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 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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01.07.2018
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| ISSN: | 1053-587X, 1941-0476 |
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| 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 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. |
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| AbstractList | 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. |
| Author | Banelli, Paolo Isufi, Elvin Barbarossa, Sergio Di Lorenzo, Paolo Leus, Geert |
| Author_xml | – sequence: 1 givenname: Paolo orcidid: 0000-0002-4130-3177 surname: Di Lorenzo fullname: Di Lorenzo, Paolo email: paolo.dilorenzo@uniroma1.it organization: Department of Information Engineering, Electronics, and Telecommunications, Sapienza University of Rome, Rome, Italy – sequence: 2 givenname: Paolo orcidid: 0000-0002-0004-6370 surname: Banelli fullname: Banelli, Paolo email: paolo.banelli@unipg.it organization: Department of Engineering, University of Perugia, Perugia, Italy – sequence: 3 givenname: Elvin orcidid: 0000-0002-1919-260X surname: Isufi fullname: Isufi, Elvin email: isufi-1@tudelft.nl organization: Department of Engineering, University of Perugia, Perugia, Italy – sequence: 4 givenname: Sergio orcidid: 0000-0001-9846-8741 surname: Barbarossa fullname: Barbarossa, Sergio email: sergio.barbarossa@uniroma1.it organization: Department of Information Engineering, Electronics, and Telecommunications, Sapienza University of Rome, Rome, Italy – sequence: 5 givenname: Geert surname: Leus fullname: Leus, Geert email: g.j.t.leus@tudelft.nl organization: Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Delft, CD, The Netherlands |
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| SubjectTerms | 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 |
| Title | Adaptive Graph Signal Processing: Algorithms and Optimal Sampling Strategies |
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