Adaptive Message Passing Sign Algorithm

A new algorithm named the Adaptive Message Passing Sign (AMPS) algorithm is introduced for online prediction, missing data imputation, and impulsive noise removal in time-varying graph signals. This work investigates the potential of message passing on spectral adaptive graph filters to define online localized node aggregations. AMPS updates a sign error derived from $l_1$-norm optimization between observation and estimation, leading to fast and robust predictions in the presence of impulsive noise. The combination of adaptive spectral graph filters with message passing reveals a different perspective on viewing message passing and vice versa. Testing on a real-world network formed by a map of nationwide weather stations, the AMPS algorithm accurately forecasts time-varying temperatures.