Multitask diffusion LMS with sparsity-based regularization

In this work, a diffusion-type algorithm is proposed to solve multitask estimation problems where each cluster of nodes is interested in estimating its own optimum parameter vector in a distributed manner. The approach relies on minimizing a global mean-square error criterion regularized by a term that promotes piecewise constant transitions in the parameter vector entries estimated by neighboring clusters. We provide some results on the mean and mean-square-error convergence. Simulations are conducted to illustrate the effectiveness of the strategy.