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Graph Reconstruction from the Observation of Diffused Signals

B. Pasdeloup, M. Rabbat, V. Gripon, D. Pastor and G. Mercier, "Graph Reconstruction from the Observation of Diffused Signals," in Proceedings of the 53rd Allerton Conference, pp. 1386--1390, October 2015.

Signal processing on graphs has received a lot of attention in the recent years. A lot of techniques have arised, inspired by classical signal processing ones, to allow studying signals on any kind of graph. A common aspect of these technique is that they require a graph correctly modeling the studied support to explain the signals that are observed on it. However, in many cases, such a graph is unavailable or has no real physical existence. An example of this latter case is a set of sensors randomly thrown in a field which obviously observe related information. To study such signals, there is no intuitive choice for a support graph. In this document, we address the problem of inferring a graph structure from the observation of signals, under the assumption that they were issued of the diffusion of initially i.i.d. signals. To validate our approach, we design an experimental protocol, in which we diffuse signals on a known graph. Then, we forget the graph, and show that we are able to retrieve it very precisely from the only knowledge of the diffused signals.

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Bibtex
@inproceedings{PasRabGriPasMer201510,
  author = {Bastien Pasdeloup and Michael Rabbat and
Vincent Gripon and Dominique Pastor and Gregoire
Mercier},
  title = {Graph Reconstruction from the Observation
of Diffused Signals},
  booktitle = {Proceedings of the 53rd Allerton
Conference},
  year = {2015},
  pages = {1386--1390},
  month = {October},
}




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