Kernel collaborative representation based dictionary learning and discriminative projection

Sparse representation based classification (SRC) has been developed and shown great potential due to its effectiveness in various classification tasks. But how to determine appropriate features that can best work with SRC remains an open question. Based on SRC and dimensionality reduction (DR) techniques, a simultaneous discriminative projection and dictionary learning method (DSRC) is proposed. However, as a linear algorithm, DSRC cannot handle the data with highly nonlinear distribution. Recently research has shown that the collaborative representation mechanism is more important to the success of SRC. Motivated by these concerns, in this paper, we propose a novel kernel collaborative representation based classifier (KCRC), and then we use it as a criterion to design a kernel collaborative representation based dictionary learning and discriminant projection method (KDL-DP). The proposed method aims at learning a projection matrix and a dictionary such that in the low dimension subspace the between-class reconstruction residual of a given data set is maximized and the within-class reconstruction residual is minimized. Extensive experimental results validate the superiority of the proposed approach when compared with the state-of-the-art methods.