Kernel sparse modeling for prototype selection

Recently, a new method termed Sparse Modeling Representative Selection (SMRS) has been proposed for selecting the most relevant instances in datasets. SMRS is based on data self-representativeness in the sense that it estimates a coding matrix using a dictionary of samples set to the data themselves. Sample relevances are derived from the matrix of coefficients with a block sparsity constraint. Due to the use of a linear model for data self-representation, SMRS cannot always provide good relevant samples. Besides, most of the selected relevant samples by SMRS are in dense regions. In this paper, we propose to overcome the shortcomings of the SMRS method by deploying non-linear data self-representativeness through the use of two kinds of data projections: kernel trick and column generation. Qualitative evaluation is performed on summarizing two video movies. Quantitative evaluations are obtained by performing classification tasks on the summarized training image datasets where the objective is to compare the relevance of selected samples for a given classification task and for a given instance selection method. The conducted experiments showed that the proposed methods can outperform state-of-the art methods including the SMRS method.