Sparsest Network Support Estimation

A Submodular Approach

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Abstract

In this work, we address the problem of identifying the underlying network structure of data. Different from other approaches, which are mainly based on convex relaxations of an integer problem, here we take a distinct route relying on algebraic properties of a matrix representation of the network. By describing what we call possible ambiguities on the network topology, we proceed to employ sub-modular analysis techniques for retrieving the network support, i.e., network edges. To achieve this we only make use of the network modes derived from the data. Numerical examples showcase the effectiveness of the proposed algorithm in recovering the support of sparse networks.