Identification of Edge Disconnections in Networks Based on Graph Filter Outputs

Shlomit Shaked, Tirza Routtenberg

Research output: Contribution to journalArticlepeer-review

5 Scopus citations
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Abstract

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.
Original languageEnglish
Pages (from-to)578-594
Number of pages17
JournalIEEE Transactions on Signal and Information Processing over Networks
Volume7
DOIs
StatePublished - 30 Aug 2021

Keywords

  • Graph signal processing (GSP)
  • identification of edge disconnections
  • likelihood ratio test (LRT)
  • network topology
  • smooth graph filters

ASJC Scopus subject areas

  • Signal Processing
  • Information Systems
  • Computer Networks and Communications

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