Graphs are fundamental mathematical structures used in various fields to model statistical and physical relationships between data, signals, and processes. In some applications, such as data processing in graphs that represent physical networks, the initial network topology is known. However, disconnections of edges in the network change the topology and may affect the signals and processes over the network. In this paper, we consider the problem of edge disconnection identification in networks by using concepts from graph signal processing (GSP). We assume that the graph signals measured over the vertices of the network can be represented as white noise that has been filtered on the graph topology by a smooth graph filter. We develop the likelihood ratio test (LRT) to detect a specific set of edge disconnections. Then, we provide the maximum likelihood (ML) decision rule for identifying general scenarios of edge disconnections in the network. It is shown that the sufficient statistics of the LRT and ML decision rule are the graph-frequency energy levels in the graph spectral domain. However, the ML decision rule leads to a high-complexity exhaustive search over the edges in the network and is practically infeasible. Thus, we propose a low-complexity greedy method that identifies a single disconnected edge at each iteration. Moreover, by using the smoothness of the considered graph filter, we suggest a local implementation of the decision rule, which is based solely on the measurements at neighboring vertices. Simulation results demonstrate that the proposed methods outperform existing detection and identification methods on a synthetic dataset and for line outage identification in power systems from the IEEE 118-bus test case.

中文翻译：

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通过特征切片和自动切片变形更好地利用 GCN 加速器的缓存


图是用于各个领域的基本数学结构，用于对数据、信号和过程之间的统计和物理关系进行建模。在某些应用中，例如表示物理网络的图中的数据处理，初始网络拓扑是已知的。然而，网络中边缘的断开会改变拓扑，并可能影响网络上的信号和进程。在本文中，我们利用图信号处理（GSP）的概念来考虑网络中的边缘断开识别问题。我们假设在网络顶点上测量的图信号可以表示为白噪声，该白噪声已通过平滑图滤波器在图拓扑上进行过滤。我们开发了似然比测试（LRT）来检测一组特定的边缘断开。然后，我们提供最大似然（ML）决策规则来识别网络中边缘断开的一般场景。结果表明，LRT和ML决策规则的充分统计量是图谱域中的图频率能级。然而，机器学习决策规则会导致对网络边缘进行高度复杂的穷举搜索，并且实际上是不可行的。因此，我们提出了一种低复杂度的贪婪方法，该方法在每次迭代时识别单个断开的边缘。此外，通过使用所考虑的图过滤器的平滑度，我们建议决策规则的本地实现，该规则仅基于相邻顶点的测量。仿真结果表明，所提出的方法在综合数据集以及 IEEE 118 总线测试用例中的电力系统线路停电识别方面优于现有的检测和识别方法。