2-Sparse Representations : Generalized Sparse Approximation and the Equivalent Family of SVM Tasks

Relation between a family of generalized Support Vector Machine (SVM) problems and the novel 2-sparse representation is provided. In defining 2-sparse representations, we use a natural generalization of the classical 2-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 componentwise sparsification. The connection between these two problems is built through the generalized Moore-Penrose inverse of the Gram matrix associated to the kernel. ∗Department of Information Systems, Eötvös Loránd University, H-1117 Budapest, Hungary; e-mail: [email protected] †Corresponding author; Department of Information Systems, Eötvös Loránd University, H-1117 Budapest, Hungary; e-mail: [email protected]