Reconstruction of enterprise debt networks based on compressed sensing

Abstract

AbstractThis study aims at the problem of reconstruction the unknown links in debt networks among enterprises. We use the topological matrix of the enterprise debt network as the object of reconstruction and use the time series data of accounts receivable and payable as input and output information in the debt network to establish an underdetermined linear system about the topological matrix of the debt network. We establish an iteratively reweighted least-squares algorithm, which is an algorithm in compressed sensing. This algorithm uses reweighted $$\ell _2$$ ℓ 2 -minimization to approximate $$\ell _1$$ ℓ 1 -norm of the target vectors. We solve the $$\ell _1$$ ℓ 1 -minimization problem of the underdetermined linear system using the iteratively reweighted least-squares algorithm and obtain the reconstructed topological matrix of the debt network. Simulation experiments show that the topology matrix reconstruction method of enterprise debt networks based on compressed sensing can reconstruct over 70% of the unknown network links, and the error is controlled within 2%.