Data reduction through kernel sparse coding

Sparse Modeling Representative Selection (SMRS) has been recently proposed for finding the most relevant instances in datasets. This method deploys a data self-representativeness coding in order to infer a coding matrix that is regularized with a row sparsity constraint. The method assumes that the score of any sample is set to the L2 norm of the corresponding row in the coding matrix. Since the SMRS method is linear, it cannot always provide good relevant instances. Moreover, many of its selected instances are already in dense areas in the input space. In this paper, we propose to alleviate the SMRS method's shortcomings. More precisely, We propose two kernel data self-representativeness coding schemes that are based on Hilbert space and column generation. Performance evaluation is carried out on reducing training image datasets used for recognition tasks. These experiments showed that the proposed kernel methods can provide better data reduction than state-of-the art selection methods including the SMRS method.