Stationary signal processing on graphs
This provides a theoretical framework for processing signals on graphs, which is important for machine learning applications dealing with structured datasets like social networks or sensor networks.
The paper generalizes wide-sense stationarity to signals on arbitrary weighted undirected graphs, showing that stationary graph signals have a well-defined Power Spectral Density that can be efficiently estimated. It leverages this concept to derive Wiener-type estimation procedures for denoising and regression tasks.
Graphs are a central tool in machine learning and information processing as they allow to conveniently capture the structure of complex datasets. In this context, it is of high importance to develop flexible models of signals defined over graphs or networks. In this paper, we generalize the traditional concept of wide sense stationarity to signals defined over the vertices of arbitrary weighted undirected graphs. We show that stationarity is expressed through the graph localization operator reminiscent of translation. We prove that stationary graph signals are characterized by a well-defined Power Spectral Density that can be efficiently estimated even for large graphs. We leverage this new concept to derive Wiener-type estimation procedures of noisy and partially observed signals and illustrate the performance of this new model for denoising and regression.