Time-varying Graph Signal Estimation via Dynamic Multi-hop Topologies

TL;DR

This paper introduces a Dynamic Multi-hop model and estimation algorithm that effectively capture and estimate time-varying signals on sparse, evolving graphs, improving modeling of complex interactions over time.

Contribution

It presents a novel dynamic graph model and estimation method that adaptively captures evolving interactions among signals, surpassing static graph assumptions.

Findings

Accurately models dynamic interactions in brain and stock market data.

Demonstrates improved estimation accuracy over static models.

Handles noisy, partially observed signals effectively.

Abstract

The assumption of using a static graph to represent multivariate time-varying signals oversimplifies the complexity of modeling their interactions over time. We propose a Dynamic Multi-hop model that captures dynamic interactions among time-varying node signals, while also accounting for time-varying edge signals, by extracting latent edges through topological diffusion and edge pruning. The resulting graphs are time-varying and sparse, capturing key dynamic node interactions and representing signal diffusion to both near and distant neighbors over time. The Dynamic Multi-hop Estimation algorithm is further proposed, accurately representing the interaction dynamics among node signals while enabling adaptive estimation of time-varying multivariate signals spatially and temporally. The Dynamic Multi-hop Estimation is evaluated under two real-world datasets of brain network and stock market for the online estimation of partially observed time-varying signals corrupted by noise.