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SCoNE: Spherical Consistent Neighborhoods Ensemble for Effective and Efficient Multi-View Anomaly Detection

Yang Xu, Hang Zhang, Yixiao Ma, Ye Zhu, Kai Ming Ting

TL;DR

The paper tackles multi-view anomaly detection by requiring consistency of local neighborhoods across views. It introduces SCoNE, which directly uses a small set of multi-view instances to define adaptive-radius spherical neighborhoods that are shared across all views, enabling a linear-time, learning-free approach. The method provides theoretical insights into density-adaptive neighborhood sizing and cross-view consistency, and it demonstrates superior accuracy and scalability on synthetic and real-world datasets, including large-scale MNIST-like data and social networks. Overall, SCoNE offers a practical, scalable paradigm for robust multi-view anomaly detection that outperforms existing learning-based representations.

Abstract

The core problem in multi-view anomaly detection is to represent local neighborhoods of normal instances consistently across all views. Recent approaches consider a representation of local neighborhood in each view independently, and then capture the consistent neighbors across all views via a learning process. They suffer from two key issues. First, there is no guarantee that they can capture consistent neighbors well, especially when the same neighbors are in regions of varied densities in different views, resulting in inferior detection accuracy. Second, the learning process has a high computational cost of $\mathcal{O}(N^2)$, rendering them inapplicable for large datasets. To address these issues, we propose a novel method termed \textbf{S}pherical \textbf{C}onsistent \textbf{N}eighborhoods \textbf{E}nsemble (SCoNE). It has two unique features: (a) the consistent neighborhoods are represented with multi-view instances directly, requiring no intermediate representations as used in existing approaches; and (b) the neighborhoods have data-dependent properties, which lead to large neighborhoods in sparse regions and small neighborhoods in dense regions. The data-dependent properties enable local neighborhoods in different views to be represented well as consistent neighborhoods, without learning. This leads to $\mathcal{O}(N)$ time complexity. Empirical evaluations show that SCoNE has superior detection accuracy and runs orders-of-magnitude faster in large datasets than existing approaches.

SCoNE: Spherical Consistent Neighborhoods Ensemble for Effective and Efficient Multi-View Anomaly Detection

TL;DR

The paper tackles multi-view anomaly detection by requiring consistency of local neighborhoods across views. It introduces SCoNE, which directly uses a small set of multi-view instances to define adaptive-radius spherical neighborhoods that are shared across all views, enabling a linear-time, learning-free approach. The method provides theoretical insights into density-adaptive neighborhood sizing and cross-view consistency, and it demonstrates superior accuracy and scalability on synthetic and real-world datasets, including large-scale MNIST-like data and social networks. Overall, SCoNE offers a practical, scalable paradigm for robust multi-view anomaly detection that outperforms existing learning-based representations.

Abstract

The core problem in multi-view anomaly detection is to represent local neighborhoods of normal instances consistently across all views. Recent approaches consider a representation of local neighborhood in each view independently, and then capture the consistent neighbors across all views via a learning process. They suffer from two key issues. First, there is no guarantee that they can capture consistent neighbors well, especially when the same neighbors are in regions of varied densities in different views, resulting in inferior detection accuracy. Second, the learning process has a high computational cost of , rendering them inapplicable for large datasets. To address these issues, we propose a novel method termed \textbf{S}pherical \textbf{C}onsistent \textbf{N}eighborhoods \textbf{E}nsemble (SCoNE). It has two unique features: (a) the consistent neighborhoods are represented with multi-view instances directly, requiring no intermediate representations as used in existing approaches; and (b) the neighborhoods have data-dependent properties, which lead to large neighborhoods in sparse regions and small neighborhoods in dense regions. The data-dependent properties enable local neighborhoods in different views to be represented well as consistent neighborhoods, without learning. This leads to time complexity. Empirical evaluations show that SCoNE has superior detection accuracy and runs orders-of-magnitude faster in large datasets than existing approaches.

Paper Structure

This paper contains 13 sections, 2 theorems, 7 equations, 7 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Key Idea and Implementation
  3. Key Idea: Multi-view instances are good representatives of Consistent Neighborhoods across all views
  4. SCoNE: Multi-View Spherical Consistent Neighborhoods Ensemble
  5. Conceptual understanding of Consistent Neighborhood
  6. Data-dependent Properties: Capturing Consistent Neighborhoods in Varied Densities
  7. Experiment
  8. Competing Methods and Setups
  9. Synthetic Data
  10. Benchmark Datasets
  11. Ablation Study
  12. Anomaly Detection in Social Networks
  13. Conclusion

Key Result

Theorem 1

Given a multi-view dataset $\mathcal{D}$, and let $\mathcal{S}\subset\mathcal{D}$ be a set of $\psi$ sampled points. For each $\mathbf{s}^v\in\mathcal{S}^v$, let $\theta(\mathbf{s}^v)$ denote the neighborhood generated by $\mathbf{s}^v$, and $\mathcal{R}(\mathbf{s}^v)$ denote the set of all normal i where $\mathbb{E}[|\cdot|]$ is the expected number of the set.

Figures (7)

  • Figure 1: An illustration of three types of anomalies.
  • Figure 2: An illustration of the single-view spherical neighborhoods. The parameters $\psi=6$ and $k=3$ are used here.
  • Figure 3: An illustration of the mapping $\Phi$ for normal instances in $\mathscr{H}$. Three sampled points $\mathbf{s}_1,\mathbf{s}_2,\mathbf{s}_3\in \mathcal{S}$ (represented as dots), define three spherical neighborhoods of normal regions in each view.
  • Figure 4: An illustration of the mapping $\Phi$ for three types of multi-view anomalies. Each violates a different kind of consistency of being normal.
  • Figure 5: Synthetic datasets with various densities of distributions. Both views derive from the same original instances.
  • ...and 2 more figures

Theorems & Definitions (6)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Theorem 1
  • Theorem 2