ϵ-sparse representations : generalized sparse approximation and the equivalent family of SVM tasks

Abstract

Relation between a family of generalized Support Vector Machine (SVM) problems and the novel ϵ-sparse representation is provided. In defining ϵ-sparse representations, we use a natural generalization of the classical ϵ-insensitive cost function for vectors. The insensitive parameter of the SVM problem is transformed into component-wise insensitivity and thus overall sparsification is replaced by component-wise sparsification. The connection between these two problems is built through the generalized Moore-Penrose inverse of the Gram matrix associated to the kernel.