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Interpretable Maximum Margin Deep Anomaly Detection

Zhiji Yang, Mei Huang, Xinyu Li, Xianli Pan, Qi Wang, Jianhua Zhao

TL;DR

Interpretable Maximum Margin Deep Anomaly Detection (IMD-AD) is proposed, which leverages a small set of labeled anomalies and a maximum margin objective to stabilize training and improve discrimination and proves an equivalence between hypersphere parameters and the network's final-layer weights.

Abstract

Anomaly detection is a crucial machine-learning task with wide-ranging applications. Deep Support Vector Data Description (Deep SVDD) is a prominent deep one-class method, but it is vulnerable to hypersphere collapse, often relies on heuristic choices for hypersphere parameters, and provides limited interpretability. To address these issues, we propose Interpretable Maximum Margin Deep Anomaly Detection (IMD-AD), which leverages a small set of labeled anomalies and a maximum margin objective to stabilize training and improve discrimination. It is inherently resilient to hypersphere collapse. Furthermore, we prove an equivalence between hypersphere parameters and the network's final-layer weights, which allows the center and radius to be learned end-to-end as part of the model and yields intrinsic interpretability and visualizable outputs. We further develop an efficient training algorithm that jointly optimizes representation, margin, and final-layer parameters. Extensive experiments and ablation studies on image and tabular benchmarks demonstrate that IMD-AD empirically improves detection performance over several state-of-the-art baselines while providing interpretable decision diagnostics.

Interpretable Maximum Margin Deep Anomaly Detection

TL;DR

Interpretable Maximum Margin Deep Anomaly Detection (IMD-AD) is proposed, which leverages a small set of labeled anomalies and a maximum margin objective to stabilize training and improve discrimination and proves an equivalence between hypersphere parameters and the network's final-layer weights.

Abstract

Anomaly detection is a crucial machine-learning task with wide-ranging applications. Deep Support Vector Data Description (Deep SVDD) is a prominent deep one-class method, but it is vulnerable to hypersphere collapse, often relies on heuristic choices for hypersphere parameters, and provides limited interpretability. To address these issues, we propose Interpretable Maximum Margin Deep Anomaly Detection (IMD-AD), which leverages a small set of labeled anomalies and a maximum margin objective to stabilize training and improve discrimination. It is inherently resilient to hypersphere collapse. Furthermore, we prove an equivalence between hypersphere parameters and the network's final-layer weights, which allows the center and radius to be learned end-to-end as part of the model and yields intrinsic interpretability and visualizable outputs. We further develop an efficient training algorithm that jointly optimizes representation, margin, and final-layer parameters. Extensive experiments and ablation studies on image and tabular benchmarks demonstrate that IMD-AD empirically improves detection performance over several state-of-the-art baselines while providing interpretable decision diagnostics.
Paper Structure (23 sections, 17 equations, 9 figures, 4 tables, 1 algorithm)

This paper contains 23 sections, 17 equations, 9 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Review of Deep Support Vector Data Description
  3. Deficiencies of the Vanilla Deep SVDD
  4. Proposed Method
  5. Implementation of Maximum Margin Principle
  6. Efficient End-to-end Optimization
  7. Neural Network Parameterization of the Hypersphere
  8. End-to-end Training of IMD-AD
  9. Interpretability of IMD-AD
  10. Intrinsic Interpretability of the IMD-AD Architecture
  11. $\nu$-Property of IMD-AD
  12. Numerical Experiments
  13. Experimental Design
  14. Datasets
  15. Baselines
  16. ...and 8 more sections

Figures (9)

  • Figure 1: Training framework of Deep SVDD and IMD-AD, respectively. Green points represent normal samples, and red points represent abnormal samples. $R$ and $\mathbf{c}$ represent the radius and center of the hypersphere, respectively. $\rho$ represents the margin between abnormal samples and the surface of the hypersphere.
  • Figure 2: Critical Difference diagrams from Friedman test with Nemenyi posthoc test ($\alpha = 0.05$).
  • Figure 3: The visualization of IMD-AD on Spiral and Moon Datasets. (a) (c) (e) (g) display the scatter plots on original data. (b) (d) (f) (h) show the extracted samples and the corresponding detection boundaries of IMD-AD.
  • Figure 4: Performance curves of IMD-AD with epochs on Spiral and Moon datasets.
  • Figure 5: Model classification results on MNIST with normal class 0 over training epochs.
  • ...and 4 more figures