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p-Laplacian Regularization of Signals on Directed Graphs

  • Zeina Abu Aisheh
  • Sébastien Bougleux
  • Olivier LézorayEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11241)

Abstract

The graph Laplacian plays an important role in describing the structure of a graph signal from weights that measure the similarity between the vertices of the graph. In the literature, three definitions of the graph Laplacian have been considered for undirected graphs: the combinatorial, the normalized and the random-walk Laplacians. Moreover, a nonlinear extension of the Laplacian, called the p-Laplacian, has also been put forward for undirected graphs. In this paper, we propose several formulations for p-Laplacians on directed graphs directly inspired from the Laplacians on undirected graphs. Then, we consider the problem of p-Laplacian regularization of signals on directed graphs. Finally, we provide experimental results to illustrate the effect of the proposed p-laplacians on different types of graph signals.

Keywords

Directed graphs p-laplacian Graph signal Regularization 

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Zeina Abu Aisheh
    • 1
  • Sébastien Bougleux
    • 1
  • Olivier Lézoray
    • 1
    Email author
  1. 1.Normandie Univ, UNICAEN, ENSICAEN, CNRS, GREYCCaenFrance

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