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arXiv · 1703.01594

Graph sampling with determinantal processes

Nicolas Tremblay·Pierre-Olivier Amblard·Simon Barthelmé
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Abstract

We present a new random sampling strategy for k-bandlimited signals defined on graphs, based on determinantal point processes (DPP). For small graphs, ie, 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, ie, 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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Nicolas Tremblay, Pierre-Olivier Amblard, Simon Barthelmé. 2017-03-05. Graph sampling with determinantal processes. https://arxiv.org/abs/1703.01594

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