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CEDL: Centre-Enhanced Discriminative Learning for Anomaly Detection

Zahra Zamanzadeh Darban, Qizhou Wang, Charu C. Aggarwal, Geoffrey I. Webb, Ehsan Abbasnejad, Mahsa Salehi

TL;DR

CEDL addresses the generalisation gap in supervised anomaly detection by embedding geometric normality into the discriminative objective. It replaces the conventional sigmoid logit with a centre-based radial logit, yielding an end-to-end, geometry-aware anomaly scoring function $a(r)=\|r-c\|_2$ and an radial distance loss $a_i = \frac{\alpha}{\sqrt{D}} \|r_i-c\|_2$ that regularises the normal cluster around a learnable centre. The resulting framework tightly couples representation geometry with label discrimination, providing interpretable, threshold-free anomaly scores and robust performance across tabular, time-series, and image data, with strong ablations confirming the benefits of radial updates and compact normality. The work demonstrates broad applicability and suggests future extensions to multiple centroids and semi-supervised/few-shot learning to further enhance normality modelling and generalisation to unseen anomalies.

Abstract

Supervised anomaly detection methods perform well in identifying known anomalies that are well represented in the training set. However, they often struggle to generalise beyond the training distribution due to decision boundaries that lack a clear definition of normality. Existing approaches typically address this by regularising the representation space during training, leading to separate optimisation in latent and label spaces. The learned normality is therefore not directly utilised at inference, and their anomaly scores often fall within arbitrary ranges that require explicit mapping or calibration for probabilistic interpretation. To achieve unified learning of geometric normality and label discrimination, we propose Centre-Enhanced Discriminative Learning (CEDL), a novel supervised anomaly detection framework that embeds geometric normality directly into the discriminative objective. CEDL reparameterises the conventional sigmoid-derived prediction logit through a centre-based radial distance function, unifying geometric and discriminative learning in a single end-to-end formulation. This design enables interpretable, geometry-aware anomaly scoring without post-hoc thresholding or reference calibration. Extensive experiments on tabular, time-series, and image data demonstrate that CEDL achieves competitive and balanced performance across diverse real-world anomaly detection tasks, validating its effectiveness and broad applicability.

CEDL: Centre-Enhanced Discriminative Learning for Anomaly Detection

TL;DR

CEDL addresses the generalisation gap in supervised anomaly detection by embedding geometric normality into the discriminative objective. It replaces the conventional sigmoid logit with a centre-based radial logit, yielding an end-to-end, geometry-aware anomaly scoring function and an radial distance loss that regularises the normal cluster around a learnable centre. The resulting framework tightly couples representation geometry with label discrimination, providing interpretable, threshold-free anomaly scores and robust performance across tabular, time-series, and image data, with strong ablations confirming the benefits of radial updates and compact normality. The work demonstrates broad applicability and suggests future extensions to multiple centroids and semi-supervised/few-shot learning to further enhance normality modelling and generalisation to unseen anomalies.

Abstract

Supervised anomaly detection methods perform well in identifying known anomalies that are well represented in the training set. However, they often struggle to generalise beyond the training distribution due to decision boundaries that lack a clear definition of normality. Existing approaches typically address this by regularising the representation space during training, leading to separate optimisation in latent and label spaces. The learned normality is therefore not directly utilised at inference, and their anomaly scores often fall within arbitrary ranges that require explicit mapping or calibration for probabilistic interpretation. To achieve unified learning of geometric normality and label discrimination, we propose Centre-Enhanced Discriminative Learning (CEDL), a novel supervised anomaly detection framework that embeds geometric normality directly into the discriminative objective. CEDL reparameterises the conventional sigmoid-derived prediction logit through a centre-based radial distance function, unifying geometric and discriminative learning in a single end-to-end formulation. This design enables interpretable, geometry-aware anomaly scoring without post-hoc thresholding or reference calibration. Extensive experiments on tabular, time-series, and image data demonstrate that CEDL achieves competitive and balanced performance across diverse real-world anomaly detection tasks, validating its effectiveness and broad applicability.

Paper Structure

This paper contains 23 sections, 5 equations, 2 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Works
  3. Classis Anomaly Detection Methods
  4. Deep Anomaly Detection
  5. Proposed method
  6. Center-Enhanced Deep Supervised Anomaly Detection
  7. Property of Center-Enhanced Discriminative Loss
  8. Anomaly Detection using CEDL
  9. Experiment
  10. Datasets
  11. Evaluation Metrics
  12. Baselines
  13. Experimental Setup
  14. Implementation Details
  15. Anomaly Detection Performance
  16. ...and 8 more sections

Figures (2)

  • Figure 1: Ablation on training anomaly proportion (1–20%) for CEDL vs. BCE on three Yahoo entities. CEDL leads at low anomaly availability and both models improve toward mid ranges; behaviour at 20% varies across entities.
  • Figure 2: t-SNE of learned representations of Campaign dataset: CEDL forms a compact normal core with an annulus of anomalies (circular push), whereas BCE exhibits a more elongated, overlapping structure.