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Communication Dans Un Congrès Année : 2015

Toward An Uncertainty Principle For Weighted Graphs

Résumé

The uncertainty principle states that a signal cannot be localized both in time and frequency. With the aim of extending this result to signals on graphs, Agaskar & Lu introduce notions of graph and spectral spreads. They show that a graph uncertainty principle holds for some families of unweighted graphs. This principle states that a signal cannot be simultaneously localized both in graph and spectral domains. In this paper, we aim to extend their work to weighted graphs. We show that a naive extension of their definitions leads to inconsistent results such as discontinuity of the graph spread when regarded as a function of the graph structure. To circumvent this problem, we propose another definition of graph spread that relies on an inverse similarity matrix. We also discuss the choice of the distance function that appears in this definition. Finally, we compute and plot uncertainty curves for families of weighted graphs.
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Dates et versions

hal-01270655 , version 1 (08-02-2016)

Identifiants

Citer

Bastien Pasdeloup, Réda Alami, Vincent Gripon, Michael Rabbat. Toward An Uncertainty Principle For Weighted Graphs. EUSIPCO 2015 : 23rd European Signal Processing Conference, Aug 2015, Nice, France. pp.1496 - 1500, ⟨10.1109/EUSIPCO.2015.7362633⟩. ⟨hal-01270655⟩
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