Time-varying graph learning from smooth and stationary graph signals with hidden nodes

Abstract

Learning graph structure from observed signals over graph is a crucial task in many graph signal processing (GSP) applications. Existing approaches focus on inferring static graph, typically assuming that all nodes are available. However, these approaches ignore the situation where only a subset of nodes are available from spatiotemporal measurements, and the remaining nodes are never observed due to application-specific constraints, resulting in time-varying graph estimation accuracy declines dramatically. To handle this problem, we propose a framework that consider the presence of hidden nodes to identify time-varying graph. Specifically, we assume that the graph signals are smooth and stationary on the graphs and only a small number of edges are allowed to change between two consecutive graphs. With these assumptions, we present a challenging time-varying graph inference problem, which models the influence of hidden nodes in terms of estimating the graph-shift operator matrices that have a form of graph Laplacian. Moreover, we emphasize similar edge pattern (column-sparsity) between different graphs. Finally, our method is evaluated on both synthetic and real-world data. The experimental results demonstrate the advantage of our method when compared to existing benchmarking methods.