论文标题
网络过程的拓扑感知关节图和边缘重量标识
Topology-Aware Joint Graph Filter and Edge Weight Identification for Network Processes
论文作者
论文摘要
通过图形过滤器成功对网络定义的数据进行了建模。但是，尽管在许多情况下，该网络的连通性是已知的，例如智能电网，社交网络等，但缺乏定义明确的交互权重阻碍了使用图形过滤器对观察到的网络数据进行建模的能力。因此，在本文中，我们专注于定义图形滤波器的系数和图形权重的联合识别，该图形滤镜最能模拟观察到的输入/输出网络数据。尽管这两个问题主要是单独解决的，但我们在这里提出了一种迭代方法，该方法利用了图形支持图形滤波器系数和边缘权重的联合识别的知识。我们进一步表明，我们的迭代方案可以保证每次迭代的非差异成本，从而确保全球范围内的行为。数值实验证实了我们提出的方法的适用性。
Data defined over a network have been successfully modelled by means of graph filters. However, although in many scenarios the connectivity of the network is known, e.g., smart grids, social networks, etc., the lack of well-defined interaction weights hinders the ability to model the observed networked data using graph filters. Therefore, in this paper, we focus on the joint identification of coefficients and graph weights defining the graph filter that best models the observed input/output network data. While these two problems have been mostly addressed separately, we here propose an iterative method that exploits the knowledge of the support of the graph for the joint identification of graph filter coefficients and edge weights. We further show that our iterative scheme guarantees a non-increasing cost at every iteration, ensuring a globally-convergent behavior. Numerical experiments confirm the applicability of our proposed approach.
