Network topology inference from non-stationary graph signals
Network topology inference from non-stationary graph signals
复制标题
从非平稳图信号推断网络拓扑
DOI：
10.1109/icassp.2017.7953282
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
G. Mateos
中科院分区：
文献类型：
--
作者：
Rasoul Shafipour;Santiago Segarra;A. Marques;G. Mateos
我们解决了从节点观测推断图的问题，节点观测被建模为依赖于所寻找网络结构的局部扩散动力学产生的非平稳图信号。使用所谓的图移算子（GSO）作为图的矩阵表示，我们首先从扩散信号的实现中识别移矩阵的特征向量，然后我们依靠这些谱模板通过在待恢复的图上施加所需的属性来估计特征值。与观测信号的GSO和协方差矩阵同时可对角化的平稳设置不同，这里它们不是。因此，估计特征向量需要首先估计未知的扩散（图）滤波器——GSO中的一个多项式，它保留了所寻找的特征基。为了执行这个初始的系统识别步骤，我们利用输入信号的不同信息源来驱动图上的扩散过程。数值测试显示了所提出的算法在恢复社会和结构脑图方面的有效性。
We address the problem of inferring a graph from nodal observations, which are modeled as non-stationary graph signals generated by local diffusion dynamics that depend on the structure of the sought network. Using the so-called graph-shift operator (GSO) as a matrix representation of the graph, we first identify the eigenvectors of the shift matrix from realizations of the diffused signals, and then we rely on these spectral templates to estimate the eigenvalues by imposing desirable properties on the graph to be recovered. Different from the stationary setting where the GSO and the covariance matrix of the observed signals are simultaneously diagonalizable, here they are not. Hence, estimating the eigenvectors requires first estimating the unknown diffusion (graph) filter - a polynomial in the GSO which does preserve the sought eigenbasis. To carry out this initial system identification step, we leverage different sources of information on the input signal driving the diffusion process on the graph. Numerical tests showcase the effectiveness of the proposed algorithms in recovering social and structural brain graphs.
DOI：
10.1073/pnas.0308538101
发表时间：
2004-06-29
影响因子：
11.1
作者：
Brovelli, A;Ding, MZ;Bressler, SL
通讯作者：
Bressler, SL