Abstract
Sparse representation involves two relevant procedures - sparse coding and dictionary learning. Learning a dictionary from data provides a concise knowledge representation. Learning a dictionary in a higher feature space might allow a better representation of a signal. However, it is usually computationally expensive to learn a dictionary if the numbers of training data and(or) dimensions are very large using existing algorithms. In this paper, we propose a kernel dictionary learning framework for three models. We reveal that the optimization has dimension-free and parallel properties. We devise fast active-set algorithms for this framework. We investigated their performance on classification. Experimental results show that our kernel sparse representation approaches can obtain better accuracy than their linear counterparts. Furthermore, our active-set algorithms are faster than the existing interior-point and proximal algorithms.