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.
| Original language | English |
|---|---|
| Article number | 8360065 |
| Pages (from-to) | 3584-3598 |
| Number of pages | 15 |
| Journal | IEEE Transactions on Signal Processing |
| Volume | 66 |
| Issue number | 13 |
| DOIs | |
| Publication status | Published - 2018 |
Bibliographical note
Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-careOtherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.
Keywords
- 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
- Tools