Adaptive Graph Signal Processing: Algorithms and Optimal Sampling Strategies

The goal of this paper is to propose novel strategies for adaptive learning of signals defined over graphs, which are observed over a (randomly) time-varying subset of vertices. We recast two classical adaptive algorithms in the graph signal processing framework, namely the least mean squares (LMS)...

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Veröffentlicht in:IEEE transactions on signal processing Jg. 66; H. 13; S. 3584 - 3598
Hauptverfasser: Di Lorenzo, Paolo, Banelli, Paolo, Isufi, Elvin, Barbarossa, Sergio, Leus, Geert
Format: Journal Article
Sprache:Englisch
Veröffentlicht: IEEE 01.07.2018
Schlagworte:
Adaptation and learning
Adaptive learning
graph signal processing
Laplace equations
sampling on graphs
Signal processing
Signal processing algorithms
Steady-state
successive convex approximation
Task analysis
ISSN:1053-587X, 1941-0476
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Beschreibung
Zusammenfassung:The goal of this paper is to propose novel strategies for adaptive learning of signals defined over graphs, which are observed over a (randomly) time-varying subset of vertices. We recast two classical adaptive algorithms in the graph signal processing framework, namely the least mean squares (LMS) and the recursive least squares (RLS) adaptive estimation strategies. For both methods, a detailed mean-square analysis illustrates the effect of random sampling on the adaptive reconstruction capability and the steady-state performance. Then, several probabilistic sampling strategies are proposed to design the sampling probability at each node in the graph, with the aim of optimizing the tradeoff between steady-state performance, graph sampling rate, and convergence rate of the adaptive algorithms. Finally, a distributed RLS strategy is derived and shown to be convergent to its centralized counterpart. Numerical simulations carried out over both synthetic and real data illustrate the good performance of the proposed sampling and recovery strategies for (distributed) adaptive learning of signals defined over graphs.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2018.2835384