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Local Smoothness of Graph Signals

Author

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  • Miloš Daković
  • Ljubiša Stanković
  • Ervin Sejdić

Abstract

Analysis of vertex-varying spectral content of signals on graphs challenges the assumption of vertex invariance and requires the introduction of vertex-frequency representations as a new tool for graph signal analysis. Local smoothness, an important parameter of vertex-varying graph signals, is introduced and defined in this paper. Basic properties of this parameter are given. By using the local smoothness, an ideal vertex-frequency distribution is introduced. The local smoothness estimation is performed based on several forms of the vertex-frequency distributions, including the graph spectrogram, the graph Rihaczek distribution, and a vertex-frequency distribution with reduced interferences. The presented theory is illustrated through numerical examples.

Suggested Citation

  • Miloš Daković & Ljubiša Stanković & Ervin Sejdić, 2019. "Local Smoothness of Graph Signals," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-14, April.
    • Handle: RePEc:hin:jnlmpe:3208569
    DOI: 10.1155/2019/3208569
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    Cited by:

    1. Jolene S. Ranek & Wayne Stallaert & J. Justin Milner & Margaret Redick & Samuel C. Wolff & Adriana S. Beltran & Natalie Stanley & Jeremy E. Purvis, 2024. "DELVE: feature selection for preserving biological trajectories in single-cell data," Nature Communications, Nature, vol. 15(1), pages 1-26, December.
    2. Ljubiša Stanković & Jonatan Lerga & Danilo Mandic & Miloš Brajović & Cédric Richard & Miloš Daković, 2021. "From Time–Frequency to Vertex–Frequency and Back," Mathematics, MDPI, vol. 9(12), pages 1-40, June.

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