Reference : Adaptive Graph Filters in Reproducing Kernel Hilbert Spaces: Design and Performance A...
Scientific journals : Article
Engineering, computing & technology : Electrical & electronics engineering
Security, Reliability and Trust
Adaptive Graph Filters in Reproducing Kernel Hilbert Spaces: Design and Performance Analysis
Elias, Vitor R. M. mailto []
Gogineni, Vinay C. mailto []
Alves Martins, Wallace mailto [University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT) > SigCom >]
Werner, Stefan mailto []
IEEE Transactions on Signal and Information Processing over Networks
Institute of Electrical and Electronics Engineers
New York
[en] Adaptive signal processing ; Distributed learning ; Kernel graph filters ; Kernel LMS ; Random Fourier features
[en] This paper develops adaptive graph filters that operate in reproducing kernel Hilbert spaces. We consider both centralized and fully distributed implementations. We first define nonlinear graph filters that operate on graph-shifted versions of the input signal. We then propose a centralized graph kernel least mean squares (GKLMS) algorithm to identify nonlinear graph filters' model parameters. To reduce the dictionary size of the centralized GKLMS, we apply the principles of coherence check and random Fourier features (RFF). The resulting algorithms have performance close to that of the GKLMS algorithm. Additionally, we leverage the graph structure to derive the distributed graph diffusion KLMS (GDKLMS) algorithms. We show that, unlike the coherence check-based approach, the GDKLMS based on RFF avoids the use of a pre-trained dictionary through its data independent fixed structure. We conduct a detailed performance study of the proposed RFF-based GDKLMS, and the conditions for its convergence both in mean and mean-squared senses are derived. Extensive numerical simulations show that GKLMS and GDKLMS can successfully identify nonlinear graph filters and adapt to model changes. Furthermore, RFF-based strategies show faster convergence for model identification and exhibit better tracking performance in model-changing scenarios.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TSIPN.2020.3046217, IEEE Transactions on Signal and Information Processing over Networks. See This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see
H2020 ; 742648 - AGNOSTIC - Actively Enhanced Cognition based Framework for Design of Complex Systems

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