Online Graph Learning under Smoothness Priors

TL;DR

This paper introduces online algorithms for dynamic graph topology inference from streaming data, enabling real-time tracking of evolving network structures with theoretical convergence guarantees.

Contribution

It develops novel proximal gradient-based methods for online graph learning that adapt to time-varying topologies while maintaining computational efficiency.

Findings

Algorithm effectively tracks slowly-varying network connectivity.

Convergence to a neighborhood of the optimal solution is established.

Simulations demonstrate successful adaptation to real financial data.

Abstract

The growing success of graph signal processing (GSP) approaches relies heavily on prior identification of a graph over which network data admit certain regularity. However, adaptation to increasingly dynamic environments as well as demands for real-time processing of streaming data pose major challenges to this end. In this context, we develop novel algorithms for online network topology inference given streaming observations assumed to be smooth on the sought graph. Unlike existing batch algorithms, our goal is to track the (possibly) time-varying network topology while maintaining the memory and computational costs in check by processing graph signals sequentially-in-time. To recover the graph in an online fashion, we leverage proximal gradient (PG) methods to solve a judicious smoothness-regularized, time-varying optimization problem. Under mild technical conditions, we establish that the online graph learning algorithm converges to within a neighborhood of (i.e., it tracks) the optimal time-varying batch solution. Computer simulations using both synthetic and real financial market data illustrate the effectiveness of the proposed algorithm in adapting to streaming signals to track slowly-varying network connectivity.