Class-specific adaptive sparse representation via reweighted ℓ 1 norm minimization for image classification

Abstract

The objective function of sparse representation to be minimized mainly consists of two parts: reconstruction error and sparsity-inducing regularization (e.g., l 0 norm or l 1 norm). A regularization parameter allows a trade-off between the two parts. In practical applications, solutions for sparse representation models are highly sensitive to the regularization parameter. To alleviate this phenomenon and improve the discrimination of sparse representation, a reweighted l 1 norm minimization-based sparse representation, named class-specific adaptive sparse representation (CSASR), is proposed. In CSASR, a class-specific weight matrix derived from observations of a class is applied to substitute the regularization parameter. The CSASR model mainly has the following two advantages: (i) the class-specific weight matrix can be calculated adaptively from observations; therefore, it is a parameter-free model and (ii) each class has a unique class-specific weight matrix, which enhances the discrimination of sparse representation. The experimental results show that the proposed algorithm achieves superior classification performance compared to traditional sparse representation-based classification algorithms.