Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Rethinking Reconstruction-based Graph-Level Anomaly Detection: Limitations and a Simple Remedy

Sunwoo Kim, Soo Yong Lee, Fanchen Bu, Shinhwan Kang, Kyungho Kim, Jaemin Yoo, Kijung Shin

TL;DR

It is argued that, while the reconstruction errors for a given graph are effective features for GLAD, leveraging the multifaceted summaries of the reconstruction errors, beyond just mean, can further strengthen the features and propose a novel and simple GLAD method, named MUSE.

Abstract

Graph autoencoders (Graph-AEs) learn representations of given graphs by aiming to accurately reconstruct them. A notable application of Graph-AEs is graph-level anomaly detection (GLAD), whose objective is to identify graphs with anomalous topological structures and/or node features compared to the majority of the graph population. Graph-AEs for GLAD regard a graph with a high mean reconstruction error (i.e. mean of errors from all node pairs and/or nodes) as anomalies. Namely, the methods rest on the assumption that they would better reconstruct graphs with similar characteristics to the majority. We, however, report non-trivial counter-examples, a phenomenon we call reconstruction flip, and highlight the limitations of the existing Graph-AE-based GLAD methods. Specifically, we empirically and theoretically investigate when this assumption holds and when it fails. Through our analyses, we further argue that, while the reconstruction errors for a given graph are effective features for GLAD, leveraging the multifaceted summaries of the reconstruction errors, beyond just mean, can further strengthen the features. Thus, we propose a novel and simple GLAD method, named MUSE. The key innovation of MUSE involves taking multifaceted summaries of reconstruction errors as graph features for GLAD. This surprisingly simple method obtains SOTA performance in GLAD, performing best overall among 14 methods across 10 datasets.

Rethinking Reconstruction-based Graph-Level Anomaly Detection: Limitations and a Simple Remedy

TL;DR

It is argued that, while the reconstruction errors for a given graph are effective features for GLAD, leveraging the multifaceted summaries of the reconstruction errors, beyond just mean, can further strengthen the features and propose a novel and simple GLAD method, named MUSE.

Abstract

Graph autoencoders (Graph-AEs) learn representations of given graphs by aiming to accurately reconstruct them. A notable application of Graph-AEs is graph-level anomaly detection (GLAD), whose objective is to identify graphs with anomalous topological structures and/or node features compared to the majority of the graph population. Graph-AEs for GLAD regard a graph with a high mean reconstruction error (i.e. mean of errors from all node pairs and/or nodes) as anomalies. Namely, the methods rest on the assumption that they would better reconstruct graphs with similar characteristics to the majority. We, however, report non-trivial counter-examples, a phenomenon we call reconstruction flip, and highlight the limitations of the existing Graph-AE-based GLAD methods. Specifically, we empirically and theoretically investigate when this assumption holds and when it fails. Through our analyses, we further argue that, while the reconstruction errors for a given graph are effective features for GLAD, leveraging the multifaceted summaries of the reconstruction errors, beyond just mean, can further strengthen the features. Thus, we propose a novel and simple GLAD method, named MUSE. The key innovation of MUSE involves taking multifaceted summaries of reconstruction errors as graph features for GLAD. This surprisingly simple method obtains SOTA performance in GLAD, performing best overall among 14 methods across 10 datasets.

Paper Structure

This paper contains 47 sections, 2 theorems, 55 equations, 9 figures, 9 tables.

Table of Contents

  1. Introduction
  2. Related Work and Preliminaries
  3. Related work
  4. Preliminary
  5. Analysis of Graph Autoencoders
  6. Synthetic graphs
  7. Empirical analysis
  8. Theoretical analysis
  9. Implications in Graph-Level Anomaly Detection
  10. Limitations of existing Graph-AEs in GLAD
  11. Enhancing the use of reconstruction errors
  12. Proposed Method: MuSE
  13. Step 1: Training a reconstruction model
  14. Step 2: Generating error representation
  15. Experiments
  16. ...and 32 more sections

Key Result

Theorem 1

For any $n \geq 12$ and $0 < \tau_1 \leq 1$, there exists $\epsilon > 0$ such that for any $0 < \gamma \leq \epsilon$ and any $0 < \tau_2 \leq 1$ (recall that $0$ and $1$ are the lower and upper bounds of $\tau$, respectively) with the initial weight matrix $\mathbf{W}^{(0)} = \mathbb{I}_{n}$,

Figures (9)

  • Figure 1: The training graphs in (a) and the unseen graph in (b) exhibit different structural characteristics, but a Graph-AE model reconstructs the graph in (b) more accurately than those in (a).
  • Figure 2: Reconstruction flip occurs. When Graph-AEs are trained on graphs sharing a primary pattern of weak strength, the trained Graph-AEs exhibit lower reconstruction errors for graphs with the same pattern but with higher strength (red lines) than those with weaker strength (blue lines).
  • Figure 3: Reconstruction flip does NOT occur. When Graph-AEs are trained on graphs sharing a primary pattern, the trained Graph-AEs exhibit higher reconstruction errors for graphs with a different pattern (red lines) than those with the same pattern (blue lines).
  • Figure 4: A clean-cycle graph and a noisy-cycle graph.
  • Figure 5: A case of Graph-AEs (specifically, GAE kipf2016variational) having similar mean reconstruction errors for two dissimilar graphs (specifically, $\mathcal{G}_{1}$ has 0.6622 and $\mathcal{G}_{2}$ has 0.6627), while their error distributions differ significantly.
  • ...and 4 more figures

Theorems & Definitions (4)

  • Theorem 1: Generalization across $\tau$
  • Theorem 2: Correlation with $\tau$
  • proof
  • proof