The Power of Side-Information in Subgraph Detection

Arun Kadavankandy (1, 2) , Konstantin Avrachenkov (1) , Laura Cottatellucci (3) , Rajesh Sundaresan (4)

1 NEO - Network Engineering and Operations
2 LANEAS - Large Networks and Systems Group
3 Eurecom [Sophia Antipolis]
4 ECE - Department of Electrical Communication Engineering [Bangalore]

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.

Mots clés: Signal processing on graphs; Detection algorithms; Clustering algorithms; Belief propagation

Domaines: Apprentissage [cs.LG]; Réseaux sociaux et d'information [cs.SI]; Statistiques [math.ST]; Traitement du signal et de l'image [eess.SP]

Arun Kadavankandy, Konstantin Avrachenkov, Laura Cottatellucci, Rajesh Sundaresan. The Power of Side-Information in Subgraph Detection. IEEE Transactions on Signal Processing, 2018, 66 (7), pp.1905 - 1919. ⟨10.1109/TSP.2017.2786266⟩. ⟨hal-01936412⟩