Properties and Applications of Gromov Matrices In Network Inference

Ji, Feng; Tang, Wenchang; Tay, Wee Peng

doi:10.1109/ssp.2018.8450846

Cited by 1 publication

(1 citation statement)

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“…In this paper, we further refine and generalize our Gromov matrix approach to weighted graphs, prove various properties of the Gromov matrices and demonstrate how to apply Gromov matrices in several network inference problems. A preliminary version of this paper was published in the conference [22].…”

Section: Introductionmentioning

confidence: 99%

On the Properties of Gromov Matrices and Their Applications in Network Inference

Tang

Tay

2019

IEEE Trans. Signal Process.

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The spanning tree heuristic is a commonly adopted procedure in network inference and estimation. It allows one to generalize an inference method developed for trees, which is usually based on a statistically rigorous approach, to a heuristic procedure for general graphs by (usually randomly) choosing a spanning tree in the graph to apply the approach developed for trees. However, there are an intractable number of spanning trees in a dense graph. In this paper, we represent a weighted tree with a matrix, which we call a Gromov matrix. We propose a method that constructs a family of Gromov matrices using convex combinations, which can be used for inference and estimation instead of a randomly selected spanning tree. This procedure increases the size of the candidate set and hence enhances the performance of the classical spanning tree heuristic. On the other hand, our new scheme is based on simple algebraic constructions using matrices, and hence is still computationally tractable. We discuss some applications on network inference and estimation to demonstrate the usefulness of the proposed method. Index TermsGromov matrix, spanning tree, network inference and estimation

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Section: Introductionmentioning

confidence: 99%