Diffusion LMS for clustered multitask networks

Recent research works on distributed adaptive networks have intensively studied the case where the nodes estimate a common parameter vector collaboratively. However, there are many applications that are multitask-oriented in the sense that there are multiple parameter vectors that need to be inferred simultaneously. In this paper, we employ diffusion strategies to develop distributed algorithms that address clustered multitask problems by minimizing an appropriate mean-square error criterion with $\ell_2$-regularization. Some results on the mean-square stability and convergence of the algorithm are also provided. Simulations are conducted to illustrate the theoretical findings.