Spectral detection in the censored block model

Alaa Saade (1) , Florent Krzakala (2) , Marc Lelarge (3) , Lenka Zdeborová (4)

1 LPS - Laboratoire de Physique Statistique de l'ENS
2 SU - Sorbonne Université
3 DYOGENE - Dynamics of Geometric Networks
4 IPHT - Institut de Physique Théorique - UMR CNRS 3681

We consider the problem of partially recovering hidden binary variables from the observation of (few) censored edge weights, a problem with applications in community detection, correlation clustering and synchronization. We describe two spectral algorithms for this task based on the non-cktracking and the Bethe Hessian operators. These algorithms are shown to be asymptotically optimal for the partial recovery problem, in that they detect the hidden assignment as soon as it is information theoretically possible to do so.

Domaines: Physique [physics]

Alaa Saade, Florent Krzakala, Marc Lelarge, Lenka Zdeborová. Spectral detection in the censored block model. ISIT 2015 - IEEE International Symposium on Information Theory, Jun 2015, Hong-Kong, China. pp.1184-1188, ⟨10.1109/ISIT.2015.7282642⟩. ⟨cea-01140716⟩