Adaptive Graph Signal Processing: Algorithms and Optimal Sampling Strategies

TL;DR

This paper introduces adaptive algorithms for graph signal processing, analyzing their performance under random sampling, and proposes probabilistic sampling strategies to optimize learning over graphs.

Contribution

It recasts LMS and RLS adaptive algorithms within graph signal processing, providing detailed analysis and novel probabilistic sampling strategies for improved adaptive learning.

Findings

Probabilistic sampling strategies enhance steady-state performance.

Distributed RLS converges to centralized algorithm performance.

Numerical results validate the effectiveness of proposed methods.

Abstract

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 is 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 reconstruction strategies for (possibly distributed) adaptive learning of signals defined over graphs.