  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.

Machine Learning;Signal Processing