UCS-WN: An Unbiased Compressive Sensing Framework for Weighted Networks

In this paper, we propose a novel framework called UCS-WN in the context of compressive sensing to efficiently recover sparse vectors representing the properties of the links from weighted networks with $n$ nodes. Motivated by network inference, we study the problem of recovering sparse link vectors with network topological constraints over weighted networks. We take sufficient number of collective additive measurements using this framework through connected paths for constructing a feasible measurement matrix. We theoretically show that only $O(k\log(n))$ path measurements via UCS-WN are sufficient for uniquely recovering any ${\mbi k}$-sparse link vector with no more than ${\mbi k}$ non-zero elements. Moreover, we demonstrate that this framework would converge to an accurate solution for a wide class of networks by experimental evaluations on both synthetic and real datasets.