On the Stability of Low Pass Graph Filter with a Large Number of Edge Rewires

• Published in: ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) pp. 5568 - 5572
• Main Authors: Nguyen, Hoang-Son, He, Yiran, Wai, Hoi-To
• Format: Conference Proceeding
• Language: English
• Published: IEEE 23.05.2022
• Subjects: low pass graph filter; Low-pass filters; Numerical models; Numerical simulation; Perturbation methods; Signal processing; Stability analysis; stability of graph filter; stochastic block model; Stochastic processes
• DOI: 10.1109/ICASSP43922.2022.9747181

Recently, the stability of graph filters has been studied as one of the key theoretical properties driving the highly successful graph convolutional neural networks (GCNs). The stability of a graph filter characterizes the effect of topology perturbation on the output of a graph filter, a fundamental building block for GCNs. Many existing results have focused on the regime of small perturbation with a small number of edge rewires. However, the number of edge rewires can be large in many applications. To study the latter case, this work departs from the previous analysis and proves a bound on the stability of graph filter relying on the filter's frequency response. Assuming the graph filter is low pass, we show that the stability of the filter depends on perturbation to the community structure. As an application, we show that for stochastic block model graphs, the graph filter distance converges to a small constant when the number of nodes approaches infinity. Numerical simulations validate our findings.