论文标题
图形信号对特征向量中心性的盲目估计：超越低通滤波
Blind Estimation of Eigenvector Centrality from Graph Signals: Beyond Low-pass Filtering
论文作者
论文摘要
本文的特征是仅从节点的数据（即没有有关网络拓扑的信息）来估算网络特征向量中心的困难。我们将此节点数据建模为通过将白噪声传递到通用（不一定是低通）图形过滤器而生成的图形信号。利用图形过滤器的光谱特性，我们估计了基础网络的邻接矩阵的特征向量。为此，提出了一种简单的选择算法，该算法选择了信号协方差矩阵的正确特征向量，对基础图滤波器上的假设最少。然后，我们介绍了该算法的渐近性和非反应性能的理论表征，从而为中心性估计提供了样本复杂性，并揭示了推动这种复杂性的关键元素。最后，我们通过在不同的随机图模型上进行的一组数值实验来说明开发的见解。
This paper characterizes the difficulty of estimating a network's eigenvector centrality only from data on the nodes, i.e., with no information about the topology of the network. We model this nodal data as graph signals generated by passing white noise through generic (not necessarily low-pass) graph filters. Leveraging the spectral properties of graph filters, we estimate the eigenvectors of the adjacency matrix of the underlying network. To this end, a simple selection algorithm is proposed, which chooses the correct eigenvector of the signal covariance matrix with minimal assumptions on the underlying graph filter. We then present a theoretical characterization of the asymptotic and non-asymptotic performance of this algorithm, thus providing a sample complexity bound for the centrality estimation and revealing key elements driving this complexity. Finally, we illustrate the developed insights through a set of numerical experiments on different random graph models.
