Spectral partitioning of time-varying networks with unobserved edges
This addresses the challenge of community detection in dynamic networks with hidden edges, which is incremental as it builds on existing stochastic blockmodel frameworks.
The paper tackles the problem of partitioning unobserved time-varying networks from observed graph signals, proposing a spectral algorithm with proven consistency guarantees for recovering the latent community structure.
We discuss a variant of `blind' community detection, in which we aim to partition an unobserved network from the observation of a (dynamical) graph signal defined on the network. We consider a scenario where our observed graph signals are obtained by filtering white noise input, and the underlying network is different for every observation. In this fashion, the filtered graph signals can be interpreted as defined on a time-varying network. We model each of the underlying network realizations as generated by an independent draw from a latent stochastic blockmodel (SBM). To infer the partition of the latent SBM, we propose a simple spectral algorithm for which we provide a theoretical analysis and establish consistency guarantees for the recovery. We illustrate our results using numerical experiments on synthetic and real data, highlighting the efficacy of our approach.