基于高斯混合模型的无向网络重构  

Gaussian mixture model based reconstruction of undirected networks

作　　者：何瑞辉 张海峰[1] 王欢[2] 马闯 He Rui-Hui;Zhang Hai-Feng;Wang Huan;Ma Chuang(School of Mathematical Science,Anhui University,Hefei 230601,China;School of Big Data and Statistics,Anhui University,Hefei 230601,China;School of Internet,Anhui University,Hefei 230039,China)

机构地区：[1]安徽大学数学科学学院,合肥230601 [2]安徽大学大数据与统计学院,合肥230601 [3]安徽大学互联网学院,合肥230039

出　　处：《物理学报》2024年第17期305-315,共11页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:12005001,61973001)资助的课题.

摘　　要：从数据中推断网络的结构作为复杂网络中一个重要科学问题已得到广泛关注.现有的网络重构方法大多将网络重构问题转化为一系列线性方程组的求解问题,然后通过某种截断方法对每个方程组的解进行截断,从而确定每个节点的局部结构.然而现有的截断方法大多存在着精度不足的问题,且少有方法衡量每个方程组解的可截断性,即节点的可重构性.为了解决这些问题,本文提出了一种基于高斯混合模型的无向网络重构方法.该方法首先将节点间连接关系的推断问题转化为一个聚类问题,然后利用高斯混合模型进行求解,得到每个节点与其他节点的连接概率,并根据概率定义一个基于信息熵的可重构指标,从而在真实网络结构未知的情况下衡量每个节点的可重构性.将该方法用于无向网络中,可以利用无向网络的对称特征,将可重构性高的节点作为训练集指导可重构性低的节点进行结构推断,从而更好地重构出无向网络.最后,通过在合成数据和真实数据上与现有的截断方法进行比较,证明了该方法可以更有效地重构出网络结构.The reconstruction of network structure from data represents a significant scientific challenge in the field of complex networks,which has attracted considerable attention from the research community.The most of existing network reconstruction methods transform the problem into a series of linear equation systems,to solve the equations.Subsequently,truncation methods are used to determine the local structure of each node by truncating the solution of each equation system.However,truncation methods frequently exhibit inadequate accuracy,and lack methods of evaluating the truncatability of solutions to each system of equations,that is to say,the reconstructability of nodes.In order to address these issues,in this work an undirected network reconstruction method is proposed based on a Gaussian mixture model.In this method,a Gaussian mixture model is first used to cluster the solution results obtainedby solving a series of linear equations,and then the probabilities of the clustering results are utilized to depict the likelihood of connections between nodes.Subsequently,an index of reconstructibility is defined based on information entropy,thus the probability of connections between each node and other nodes can be used to measure the reconstructibility of each node.The proposed method is ultimately applied to undirected networks.Nodes identified with high reconstructibility are used as a training set to guide the structural inference of nodes with lower reconstrucibility,thus enhancing the reconstruction of the undirected network.The symmetrical properties of the undirected network are then employed to infer the connection probabilities of the remaining nodes with other nodes.The experiments on both synthetic and real data are conducted and a variety of methods are used for constructing linear equations and diverse dynamical models.Compared with the results from a previous truncated reconstruction method,the reconstruction outcomes are evaluated.The experimental results show that the method proposed in this work out

关 键 词：网络重构 高斯混合模型 可重构性 无向网络 

分 类 号：O157.5[理学—数学]