稀疏复杂网络邻接拓扑的l_(1)–正则化辨识方法  

l_(1)-regularization identification method for the adjacency topology of sparse complex networks

作　　者：朱芸烽 邹林峰 顾杰 蒋景飞 张路[1] ZHU Yun-Feng;ZOU Lin-Feng;GU Jie;JIANG Jing-Fei;ZHANG Lu(School of Mathematics,Sichuan University,Chengdu 610064,China;National Key Laboratory of Electromagnetic Space Security,Chengdu 610036,China)

机构地区：[1]四川大学数学学院,成都610064 [2]电磁空间安全全国重点实验室,成都610036

出　　处：《四川大学学报(自然科学版)》2025年第1期38-44,共7页Journal of Sichuan University(Natural Science Edition)

基　　金：四川省科技厅项目(2023NSFSC1013)。

摘　　要：针对节点状态受噪声干扰且邻接拓扑随机变化的复杂网络,本文基于稀疏重构原理将其辨识问题转换成线性观测方程组的求解问题,并采用基于l_(1)-正则化的内点法进行求解,进而提出了l_(1)–正则化辨识方法.关于小世界网络的仿真结果表明,该方法简单易行、复杂度较低,仅需少量观测数据便可实现有效辨识,且相较于基于经典最小二乘或随机最小二乘的辨识方法具有更强的抗噪能力、更低的辨识误差.Due to the complexity of complex networks,the parameter identification of complex networks is a difficult problem.In this paper,for sparse complex networks with node state subjected to noise interference and adjacency topology undergoing random change,an l_(1)–regularization method is proposed for the identification of adjacency topology of networks.The key idea behind this method is to leverage the sparse reconstruction principle,which states that complex networks can be described by a small number of influential nodes.By identifying these key nodes,the entire network can be effectively characterized.In fact,practical largescale complex networks are often very sparse,which means that their adjacency matrix can be regarded as a sparse matrix.Based on the sparse reconstruction principle,we transform the identification problem of adjacency topology of networks into solving some linear observation equations.Then the interior-point method based on l_(1)–regularization is used to solve these equations and thus helps in promoting sparsity and improving the robustness of identification process.Simulation results on the small-world networks show that this method is simple and feasible with low complexity.It requires only a small amount of observation data to achieve effective identification.Comparing with the identification methods based on classical least squares and random least squares,this method exhibits stronger noise resistance and lower identification errors.This method is particularly useful for the networks with noisy node states and changing topologies,as it allows for robust identification even in challenging conditions.To summarize,we present a novel method for the identification of adjacency topology of sparse complex networks with noisy and changing states.By leveraging the sparse reconstruction principle and l_(1)–regularization,the method achieves robust and accurate identification.It is expected that this method can demonstrate its potential in diverse applications of network analysis and modeling

关 键 词：复杂网络 邻接拓扑 稀疏重构 正则化 

分 类 号：O29[理学—应用数学]