Distributed adaptive filtering has been considered as an effective approach for data processing and estimation over distributed networks. Most existing distributed adaptive filtering algorithms focus on designing different information diffusion rules, regardless of the nature evolutionary characteristic of a distributed network. In this paper, we study the adaptive network from the game theoretic perspective and formulate the distributed adaptive filtering problem as a graphical evolutionary game. With the proposed formulation, the nodes in the network are regarded as players and the local combiner of estimation information from different neighbors is regarded as different strategies selection. We show that this graphical evolutionary game framework is very general and can unify the existing adaptive network algorithms. Based on this framework, as examples, we further propose two error-aware adaptive filtering algorithms. Moreover, we use graphical evolutionary game theory to analyze the information diffusion process over the adaptive networks and evolutionarily stable strategy of the system. Finally, simulation results are shown to verify the effectiveness of our analysis and proposed methods.
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