Dictionary Training for Sparse Representation as Generalization of K-Means Clustering

Recent dictionary training algorithms for sparse representation like K-SVD, MOD, and their variation are reminiscent of K-means clustering, and this letter investigates such algorithms from that viewpoint. It shows: though K-SVD is sequential like K-means, it fails to simplify to K-means by destroying the structure in the sparse coefficients. In contrast, MOD can be viewed as a parallel generalization of K-means, which simplifies to K-means without perturbing the sparse coefficients. Keeping memory usage in mind, we propose an alternative to MOD; a sequential generalization of K-means (SGK). While experiments suggest a comparable training performances across the algorithms, complexity analysis shows MOD and SGK to be faster under a dimensionality condition.