Graph Learning Based on Spatiotemporal Smoothness for Time-Varying Graph Signal

Abstract

Graph learning often boils down to uncovering the hidden structure of data, which has been applied in various fields such as biology, sociology, and environmental studies. However, distributed sensing in realistic application often gives rise to spatiotemporal signals, which can be characterized through new tools of graph signal processing as a time-varying graph signal. It calls upon the development from static graph signal studies to the joint space-time analysis. In this paper, we study the problem of learning graphs from time-varying graph signals. Based on the correlated properties in observed signals, a dynamic graph-based model is first presented, which particularly takes into account space-time interactions in signal representation. Considering the case that the time correlation pattern is unavailable, the graph learning problem is cast as a joint correlation detecting and graph refining problem. Then it is solved by the proposed correlation-aware and spatiotemporal smoothness-based graph learning method (CASTS), which novelly introduces the spatiotemporal smooth prior to the field of time-vertex signal analysis. By promoting such smoothness in each learning steps, the graph learning accuracy can be efficiently improved. The experiments on both synthetic and real-world datasets demonstrate the improvement of the proposed CASTS over current state-of-the-art graph learning methods, and meanwhile show the capability of dynamic prediction in climate analysis.

Keywords

• Graph learning
• time-varying graph signal
• spatiotemporal smoothness
• correlation
• space-time interaction