Adaptive Spatio-temporal Estimation on the Graph Edges via Line Graph Transformation
This work addresses the challenge of estimating time-varying signals on graph edges for applications like transportation and meteorology, representing an incremental advancement by adapting existing node-based methods to edges.
The paper tackled the problem of spatio-temporal estimation of signals on graph edges, which is challenging as conventional Graph Signal Processing techniques are defined on nodes, and proposed the Line Graph Least Mean Square (LGLMS) algorithm to adaptively estimate time-varying edge signals by projecting them to node space, confirming its suitability for online prediction in experiments with transportation and meteorological graphs under noisy and missing data conditions.
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.