论文标题
具有网络分析应用的部分已知矩阵的功能和特征向量
Functions and eigenvectors of partially known matrices with applications to network analysis
论文作者
论文摘要
矩阵函数在应用数学中起重要作用。特别是在网络分析中，与网络关联的邻接矩阵的指数提供了有关连接性的有价值信息，以及节点的相对重要性或中心性。对网络节点进行排名的另一种流行方法是计算网络邻接矩阵的左Perron向量。本文解决了评估矩阵函数的问题，并计算与左Perron矢量的近似值，当时仅知道邻接矩阵的某些列和/或某些行。当仅使用定义网络的邻接矩阵的一些采样列和/或行时，考虑了网络分析的应用。描述了一种考虑到网络连接性的采样方案。计算的示例说明了讨论的方法的性能。
Matrix functions play an important role in applied mathematics. In network analysis, in particular, the exponential of the adjacency matrix associated with a network provides valuable information about connectivity, as well as about the relative importance or centrality of nodes. Another popular approach to rank the nodes of a network is to compute the left Perron vector of the adjacency matrix for the network. The present article addresses the problem of evaluating matrix functions, as well as computing an approximation to the left Perron vector, when only some of the columns and/or some of the rows of the adjacency matrix are known. Applications to network analysis are considered, when only some sampled columns and/or rows of the adjacency matrix that defines the network are available. A sampling scheme that takes the connectivity of the network into account is described. Computed examples illustrate the performance of the methods discussed.
