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

Spatial-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 unifies the Line Graph transformation with classical adaptive filters, reinterpreting online estimation techniques for time-varying signals on graph edges. LGLMS leverages the full power of existing GSP techniques on signals on edges by embedding edge signals into node representations, eliminating the necessity of redefining edge-specific techniques. 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.