Qiyu Sun

Graph Fourier transform (GFT) is one of the fundamental tools in graph signal processing to decompose graph signals into different frequency components and effectively represent graph signals with strong correlations using various modes of variation. The GFT on undirected graphs has been well-studied, with a conventional approach based on the eigen decomposition of the graph Laplacian. However, this method does not apply to directed graph settings. Several approaches have been proposed to define GFTs on directed graphs, including Jordan decomposition of the graph Laplacian, eigen decomposition of the magnetic Laplacian, and their variants. In this webinar, the presenter will primarily discuss GFT based on the singular value decompositions of graph shifts. The proposed GFT efficiently represents datasets on directed graphs with strong correlations, and in the corresponding frequency domain, the band limiting procedure provides a good approximation for smooth signals.