On the Use of Vertex-Frequency Analysis for Anomaly Detection in Graph Signals

Graph signals (GS) are widespread in many areas of data analysis, such as in social, genetics, and biomolecular networks as well as in several engineering applications. Detecting localized properties of GS using spectral tools while taking into account the underlying graph topology is still an active research topic called vertex-frequency analysis (VFA). This paper provides a brief and up-to-date overview on state-of-the-art VFA tools, namely windowed graph Fourier transform and spectral graph wavelet transform. In addition, the paper shows how VFA can be applied to detect and localize anomalies in GS. In the particular example of localizing a malfunctioning weather station, the average area under ROC curve achieved by the local factor outlier technique can be improved from 72% to 87% when fed with VFA-extracted features to detect small drifts in temperature measurements, ranging from 0.5C to 4C. Keywords— GSP, vertex-frequency analysis, Fourier transform, wavelets, anomaly detection