Learning directed Graph Shifts from High-Dimensional Time Series

Graph Signal Processing is an emerging field of signal processing that combines classical signal processing with graph theory. There are two approaches which either use undirected weighted graphs that allow the usage of Laplacian matrix, or the more general approach, which is based on algebraic features, including all weighted directed graphs. We investigate the concept of causal graph signal processing that was proposed by J. Mei and J.M.F. Moura. In a causal graph process, the current signal depends on the past signals through graph filters that consist of a polynomial of the graph shift matrix. With their algorithm, the graph shift matrix and filter coefficients can be learned from a sequence of observed data vectors. We evaluate the performance for estimating the shift matrix from an artificially generated causal graph process. Furthermore, we apply the estimation algorithm on two real-world data sets. The first data set contains daily temperature data from different countries. In the second example, we tried to model Austrian stock prices with causal graph processes.