Sparsity-enforced regression based on over-complete dictionary

Nonlinear regression has broad applications in various research areas, and kernel-based regression is very popular in machine learning literature. However, the selection of basis-function parameters is often difficult. In this paper we propose a new sparsity-enforced regression method based on an over-complete dictionary. The over-complete dictionary comprises basis functions with quantized parameters, and we employ ℓ₁-regularized minimization to obtain a sparse weight vector of the basis. The ℓ₁-regularized minimization automatically selects the most suitable basis function parameters. Performance analysis shows that this new method provides improved regression accuracy with small model complexity as measured by the number of non-zero entries of the weight vector.