Graph Learning for Spatiotemporal Signals with Long- and Short-Term Characterization

Abstract

Mining natural associations from high-dimensional spatiotemporal signals have received significant attention in various fields including biology, climatology and financial analysis, etcetera. Due to the widespread correlation in diverse applications, ideas that taking full advantage of correlated property to find meaningful insights of spatiotemporal signals have begun to emerge. In this paper, we study the problem of uncovering graphs that better reveal the relations behind data, with the help of long and short term correlated property in spatiotemporal signals. A spatiotemporal signal model considering both spatial and temporal relationship is firstly presented. Particularly, a lowrank representation together with a Gaussian Markov process is adopted to describe the signals' time-correlated behavior. Next, we cast the graph learning problem as a joint low-rank component estimation and graph Laplacian inference problem. A Low-Rank and Spatiotemporal Smoothness-based graph learning method (GL-LRSS) is proposed, which novelly introduces spatiotemporal smooth prior to the field of time-vertex signal analysis. Through jointly exploiting the low-rank property of longtime observations and the smoothness of short-time observations, the overall performance is effectively improved. Experiments on both synthetic and real-world datasets demonstrate the significant improvement on learning accuracy of the proposed GL-LRSS over current state-of-the-art low-rank estimation and graph learning methods.

Kernel-based Graph Learning from Smooth Signals: A Functional Viewpoint

“…In terms of the observation-side dependency, there exist some GSP graph learning models that consider temporal dependency in graph signals. A so-called spatiotemporal smoothness was proposed in [45], [46] to transform the graph signals using a temporally weighed difference operator. If every timestamp is equally important, the operator is equivalent to a prepossessing step to make the time series observed on each node stationary.…”