrates robust detection of global, local, and dependency anomalies in large-scale settings.

Abstract

Anomaly detection aims to identify data instances that deviate significantly from majority of data, which has been widely used in fraud detection, network security, and industrial quality control. Existing methods struggle with datasets exhibiting varying local densities: distance-based methods miss local anomalies, while density-based approaches require careful parameter selection and incur quadratic time complexity. We observe that local anomalies, though indistinguishable under global analysis, become conspicuous when the data space is decomposed into restricted regions and each region is examined independently. Leveraging this geometric insight, we propose SVEAD (Stochastic Voronoi Ensembles Anomaly Detector), which constructs ensemble random Voronoi diagrams and scores points by normalized cell-relative distances weighted by local scale. The proposed method achieves linear time complexity and constant space complexity. Experiments on 45 datasets demonstrate that SVEAD outperforms 12 state-of-the-art approaches.

Stochastic Voronoi Ensembles for Anomaly Detection

TL;DR

This work tackles anomaly detection in datasets with heterogeneous local densities by introducing SVEAD, a Stochastic Voronoi Ensembles Anomaly Detector. It builds an ensemble of random Voronoi partitions via anchor sampling and computes a dual-factor per-point score that combines normalized relative distance to an anchor with a local-density proxy, then averages scores across partitions to produce a final anomaly score. The authors prove that random anchor sampling provides density-adaptive partitioning, ensemble averaging reduces variance, and the dual-factor scoring yields a clear separation between anomalies and normal points. Empirically, SVEAD achieves state-of-the-art performance on 45 datasets against 12 baselines, with linear-time and constant-space complexity, and demonstrates robust detection of global, local, and dependency anomalies in large-scale settings.

Abstract

Anomaly detection aims to identify data instances that deviate significantly from majority of data, which has been widely used in fraud detection, network security, and industrial quality control. Existing methods struggle with datasets exhibiting varying local densities: distance-based methods miss local anomalies, while density-based approaches require careful parameter selection and incur quadratic time complexity. We observe that local anomalies, though indistinguishable under global analysis, become conspicuous when the data space is decomposed into restricted regions and each region is examined independently. Leveraging this geometric insight, we propose SVEAD (Stochastic Voronoi Ensembles Anomaly Detector), which constructs ensemble random Voronoi diagrams and scores points by normalized cell-relative distances weighted by local scale. The proposed method achieves linear time complexity and constant space complexity. Experiments on 45 datasets demonstrate that SVEAD outperforms 12 state-of-the-art approaches.
Paper Structure (16 sections, 3 theorems, 10 equations, 5 figures, 4 tables, 1 algorithm)

This paper contains 16 sections, 3 theorems, 10 equations, 5 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Related Work
  4. Shallow methods
  5. Deep learning methods
  6. Methodology
  7. Stochastic Voronoi diagrams via anchor sampling
  8. Anomaly Scoring Mechanism
  9. Theoretical Properties
  10. Algorithm and Complexity Analysis
  11. Experiments
  12. Experimental Setup
  13. Overall Performance and Statistical Analysis
  14. Sensitivity and Scalability Analysis
  15. Conclusion
  16. ...and 1 more sections

Key Result

Proposition 4.1

Consider a region $R \subset \mathbb{R}^d$ with local density $\rho(R)$. When uniformly sampling $m$ anchors from dataset $\mathcal{X}$, the expected number of anchors falling in $R$ is proportional to $\rho(R) \cdot |R|$, where $|R|$ denotes the volume of $R$. Consequently, the expected Voronoi cel

Figures (5)

  • Figure 1: Demonstration of anomaly score heatmap on Lanting Xu calligraphy pixel data. (a) Original image with black characters considered as anomalies. (b) Anomaly score Heatmap from IDK. (c)Anomaly score Heatmap from SVEAD.
  • Figure 2: Illustration of SVEAD's space partition and ensemble approach. Left: Original dataset with normal points (purple) and anomalies (black). Middle and Right: demonstration of two random partitions with different anchor sets (red stars). Each partition creates distinct Voronoi cells (dashed lines), assigning points to nearest anchors.
  • Figure 3: Friedman-Nemenyi test for anomaly detectors at significance level 0.1. If two algorithms are connected by a CD (critical difference) line, there is no significant difference between them.
  • Figure 4: The AUC-ROC and AUC-PR performance with different values of $m$ and $t$.
  • Figure 5: The runtime comparison on donors dataset.

Theorems & Definitions (4)

  • Proposition 4.1: Cell Size and Density
  • proof
  • Proposition 4.2: Score Variance Reduction
  • Proposition 4.3: Expected Score Separation