Abstract: In this paper, (1,3)L₁1(1,3) norm is employed to loose the bound of the VC dimension, and thus a new structure risk based on the (1,3)L₁1(1,3) norm is developed. Utilizing this structure risk in the hidden space, we propose a sparse hidden space support vector machine (SHSSVM). Attributing to the merit of the (1,3)L₁1(1,3) norm, a good sparsity is achieved by the SHSSVM. Like the hidden space support vector machine (HSSVM), the kernel functions used in the SHSSVM are not required to satisfy the Mercer condition, so they can be chosen from a wide range. Simulations on artificial and benchmark data sets for regression and classification prove that the SHSSVM has as good generalization performance as the support vector machine (SVM), and better than the HSSVM. Furthermore, the SHSSVM obtains a sparser decision function than SVM and HSSVM, thus increasing the speed of function evaluation.

Key words: support vector machine, VC bound, structure risk, sparsity