Stochastic graph filtering on time-varying graphs

Conference paper (2016)

Authors

E. Isufi Signal Processing Systems - EEMCS
A. Simonetto Signal Processing Systems - EEMCS
A. Loukas Technical University of Berlin
G.J.T. Leus Signal Processing Systems - EEMCS
Research Group
Signal Processing Systems (EEMCS) (TU Delft)
Steady-state Frequency response Upper bound Laplace equations Eigenvalues and eigenfunctions Random processes Vovariance matrices
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Published Date

21-01-2016

Language

English

Reuse Rights

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Microelectronics

Research Group

Signal Processing Systems

Abstract

We have recently seen a surge of work on distributed graph filters, extending classical results to the graph setting. State of the art filters have however only been examined from a deterministic standpoint, ignoring the impact of stochasticity in the computation (e.g., temporal fluctuation of links) and input (e.g., the value of each node is a random process). Initiating the study of stochastic graph signal processing, this paper shows that a prominent class of graph filters, namely autoregressive moving average (ARMA) filters, are suitable for the stochastic setting. In particular, we prove that an ARMA filter that operates on a stochastic signal over a stochastic graph is equivalent, in the mean, to the same filter operating on the expected signal over the expected graph. We also characterize the variance of the output and we provide an upper bound for its average value among different nodes. Our results are validated by numerical simulations.