Community-based anomaly detection using spectral graph filtering

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 São José dos Campos, Brazil.

Graph Filters for Signal Processing and Machine Learning on Graphs

“…VI-C) to reconstruct the data under normal behavior and the low-pass signal components are used to detect and localize anomalous sensors. This idea is further extended in [212] to identify a cluster of abnormal nodes. The work in [213] proposes an unsupervised setting for the scenario when we do not have knowledge of how normal and/or anomalous data behave on the graph.…”