A Multi-Resolution Approach with Sparseness Property for Input-Output Approximation

Abstract

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 rened by minimizing the l 2 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 .