Tracking Time-Vertex Propagation using Dynamic Graph Wavelets

TL;DR

This paper introduces Dynamic Graph Wavelets, a new method for analyzing time-evolving signals on graphs, demonstrated on seismic data to identify earthquake epicenters.

Contribution

It proposes a novel class of wavelet frames for dynamic graph signals, enabling better analysis of evolving processes on networks.

Findings

Effective in estimating earthquake epicenters from seismic data

Combines wavelet frames with sparsity-based methods like compressive sensing

Demonstrates improved analysis of dynamic processes on graphs

Abstract

Graph Signal Processing generalizes classical signal processing to signal or data indexed by the vertices of a weighted graph. So far, the research efforts have been focused on static graph signals. However numerous applications involve graph signals evolving in time, such as spreading or propagation of waves on a network. The analysis of this type of data requires a new set of methods that fully takes into account the time and graph dimensions. We propose a novel class of wavelet frames named Dynamic Graph Wavelets, whose time-vertex evolution follows a dynamic process. We demonstrate that this set of functions can be combined with sparsity based approaches such as compressive sensing to reveal information on the dynamic processes occurring on a graph. Experiments on real seismological data show the efficiency of the technique, allowing to estimate the epicenter of earthquake events recorded by a seismic network.