Frequency Analysis of Temporal Graph Signals

The recent availability of complex and high-dimensional datasets has spurred the need for new data analysis methods. One prominent research direction in signal processing has been the focus on data supported over graphs [1]. Graph signals, i.e., signals taking values on the nodes of combinatorial graphs, represent a convenient solution to model data exhibiting complex and nonuniform properties, such as those found in social, biological, and transportation networks, among others. Arguably, the most fundamental tool in the analysis of graph signals is the graph Fourier transform (GFT) [1]-[3]. In an analogous manner to the discrete Fourier transform (DFT), using GFT one may examine graph signals in the graph frequency domain, and, for instance, remove noise by attenuating high graph-frequencies. GFT has also lead to significant new insights in problems such as smoothing and denoising [4]-[6], segmentation [7], sampling and approximation [8]-[10], and classification [11]-[13] of graph data.