Learning Directed Graphs From Data Under Structural Constraints

For real-world graph signals, the relationships between two nodes may not always be symmetric. Hence, a directed graph would be more flexible to characterize such relationships between signals. In this paper, we propose a two-stage algorithm to learn directed graphs from the observed data, i.e., designing the graph frequency components and afterward estimating the graph shift matrix. The graph frequency components are designed to improve the sparsity of graph signals in graph frequency domain, and the estimation of directed shift matrix is thereafter modelled as a convex problem, where the structural constraints of graph signals could be taken into account. Such a directed graph shift matrix would greatly facilitate further processing of the associated graph signals such as sampling and graph filtering in frequency domain since the graph frequency components are specifically designed and the signals over the graph are sparse. Numerical results demonstrate the effectiveness of the proposed method.