Diffusion Adaptation Over Clustered Multitask Networks Based on the Affine Projection Algorithm

Distributed adaptive networks are suitable for decentralized inference tasks. Recent works have intensively studied distributed optimization problems in the case where the nodes have to estimate a single optimum parameter vector collaboratively. However, there are many important applications that are multi task oriented in the sense that there are multiple optimum parameter vectors to be estimated simultaneously, in a collaborative manner over the area covered by the network. This paper presents diffusion strategies based on the Affine Projection Algorithm (APA) that address multi task distributed estimation over adaptive networks by minimizing an appropriate mean-square error criterion with $l_{2}$-regularization. The usage of APA makes the algorithm robust against the correlated input. The stability and performance of the algorithm in the mean and mean square error sense are analyzed. Simulations are conducted to verify the analytical results