Adaptive Least Mean Squares Estimation of Graph Signals

Abstract

The aim of this paper is to propose a least mean squares (LMS) strategy for adaptive estimation of signals defined over graphs. Assuming the graph signal to be band-limited, over a known bandwidth, the method enables reconstruction, with guaranteed performance in terms of mean-square error, and tracking from a limited number of observations over a subset of vertices. A detailed mean square analysis provides the performance of the proposed method, and leads to several insights for designing useful sampling strategies for graph signals. Numerical results validate our theoretical findings, and illustrate the performance of the proposed method. Furthermore, to cope with the case where the bandwidth is not known beforehand, we propose a method that performs a sparse online estimation of the signal support in the (graph) frequency domain, which enables online adaptation of the graph sampling strategy. Finally, we apply the proposed method to build the power spatial density cartography of a given operational region in a cognitive network environment.

Submitted to IEEE Transactions on Signal and Information Processing over Networks

References in corpus (4)

• Discrete Signal Processing on Graphs
• Signals on Graphs: Uncertainty Principle and Sampling
• Sampling of graph signals with successive local aggregations
• Local-set-based Graph Signal Reconstruction

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• Adaptive Propagation Graph Convolutional Network
• Filtering Random Graph Processes Over Random Time-Varying Graphs
• Semi-Blind Inference of Topologies and Dynamical Processes over Graphs
• Distributed Adaptive Learning of Graph Signals
• Reconstruction of Time-varying Graph Signals via Sobolev Smoothness
• Inference of Spatio-Temporal Functions over Graphs via Multi-Kernel Kriged Kalman Filtering
• Gegenbauer Graph Neural Networks for Time-varying Signal Reconstruction
• Graph Normalized-LMP Algorithm for Signal Estimation Under Impulsive Noise
• Sampling and Inference of Networked Dynamics using Log-Koopman Nonlinear Graph Fourier Transform