Adaptive Spatio-temporal Estimation on the Graph Edges via Line Graph Transformation

Abstract: Spatio-temporal estimation of signals on graph edges is challenging because most conventional Graph Signal Processing techniques are defined on the graph nodes. Leveraging the Line Graph transform, the Line Graph Least Mean Square (LGLMS) algorithm is proposed to conduct adaptive estimation of time-varying edge signals by projecting the edge signals from edge space to node space. LGLMS is an adaptive algorithm analogous to the classical LMS algorithm but applied to graph edges. Unlike edge-specific methods, LGLMS retains all GSP concepts and techniques originally designed for graph nodes, without the need for redefinition on the edges. Experimenting with transportation graphs and meteorological graphs, with the signal observations having noisy and missing values, we confirmed that LGLMS is suitable for the online prediction of time-varying edge signals.