# Spectral partitioning of time-varying networks with unobserved edges

## TL;DR

This paper introduces a spectral algorithm for community detection in time-varying networks with unobserved edges, leveraging filtered graph signals and a stochastic blockmodel framework, with proven consistency guarantees.

## Contribution

It presents a novel spectral method for blind community detection in dynamic networks modeled by latent SBMs, with theoretical analysis and empirical validation.

## Key findings

- The algorithm achieves consistent recovery of latent communities.
- Numerical experiments demonstrate effectiveness on synthetic and real data.
- The method handles unobserved edges in time-varying networks.

## Abstract

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.