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

TL;DR

This paper introduces LGLMS, an adaptive filtering method that transforms edge signals into node signals via line graph transformation, enabling effective online estimation of dynamic signals on graph edges.

Contribution

The paper proposes a novel line graph-based adaptive filtering algorithm for edge signals, unifying graph signal processing with classical adaptive filters.

Findings

LGLMS effectively predicts time-varying edge signals in transportation and meteorological graphs.

LGLMS handles noisy and missing data in edge signal estimation.

The method outperforms traditional node-based approaches in online edge signal prediction.

Abstract

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.