An adaptive regularization method for sparse representation

Abstract

Sparse representation (SR) or sparse coding (SC), which assumes the data vector can be sparse represented by linear combination over basis vectors, has been successfully applied in machine learning and computer vision tasks. In order to solve sparse representation problem, regularization technique is applied to constrain the sparsity of coefficients of linear representation. In this paper, a reconstruction-error-based adaptive regularization parameter estimation method is proposed to improve the representation ability of SR. The adaptive regularization parameter aims to balance the reconstruction error and the sparsity of coefficient vector and to minimize reconstruction error. Substantial experiments are performed on some benchmark databases. Simulation results demonstrate that this adaptive regularization parameter estimation method can find a proper parameter for each test sample, consequently, can improve the accuracy of SR and eliminate a time-consuming cross-validation process.