Online Topology Inference from Streaming Stationary Graph Signals with Partial Connectivity Information

We develop online graph learning algorithms from streaming network data. Our goal is to track the (possibly) time-varying network topology, and affect memory and computational savings by processing the data on-the-fly as they are acquired. The setup entails observations modeled as stationary graph s...

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Vydané v:Algorithms Ročník 13; číslo 9; s. 228
Hlavní autori: Shafipour, Rasoul, Mateos, Gonzalo
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Basel MDPI AG 01.09.2020
Predmet:
Algorithms
Covariance matrix
graph signal processing
Inference
Inverse problems
Machine learning
Network topologies
network topology inference
online optimization
proximal gradient algorithm
Signal processing
streaming data
ISSN:1999-4893, 1999-4893
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Shrnutí:We develop online graph learning algorithms from streaming network data. Our goal is to track the (possibly) time-varying network topology, and affect memory and computational savings by processing the data on-the-fly as they are acquired. The setup entails observations modeled as stationary graph signals generated by local diffusion dynamics on the unknown network. Moreover, we may have a priori information on the presence or absence of a few edges as in the link prediction problem. The stationarity assumption implies that the observations’ covariance matrix and the so-called graph shift operator (GSO—a matrix encoding the graph topology) commute under mild requirements. This motivates formulating the topology inference task as an inverse problem, whereby one searches for a sparse GSO that is structurally admissible and approximately commutes with the observations’ empirical covariance matrix. For streaming data, said covariance can be updated recursively, and we show online proximal gradient iterations can be brought to bear to efficiently track the time-varying solution of the inverse problem with quantifiable guarantees. Specifically, we derive conditions under which the GSO recovery cost is strongly convex and use this property to prove that the online algorithm converges to within a neighborhood of the optimal time-varying batch solution. Numerical tests illustrate the effectiveness of the proposed graph learning approach in adapting to streaming information and tracking changes in the sought dynamic network.
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ISSN:1999-4893
1999-4893
DOI:10.3390/a13090228