DIRECTED NETWORK TOPOLOGY INFERENCE VIA GRAPH FILTER IDENTIFICATION
DIRECTED NETWORK TOPOLOGY INFERENCE VIA GRAPH FILTER IDENTIFICATION
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DOI：
10.1109/dsw.2018.8439888
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发表时间：
2018-06
期刊：
影响因子：
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通讯作者：
Rasoul Shafipour;Santiago Segarra;A. Marques;G. Mateos
中科院分区：
文献类型：
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作者：
Rasoul Shafipour;Santiago Segarra;A. Marques;G. Mateos
我们解决的问题，推断一个有向网络节点观察所产生的线性扩散动力学图上寻求图的图形信号。观测被建模为线性图滤波器的输出（即，编码未知图形拓扑的局部扩散图形移位算子上的多项式），用具有任意相关节点分量的独立图形信号的集合来激励。在这种情况下，我们首先依赖于输出信号的观察沿着与输入上的先验统计信息一起来识别扩散滤波器。这样的问题需要解决一个系统的二次矩阵方程，我们重铸作为一个光滑的二次最小化受Stiefel流形约束。随后的网络拓扑结构的识别给出了图滤波器估计归结为找到一个稀疏的和结构上可接受的移位，与给定的滤波器交换，从而迫使后者是一个多项式在寻求图移位运算符。初步的数值试验证实了所提出的算法在恢复合成和现实世界的有向图的有效性。
We address the problem of inferring a directed network from nodal observations of graph signals generated by linear diffusion dynamics on the sought graph. Observations are modeled as the outputs of a linear graph filter (i.e., a polynomial on a local diffusion graph-shift operator encoding the unknown graph topology), excited with an ensemble of independent graph signals with arbitrarily-correlated nodal components. In this context, we first rely on observations of the output signals along with prior statistical information on the inputs to identify the diffusion filter. Such problem entails solving a system of quadratic matrix equations, which we recast as a smooth quadratic minimization subject to Stiefel manifold constraints. Subsequent identification of the network topology given the graph filter estimate boils down to finding a sparse and structurally admissible shift that commutes with the given filter, thus forcing the latter to be a polynomial in the sought graph-shift operator. Preliminary numerical tests corroborating the effectiveness of the proposed algorithms in recovering synthetic and real-world digraphs are provided.