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The Power of Side-Information in Subgraph Detection

Kadavankandy, Arun and Avrachenkov, Konstantin and Cottatellucci, Laura and Sundaresan, Rajesh (2018) The Power of Side-Information in Subgraph Detection. In: IEEE TRANSACTIONS ON SIGNAL PROCESSING, 66 (7). pp. 1905-1919.

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Official URL: http://dx.doi.org/10.1109/TSP.2017.2786266

Abstract

In this paper, 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 parameter falls below a threshold. In contrast, in the presence of nontrivial 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.

Item Type: Journal Article
Additional Information: Copy right for the article belong to IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 445 HOES LANE, PISCATAWAY, NJ 08855-4141 USA
Department/Centre: Division of Electrical Sciences > Electrical Communication Engineering
Depositing User: Id for Latest eprints
Date Deposited: 19 Mar 2018 18:29
Last Modified: 19 Mar 2018 18:29
URI: http://eprints.iisc.ac.in/id/eprint/59221

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