Independent component analysis with soft reconstruction cost (RICA) has been recently proposed to linearly learn sparse representation with an overcomplete basis, and this technique exhibits promising performance even on unwhitened data. However, linear RICA may not be effective for the majority of real-world data because nonlinearly separable data structure pervasively exists in original data space. Meanwhile, RICA is essentially an unsupervised method and does not employ class information. Motivated by the success of the kernel trick that maps a nonlinearly separable data structure into a linearly separable case in a high-dimensional feature space, we propose a kernel RICA (kRICA) model to nonlinearly capture sparse representation in feature space. Furthermore, we extend the unsupervised kRICA to a supervised one by introducing a class-driven discrimination constraint, such that the data samples from the same class are well represented on the basis of the corresponding subset of basis vectors. This discrimination constraint minimizes inhomogeneous representation energy and maximizes homogeneous representation energy simultaneously, which is essentially equivalent to maximizing between-class scatter and minimizing within-class scatter at the same time in an implicit manner. Experimental results demonstrate that the proposed algorithm is more effective than other state-of-the-art methods on several datasets.