Classical signal processing focuses on extracting frequency characteristics of time or spatial-domain data. For example, Fourier transform can be defined as the inner product of the signal and eigenfunctions of the one-dimensional Laplacian operator. Graph signal is defined as discrete signal located on vertices of a graph. Analogous to classical signal processing, graph Fourier transform is defined as the inner product of the graph signal and eigenfunctions of graph Laplacian matrix. In this paper, we describe fundamentals and recent advances of graph signal processing, which include; graph Fourier/wavelet transforms, filtering/sampling of graph signal, theoretical progress, and applications of graph signal processing.
2014 The Institute of Electronics, Information and Communication Engineers