Fast High-Quality Directed Graph Learning

There has been significant progress in the field of graph signal processing for learning symmetric (undirected) graphs, which are widely used in modelling various networked systems. However, in many real-world applications, such as communication networks, directionality of the interactions, that enforce the use of directed graphs (digraphs), plays a key role in the structure and dynamics of the system. The rather recent introduction of effective Fourier basis for digraphs presents an opportunity to unlock the full potential of digraph applications in communications and beyond. In this paper, we present a method for learning digraphs within the GSP framework. Our method provides a flexible representation of the interplay between the nodes within the digraph, and facilitates the analysis of signals on digraphs. A key advantage of our approach is its efficiency and scalability, making it suitable for large-scale and real-time applications of processing over digraphs.