A multi-resolution approach with sparseness property for input-output approximation

This paper presents a multi-resolution approach for the modeling of input-output data with a sparse basis function set. The two key tools of our approach are the sparse approximation method through ℓ ¹ norm regularization and a powerful averaging process which allows one to blend independent and arbitrary local models to obtain a global model without introducing discontinuities on the boundaries. The ability of choosing arbitrary local models makes using sparse approximation for obtaining local models possible. Local approximation selects a sparse solution from a larger number of basis functions, while the averaging process blends these sparse local models to obtain a global model, which is further refined by minimizing the l2 norm of the global approximation error. The proposed approach is tested on two numerical simulation examples. The results show the proposed multi-resolution sparse approximation approach can provide accurate models with only the best available basis functions in the basis dictionary.