Paper Title
Image Selection using Non-linear Sparse Representation Schemes

Sparse Modeling Representative Selection (SMRS) has been recently introduced for selecting the most relevant instances in datasets. SMRS utilizes data self-representativeness coding in order to infer a coding matrix with block sparsity constraint. The relevance scores of any instance is then set to the ℓ2-norm of the corresponding row in the coding matrix. Since SMRS is based on a linear model for data self-representation, it cannot always provide good relevant representative instances. Besides, most of its selected instances can be found in dense areas in the input space. In this chapter, we propose to overcome the SMRS method's shortcomings that are related to the coding matrix estimation. We introduce two non-linear data self-representativeness coding schemes that are based on Hilbert space and column generation. Experimental evaluation is carried out on summarizing a video movie and on summarizing training image datasets used for classification tasks. These experiments demonstrated that the proposed non-linear methods can outperform state-of-the-art selection methods including the SMRS method. Keywords - Block Sparsity, Column Generation, Data Self-Representativeness, Hilbert Space, Instance Selection, Kernel Representation.