Tensor decompositions for identifying directed graph topologies and tracking dynamic networks

Yanning Shen, Brian Baingana, Georgios B. Giannakis

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

Abstract

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 structures are often unobservable, in order to facilitate network analytics, one generally resorts to approaches capitalizing onmeasurable nodal processes to infer the unknown topology. Structural equation models (SEMs) are capable of incorporating exogenous inputs to resolve inherent directional ambiguities. However, conventional SEMs assume full knowledge of exogenous inputs, which may not be readily available in some practical settings. This paper advocates a novel SEM-based topology inference approach that entails factorization of a three-way tensor, constructed from the observed nodal data, using the well-known parallel factor (PARAFAC) decomposition. It turns out that second-order piecewise stationary statistics of exogenous variables suffice to identify the hidden topology. Capitalizing on the uniqueness properties inherent to high-order tensor factorizations, it is shown that topology identification is possible under reasonably mild conditions. In addition, to facilitate real-Time operation and inference of time-varying networks, an adaptive (PARAFAC) tensor decomposition scheme that tracks the topology-revealing tensor factors is developed. Extensive tests on simulated and real stock quote data demonstrate the merits of the novel tensor-based approach.

Original languageEnglish (US)
Article number7912297
Pages (from-to)3675-3687
Number of pages13
JournalIEEE Transactions on Signal Processing
Volume65
Issue number14
DOIs
StatePublished - Jul 15 2017

Bibliographical note

Funding Information:
This work was supported by in part by NSF Grant 1500713 and in part by NIH Grant 1R01GM104975-01.

Publisher Copyright:
© 2017 IEEE.

Keywords

  • CANDECOMP/ PARAFAC (CP) decomposition
  • Network topology inference
  • Structural equation models

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