Dictionary Learning for Directed Graph Signals via Augmented GFT

This paper proposes a method for designing directed graph (digraph) filters through a dictionary learning approach. Practical digraph filtering methods have not yet been established because of the difficulties posed by asymmetry of the adjacency matrix of a digraph. Augmented graph Fourier transform (AuGFT), proposed by Kitamura et al., defines a new graph Laplacian and extends the conventional graph Fourier transform (GFT) for undirected graph signals to directed ones. However, challenges remain in filter design through AuGFT, particularly in determining the skew intensity parameters. Therefore, this study aims to establish a design method for digraph filters with AuGFT. Filters are parameterized with AuGFT, and parameter optimization is performed using a dictionary learning technique. To verify the effectiveness of the proposed method, experimental results of digraph filtering are shown for temperature data of contiguous US and the GSP-traffic-dataset. Compared with undirected graph filtering, the proposed method is shown to have high steerability in designing digraph filters.