Multitask diffusion adaptation over networks

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 multitask-oriented in the sense that there are multiple optimum parameter vectors to be inferred simultaneously, in a collaborative manner, over the area covered by the network. In this paper, we employ diffusion strategies to develop distributed algorithms that address multitask problems by minimizing an appropriate mean-square error criterion with $\ell ₂ -regularization. The stability and performance of the algorithm in the mean and mean-square error sense are analyzed. Simulations are conducted to verify the theoretical findings, and to illustrate how the distributed strategy can be used in several useful applications related to target localization and hyperspectral data unmixing.