Network Inference from Consensus Dynamics

We consider the problem of identifying the topology of a weighted, undirected network $\mathcal G$ from observing snapshots of multiple independent consensus dynamics. Specifically, we observe the opinion profiles of a group of agents for a set of $M$ independent topics and our goal is to recover the precise relationships between the agents, as specified by the unknown network $\mathcal G$. In order to overcome the under-determinacy of the problem at hand, we leverage concepts from spectral graph theory and convex optimization to unveil the underlying network structure. More precisely, we formulate the network inference problem as a convex optimization that seeks to endow the network with certain desired properties -- such as sparsity -- while being consistent with the spectral information extracted from the observed opinions. This is complemented with theoretical results proving consistency as the number $M$ of topics grows large. We further illustrate our method by numerical experiments, which showcase the effectiveness of the technique in recovering synthetic and real-world networks.Comment: Will be presented at the 2017 IEEE Conference on Decision and Control (CDC

Spectral partitioning of time-varying networks with unobserved edges

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.Comment: 5 pages, 2 figure

State-Space Network Topology Identification from Partial Observations

In this work, we explore the state-space formulation of a network process to recover, from partial observations, the underlying network topology that drives its dynamics. To do so, we employ subspace techniques borrowed from system identification literature and extend them to the network topology identification problem. This approach provides a unified view of the traditional network control theory and signal processing on graphs. In addition, it provides theoretical guarantees for the recovery of the topological structure of a deterministic continuous-time linear dynamical system from input-output observations even though the input and state interaction networks might be different. The derived mathematical analysis is accompanied by an algorithm for identifying, from data, a network topology consistent with the dynamics of the system and conforms to the prior information about the underlying structure. The proposed algorithm relies on alternating projections and is provably convergent. Numerical results corroborate the theoretical findings and the applicability of the proposed algorithm.Comment: 13 pages, 3 appendix page