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.
Original languageEnglish
Title of host publicationProceedings of the 2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing
EditorsC Richard, F Gini
Place of PublicationPiscataway, NJ, USA
PublisherIEEE Society
Pages89-92
Number of pages4
ISBN (Print)978-1-4799-1963-5
DOIs
Publication statusPublished - 21 Jan 2016
EventCAMSAP 2015, Cancun, Mexico - Piscataway, NJ, USA
Duration: 13 Dec 021516 Dec 2015

Publication series

Name
PublisherIEEE

Conference

ConferenceCAMSAP 2015, Cancun, Mexico
Period13/12/1516/12/15

    Research areas

  • Steady-state, Upper bound, Laplace equations, Eigenvalues and eigenfunctions, Frequency response, Vovariance matrices, Random processes

ID: 3912868