Data-driven processing of graph signals for anomaly detection and forecasting

Abstract

Graph signal processing (GSP) is an emerging field that extends traditional signal processing theory and techniques to analyze and process data defined over graphs. This dissertation presents fundamental topics of GSP, such as Fourier analysis, sampling graph signals, and vertex-frequency analysis (VFA), and proposes two different applications. In the first one, we apply VFA to the problem of anomaly detection in time-varying graph signals. In the particular example of localizing a malfunctioning weather station, the accuracy achieved by outlier detection algorithms is improved when fed with VFA-extracted features to detect small drifts in temperature measurements. The second GSP application proposed in this dissertation combines GSP and recurrent neural networks in order to jointly forecast and interpolate graph signals. The proposed learning model, namely spectral graph gated recurrent unit, outperforms state-of-the-art deep learning techniques, especially when only a small fraction of the graph signals is accessible, considering two distinct real world datasets: temperatures in the US and speed flow in Seattle.