Exploring the natural discriminative information of sparse representation for feature extraction

Sparse representation has been extensively studied in the signal processing community, which shows that one target sample can be accurately recovered by a sparse linear combination of the overall data. Such discovery has soon been applied to the pattern recognition task and, more recently, given rise to two new feature extraction methods, namely sparsity preserving projections (SPP) and global sparse representation projections (GSRP). However, both methods utilized the sparse representation by simply preserving it in the embedded space, but none of them investigates its natural discriminative information and therefore may have limited classifying power for the recognition task. In this paper, we propose a novel feature extraction method by exploring the discriminative information naturally embodied in the sparse representation. Based on the idea that one target sample shall ideally be more accurately reproduced by the intra-class data associated with the sparse coefficients than by the inter-class data, we seek a linearly transformed space where the reconstructive errors of samples caused by intra-class data are minimized and the reconstructive errors caused by inter-class data are simultaneously maximized. We name the proposed method sparse representation-based discriminative information exploring transform (DIET) and experiments on two face databases, i.e., Yale and ORL validate the effectiveness of DIET, as compared with several representative linear feature extraction methods.