Sparse functional link adaptive filter using an ℓ1-norm regularization

Linear-in-the-parameters nonlinear adaptive filters often show some sparse behavior due to the fact that not all the coefficients are equally useful for the modeling of any nonlinearity. Recently, proportionate algorithms have been proposed to leverage sparsity behaviors in nonlinear filtering. In this paper, we deal with this problem by introducing a proportionate adaptive algorithm based on an ℓ1-norm penalty of the cost function, which regularizes the solution, to be used for a class of nonlinear filters based on functional links. The proposed algorithm stresses the difference between useful and useless functional links for the purpose of nonlinear modeling. Experimental results clearly show faster convergence performance with respect to the standard (i.e., non-regularized) version of the algorithm.