Community-based anomaly detection using spectral graph filtering

TL;DR

This paper introduces SpecF, a spectral graph filtering method that leverages community structure for improved anomaly detection in attributed networks, demonstrating superior performance especially in overlapping communities.

Contribution

It proposes a novel community-aware spectral graph filter for anomaly detection, integrating community structure into the Laplacian matrix and cutoff frequency selection.

Findings

SpecF outperforms baseline methods in detecting anomalies.

The method is effective in networks with high community overlap.

Case study validates applicability to real-world COVID-19 data.

Abstract

Several applications have a community structure where the nodes of the same community share similar attributes. Anomaly or outlier detection in networks is a relevant and widely studied research topic with applications in various domains. Despite a significant amount of anomaly detection frameworks, there is a dearth on the literature of methods that consider both attributed graphs and the community structure of the networks. This paper proposes a community-based anomaly detection algorithm using a spectral graph-based filter that includes the network community structure into the Laplacian matrix adopted as the basis for the Fourier transform. In addition, the choice of the cutoff frequency of the filter considers the number of communities found. In computational experiments, the proposed strategy, called SpecF, showed an outstanding performance in successfully identifying even discrete anomalies. SpecF is better than a baseline disregarding the community structure, especially for networks with a higher community overlapping. Additionally, we present a case study to validate the proposed method to study the dissemination of COVID-19 in the different districts of S\~ao Jos\'e dos Campos, Brazil.