Graph sampling with determinantal processes
Résumé
We present a new random sampling strategy for k-bandlimited signals defined on graphs, based on determinantal point processes (DPP). For small graphs, i.e., in cases where the spectrum of the graph is accessible, we exhibit a DPP sampling scheme that enables perfect recovery of bandlimited signals. For large graphs, i.e., in cases where the graph's spectrum is not accessible, we investigate, both theoretically and empirically, a sub-optimal but much faster DPP based on loop-erased random walks on the graph. Preliminary experiments show promising results especially in cases where the number of measurements should stay as small as possible and for graphs that have a strong community structure. Our sampling scheme is efficient and can be applied to graphs with up to 10^6 nodes.
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paper.pdf (418.6 Ko)
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results_EUSIPCO_N=100_comnum=2_K=2_known_Uk_sigma=0p0001_with_EB.pdf (146.49 Ko)
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results_EUSIPCO_N=100_comnum=2_K=2_unknown_Uk_sigma=0p0001_gmres=True_est_weights=True_vs_EASINESS.pdf (97.81 Ko)
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results_EUSIPCO_N=100_comnum=2_K=2_unknown_Uk_sigma=0p0001_gmres=True_est_weights=True_vs_gamma.pdf (97.44 Ko)
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Origine : Fichiers produits par l'(les) auteur(s)
Origine : Fichiers produits par l'(les) auteur(s)
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