One of the cornerstones of the field of signal processing on graphs are graph filters, direct analogues of classical filters, but intended for signals defined on graphs. This work brings forth new insights on the distributed graph filtering problem. We design a family of autoregressive moving average (ARMA) recursions, which (i) are able to approximate any desired graph frequency response, and (ii) give exact solutions for tasks such as graph signal denoising and interpolation. The design philosophy, which allows us to design the ARMA coefficients independently from the underlying graph, renders the ARMA graph filters suitable in static and, particularly, time-varying settings. The latter occur when the graph signal and/or graph are changing over time. We show that in case of a time-varying graph signal our approach extends naturally to a two-dimensional filter, operating concurrently in the graph and regular time domains. We also derive sufficient conditions for filter stability when the graph and signal are time-varying. The analytical and numerical results presented in this paper illustrate that ARMA graph filters are practically appealing for static and time-varying settings, as predicted by theoretical derivations.
ARMA Block: A CNN-Based Autoregressive and Moving Average Module for Long-Term Time Series Forecasting
AI Lab, Grepp（Grepp人工智能实验室）；Department of Computer Science and Engineering, Hankuk University of Foreign Studies（韩国外国语大学计算机科学与工程系）；Department of Radiation Physics, The University of Texas MD Anderson Cancer Center（德克萨斯MD安德森癌症中心辐射物理系）
