Online Graph Filtering Over Expanding Graphs

TL;DR

This paper introduces an online graph filtering framework that adapts to evolving graph topologies, addressing the limitations of traditional fixed-graph filters in dynamic real-world networks.

Contribution

It develops an adaptive online filtering method capable of handling both known and unknown graph growth, with theoretical regret analysis and empirical validation.

Findings

Effective in dynamic graph scenarios

Competitive performance against state-of-the-art methods

Theoretical insights into filter adaptation and regret bounds

Abstract

Graph filters are a staple tool for processing signals over graphs in a multitude of downstream tasks. However, they are commonly designed for graphs with a fixed number of nodes, despite real-world networks typically grow over time. This topological evolution is often known up to a stochastic model, thus, making conventional graph filters ill-equipped to withstand such topological changes, their uncertainty, as well as the dynamic nature of the incoming data. To tackle these issues, we propose an online graph filtering framework by relying on online learning principles. We design filters for scenarios where the topology is both known and unknown, including a learner adaptive to such evolution. We conduct a regret analysis to highlight the role played by the different components such as the online algorithm, the filter order, and the growing graph model. Numerical experiments with synthetic and real data corroborate the proposed approach for graph signal inference tasks and show a competitive performance w.r.t. baselines and state-of-the-art alternatives.