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

arXiv: https://arxiv.org/abs/2411.01567 · HTML: https://mlsanity.com/paper/2411.01567/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 65 references that are in the map.
- First posted on arXiv 3 Nov 2024.

## Builds on (most cited first, 17 of 17)

- [Modeling polypharmacy side effects with graph convolutional networks](https://mlsanity.com/paper/1802.00543/) (2018)
- [Discrete Graph Structure Learning for Forecasting Multiple Time Series](https://mlsanity.com/paper/2101.06861/) (2021)
- [How to learn a graph from smooth signals](https://mlsanity.com/paper/1601.02513/) (2016)
- [Network Topology Inference from Spectral Templates](https://mlsanity.com/paper/1608.03008/) (2016)
- [Learning heat diffusion graphs](https://mlsanity.com/paper/1611.01456/) (2016)
- [Stationary Graph Processes and Spectral Estimation](https://mlsanity.com/paper/1603.04667/) (2016)
- [Signal Processing on Graphs: Causal Modeling of Unstructured Data](https://mlsanity.com/paper/1503.00173/) (2015)
- [Forecasting Time Series with VARMA Recursions on Graphs](https://mlsanity.com/paper/1810.08581/) (2018)
- [Sparse Graph Learning from Spatiotemporal Time Series](https://mlsanity.com/paper/2205.13492/) (2022)
- [Sparsity-Aware Adaptive Algorithms Based on Alternating Optimization with Shrinkage](https://mlsanity.com/paper/1401.0463/) (2014)
- [Adaptive Least Mean Squares Estimation of Graph Signals](https://mlsanity.com/paper/1602.05703/) (2016)
- [Adaptive Sign Algorithm for Graph Signal Processing](https://mlsanity.com/paper/2201.05821/) (2022)
- [Online Topology Identification from Vector Autoregressive Time Series](https://mlsanity.com/paper/1904.01864/) (2019)
- [Tracking Switched Dynamic Network Topologies from Information Cascades](https://mlsanity.com/paper/1606.08882/) (2016)
- [A Class of Doubly Stochastic Shift Operators for Random Graph Signals and their Boundedness](https://mlsanity.com/paper/1908.01596/) (2019)
- [Distributed Adaptive Learning of Graph Signals](https://mlsanity.com/paper/1609.06100/) (2016)
- [Methods of Adaptive Signal Processing on Graphs Using Vertex-Time Autoregressive Models](https://mlsanity.com/paper/2003.05729/) (2020)

## Built on by (most cited first, 1 of 1)

- [Bayesian-based Online Label Shift Estimation with Dynamic Dirichlet Priors](https://mlsanity.com/paper/2511.18615/) (2025)

## Abstract (arXiv)

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.