The Power of Side-Information in Subgraph Detection

Abstract : In this work, we tackle the problem of hidden community detection. We consider Belief Propagation (BP) applied to the problem of detecting a hidden Erdos-Renyi (ER) graph embedded in a larger and sparser ER graph, in the presence of side-information. We derive two related algorithms based on BP to perform subgraph detection in the presence of two kinds of side-information. The first variant of side-information consists of a set of nodes, called cues, known to be from the subgraph. The second variant of side-information consists of a set of nodes that are cues with a given probability. It was shown in past works that BP without side-information fails to detect the subgraph correctly when a so-called effective signal-to-noise ratio (SNR) parameter falls below a threshold. In contrast, in the presence of non-trivial side-information, we show that the BP algorithm achieves asymptotically zero error for any value of a suitably defined phase-transition parameter. We validate our results on synthetic datasets and a few real world networks.
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Submitted on : Tuesday, November 27, 2018 - 1:52:04 PM
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Arun Kadavankandy, Konstantin Avrachenkov, Laura Cottatellucci, Rajesh Sundaresan. The Power of Side-Information in Subgraph Detection. IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, 2018, 66 (7), pp.1905 - 1919. ⟨10.1109/TSP.2017.2786266⟩. ⟨hal-01936412⟩

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