Inferring Directed Network Topologies Via Tensor Factorization

Directed networks are pervasive both in nature and engineered systems, often underlying the complex behavior observed in biological systems, microblogs and social interactions over the web, as well as global financial markets. Since their explicit structures are often unobservable, in order to facilitate network analytics, one generally resorts to approaches capitalizing on measurable nodal processes to infer the unknown topology. Prominent among these are structural equation models (SEMs), capable of incorporating exogenous inputs to resolve inherent directional ambiguities. However, this assumes full knowledge of exogenous inputs, which may not be readily available in some practical settings. The present paper advocates a novel SEM-based topology inference approach that entails a PARAFAC decomposition of a three-way tensor, constructed from the observed nodal data. It turns out that second-order statistics of exogenous variables suffice to identify the hidden topology. Leveraging the uniqueness properties inherent to high-order tensor factorizations, it is shown that topology identification is possible under reasonably mild conditions. Tests on simulated data corroborate the effectiveness of the novel tensor-based approach.