Online Graph Topology Learning via Time-Vertex Adaptive Filters: From Theory to Cardiac Fibrillation

TL;DR

This paper introduces AdaCGP, an adaptive graph topology learning algorithm for real-time analysis of dynamic systems, demonstrating superior performance in simulations and cardiac fibrillation data for biomedical applications.

Contribution

AdaCGP is a novel sparsity-aware, recursive algorithm for online graph topology estimation from multivariate time series data, addressing time-varying systems and real-time constraints.

Findings

Outperforms baseline methods with over 83% improvement in GSO estimation.

Effectively tracks dynamic propagation patterns in cardiac fibrillation.

Identifies stability features in conduction patterns relevant for clinical diagnosis.

Abstract

Graph Signal Processing (GSP) provides a powerful framework for analysing complex, interconnected systems by modelling data as signals on graphs. While recent advances have enabled graph topology learning from observed signals, existing methods often struggle with time-varying systems and real-time applications. To address this gap, we introduce AdaCGP, a sparsity-aware adaptive algorithm for dynamic graph topology estimation from multivariate time series. AdaCGP estimates the Graph Shift Operator (GSO) through recursive update formulae designed to address sparsity, shift-invariance, and bias. Through comprehensive simulations, we demonstrate that AdaCGP consistently outperforms multiple baselines across diverse graph topologies, achieving improvements exceeding 83% in GSO estimation compared to state-of-the-art methods while maintaining favourable computational scaling properties. Our variable splitting approach enables reliable identification of causal connections with near-zero false alarm rates and minimal missed edges. Applied to cardiac fibrillation recordings, AdaCGP tracks dynamic changes in propagation patterns more effectively than established methods like Granger causality, capturing temporal variations in graph topology that static approaches miss. The algorithm successfully identifies stability characteristics in conduction patterns that may maintain arrhythmias, demonstrating potential for clinical applications in diagnosis and treatment of complex biomedical systems.