TY - GEN
T1 - Stochastic graph filtering on time-varying graphs
AU - Isufi, Elvin
AU - Simonetto, Andrea
AU - Loukas, Andreas
AU - Leus, Geert
N1 - Publisher Copyright:
© 2015 IEEE.
PY - 2015/1/1
Y1 - 2015/1/1
N2 - 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.
AB - 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.
U2 - 10.1109/CAMSAP.2015.7383743
DO - 10.1109/CAMSAP.2015.7383743
M3 - Conference contribution
AN - SCOPUS:84963815775
T3 - 2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015
SP - 89
EP - 92
BT - 2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 6th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015
Y2 - 13 December 2015 through 16 December 2015
ER -