Ricerc@Sapienza

Sparsity phenomena in learning processes have been extensively studied, since their detection allows to derive suited regularized optimization algorithms capable of improving the overall learning performance. In this paper, we investigate the sparsity behavior that may occur in nonlinear adaptive filtering problems and how to leverage it and develop enhanced algorithms. In particular, we focus on a particular class of linear-in-the-parameters nonlinear adaptive filters, whose nonlinear transformation is based on a functional link expansion.

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, a class of proportionate algorithms has been proposed for nonlinear filters to leverage sparsity of their coefficients. However, the choice of the norm penalty of the cost function may be not always appropriate depending on the problem.

In this paper, the problem of the online modeling of nonlinear speech signals is addressed. In particular, the goal of this work is to provide a nonlinear model yielding the best tradeoff between performance results and required computational resources. Functional link adaptive filters were proved to be an effective model for this problem, providing the best performance when trigonometric expansion is used as a nonlinear transformation.