Department of Mathematics, Zhongkai University of Agriculture and Engineering, Guangzhou, 510225, China.
College of Economics and Trade, Zhongkai University of Agriculture and Engineering, Guangzhou, 510225, China.
Sci Rep. 2023 Feb 13;13(1):2514. doi: 10.1038/s41598-023-29595-9.
This 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 [Formula: see text]-minimization to approximate [Formula: see text]-norm of the target vectors. We solve the [Formula: see text]-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%.
本研究旨在解决企业债务网络中未知链路的重构问题。我们将企业债务网络的拓扑矩阵作为重构对象，以应收账款和应付账款的时间序列数据作为债务网络中的输入和输出信息，建立关于债务网络拓扑矩阵的欠定线性系统。我们建立了一种迭代重加权最小二乘算法，这是一种压缩感知算法。该算法使用重加权 [Formula: see text]-最小化来逼近目标向量的 [Formula: see text]-范数。我们使用迭代重加权最小二乘算法求解欠定线性系统的 [Formula: see text]-最小化问题，得到重构的债务网络拓扑矩阵。仿真实验表明，基于压缩感知的企业债务网络拓扑矩阵重构方法可以重构超过 70%的未知网络链路，且误差控制在 2%以内。
