Visual Analytics via Graph Signal Processing

This dissertation presents an overview of the extension of the classical signal processing theory to graph domains. Furthermore, we introduce in this dissertation a novel method for visual analysis of dynamic networks, which relies on the graph wavelet theory. Our method enables the automatic analysis of a signal defined on the nodes of a network. We use a fast approximation of the graph wavelet transform to derive a set of wavelet coefficients, which are then used to identify activity patterns on large networks, including their temporal recurrence. The wavelet coefficients naturally encode spatial and temporal variations of the signal, leading to an efficient and meaningful representation. This method allows for the exploration of the structural evolution of the network and their patterns over time. The effectiveness of our approach is demonstrated using different scenarios and comparisons involving real dynamic networks.