Reconstruction of graph signals from traffic data on directed road networks using kernel methods

The completeness of traffic data sets is endangered by distinct reasons, such as implementation costs or privacy concerns. Modelling an urban network as a road graph (i.e., with roads as nodes, and edges representing intersections) allows the use of graph signal recovery methods (e.g., kernel ridge regression) to reconstruct missing traffic information (e.g., vehicular volume, average speed, and density) in the form of a graph signal. We implement a directed road graph by considering the driving directions of the roads within an urban network and recover incomplete traffic graph signals via kernel ridge regression. Moreover, we combine the graph signal recovery with meshless approximation with radial basis functions along the roads to obtain smooth transitions for the recovered traffic states. Evaluating distinct directed graph kernel matrices based on the random walk Laplacian shows that volume and density signals exhibit a positive correlation, while volume and average speed display a negative one. Moreover, we unveil the viability of obtaining small absolute differences in estimations when using either a directed or an undirected road graph.