Advances in Distributed Graph Filtering

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29 Citations (Scopus)
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Abstract

Graph filters are one of the core tools in graph signal processing. A central aspect of them is their direct distributed implementation. However, the filtering performance is often traded with distributed communication and computational savings. To improve this tradeoff, this paper generalizes state-of-the-art distributed graph filters to filters where every node weights the signal of its neighbors with different values while keeping the aggregation operation linear. This new implementation, labeled as edge-variant graph filter, yields a significant reduction in terms of communication rounds while preserving the approximation accuracy. In addition, we characterize a subset of shift-invariant graph filters that can be described with edge-variant recursions. By using a low-dimensional parameterization, these shift-invariant filters provide new insights in approximating linear graph spectral operators through the succession and composition of local operators, i.e., fixed support matrices. A set of numerical results shows the benefits of the edge-variant graph filters over current methods and illustrates their potential to a wider range of applications than graph filtering.

Original languageEnglish
Article number8666778
Pages (from-to)2320-2333
Number of pages14
JournalIEEE Transactions on Signal Processing
Volume67
Issue number9
DOIs
Publication statusPublished - 2019

Keywords

  • ARMA
  • Consensus
  • distributed beamforming
  • distributed signal processing
  • edge-variant graph filters
  • FIR
  • graph filters
  • graph signal processing
  • IIR

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