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Translation and Stationarity for Graph Signals

Benjamin Girault 1, 2 Paulo Gonçalves 1, 2 Eric Fleury 1, 2
1 DANTE - Dynamic Networks : Temporal and Structural Capture Approach
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme, IXXI - Institut Rhône-Alpin des systèmes complexes
Abstract : We propose a novel time shift like operator called the graph translation. We enforce that it is isometric and define it such that it shares with the time shift operator its key properties. Using the graph translation operator and its isometry, we propose a tractable definition of stationary graph signals and characterise stationary graph signals using their spectral properties. We illustrate this characterisation on synthetic stationary random graph signals. Finally we propose a method to test the stationarity of a real dataset.
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Submitted on : Thursday, April 23, 2015 - 2:51:13 PM
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Benjamin Girault, Paulo Gonçalves, Eric Fleury. Translation and Stationarity for Graph Signals. [Research Report] RR-8719, École Normale Supérieure de Lyon; Inria Rhône-Alpes; INRIA. 2015. ⟨hal-01144991⟩

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